text stringlengths 148 4.25k | __index_level_0__ int64 0 97.5k |
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<|im_start|>user
How many numbers from 10 to 31 are exactly divisible by 3?
Answer Choices: (A) 13 (B) 15 (C) 16 (D) 7 (E) 18<|im_end|>
<|im_start|>assistant
<think>
</think>
12, 15, 18, 21, 24, 27, 30.
7 Numbers.
10/3 = 3 and 31/3 = 10 ==> 10 - 3 = 7. Therefore 7 digits
D)
The answer is D<|endoftext|> | 29,166 |
<|im_start|>user
A tradesman by means of his false balance defrauds to the extent of 15%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Answer Choices: (A) 37.5 (B) 32.25 (C) 24.45 (D) 26.46 (E) 27.35<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
g% = 15 + 1... | 68,575 |
<|im_start|>user
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 60 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
Answer Choices: (A) 80% (B) 32% (C) 48% (D) 84% (E) 92%<|i... | 20,623 |
<|im_start|>user
A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 19% home electronics; 10% food additives; 24% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the gr... | 92,624 |
<|im_start|>user
If q is an integer, what is the greatest possible value for q that would still make the following statement true: 11*10^q < 1/10 ?
Answer Choices: (A) –4 (B) –3 (C) –2 (D) –1 (E) 0<|im_end|>
<|im_start|>assistant
<think>
</think>
Just putting values, the LHS becomes
q=0 --> 11
q=-1 --> 11/10
q=-... | 47,166 |
<|im_start|>user
If Sharon's weekly salary increased by 15 percent, she would earn $460 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week?
Answer Choices: (A) Rs.400 (B) Rs.440 (C) Rs.150 (D) Rs.460 (E) Rs.520<|im_end|>
<|im_start|>assistant
<think>
</think>
Soln... | 80,326 |
<|im_start|>user
If x^2 - 9 = 0 and x > 0, which of the following must be equal to 0 ?
Answer Choices: (A) x^2 - 9x (B) x^2 - 9x + 20 (C) x^2 - 2x + 3 (D) x^2 + 2x - 3 (E) x^2 - 5x + 6<|im_end|>
<|im_start|>assistant
<think>
</think>
x^2-9 = 0
x= +3 or x = -3
if we substitute x= 3 in the equation x^2 -5x+6 = 9-1... | 9,292 |
<|im_start|>user
What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
Answer Choices: (A) 34 (B) 42 (C) 48 (D) 49 (E) 53<|im_end|>
<|im_start|>assistant
<think>
</think>
According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f... | 48,013 |
<|im_start|>user
Type the missing number.
-95,-90,-85,x, -75,-70
Answer Choices: (A) -82 (B) -86 (C) -76 (D) -60 (E) -80<|im_end|>
<|im_start|>assistant
<think>
</think>
Added with +5 Previous Number get next number
-85+5 =-80
The answer is E<|endoftext|> | 46,021 |
<|im_start|>user
The ratio of red, yellow, and green jelly beans in a jar is 2:4:5. If the number of jelly beans is increased by 60%, 50%, and 40% respectively, what will be the new ratio?
Answer Choices: (A) 10:18:27 (B) 12:25:30 (C) 14:27:32 (D) 16:30:35 (E) 18:34:39<|im_end|>
<|im_start|>assistant
<think>
</think>
... | 94,390 |
<|im_start|>user
There are five thieves, each loot a bakery one after the other such that the first one takes 1/2 of the total no. of the breads plus 1/2 of a bread. Similarly 2nd, 3rd,4th and 5fth also did the same. After the fifth one no. of breads remained are 3. Initially how many breads were there?
Answer Choices:... | 20,653 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Minerals are the building blocks of rocks. A rock can be made of one or more minerals.
Minerals and rocks have the following properties:
Property | Mineral | Rock
It is a solid. | Yes | Yes
It is formed in nature. | Yes | Ye... | 3,655 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Measurements are written with both a number and a unit. The unit comes after the number. The unit shows what the number means.
Imagine being told that the bus leaves in 7. You might be thinking, 7 what? Does the bus leave in... | 3,794 |
<|im_start|>user
The conversion factor between solubility and molar solubility of a compound is known as what?
Answer choice: (A) molar mass (B) mass effect (C) stochastic mass (D) molar value<|im_end|>
<|im_start|>assistant
<think>
</think>
Solubility is normally expressed in g/L of saturated solution. However, solu... | 11,382 |
<|im_start|>user
At Parkins gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
Answer Choices: (A) 20 (B) 24 (C) 36 (D) 48 (E) 96<|im_end|>
<|im_start|>assista... | 14,451 |
<|im_start|>user
If the ratio of the change in the book's price to its new price is 1 : 5, What is the % price increase?
Answer Choices: (A) 25% (B) 50% (C) 75% (D) 90% (E) 100%<|im_end|>
<|im_start|>assistant
<think>
</think>
Solution:-
Given
ratio of change in book price/ new price = 1 /5
=>(new price−old price)/ne... | 2,969 |
<|im_start|>user
A trader marked the selling price of an article at 12% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed a discount of :
Answer Choices: (A) 10 % (B) 10.5 % (C) 11 % (D) 12.5 % (E) 9.8<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol.
Le... | 56,679 |
<|im_start|>user
How many three digit numbers that do not contain the digit 3 are there?
Answer Choices: (A) 100 (B) 200 (C) 648 (D) 680 (E) 729<|im_end|>
<|im_start|>assistant
<think>
</think>
Applying combinations....8 * 9 * 9 = 648...
8 for first digit...cant be 0 or 3
9 and 9 for 2nd and 3rd....cant be 3
The answ... | 13,918 |
<|im_start|>user
If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
Answer Choices: (A) 16 2/3% (B) 20% (C) 22 1/3% (D) 15% (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the price of the article be Rs. 100.
20% of ... | 92,880 |
<|im_start|>user
Two airplanes take off from one airfield at noon. One flies due east at 206 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
Answer Choices: (A) 412 (B) 332 (C) 400 (D) 483 (E) 566<|im_end|>
<|im_start|>assist... | 14,211 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Measurements are written with both a number and a unit. The unit comes after the number. The unit shows what the number means.
Imagine being told that the bus leaves in 7. You might be thinking, 7 what? Does the bus leave in... | 359 |
<|im_start|>user
Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
Answer Choices: (A) 8 1/8 (B) 8 1/9 (C) 8 1/4 (D) 8 1/1 (E) 8 1/5<|im_end|>
<|im_start|>assistant
<think>
</think>
... | 16,583 |
<|im_start|>user
How many numbers between 100 and 714 are divisible by 2, 3, and 7 together?
Answer Choices: (A) 112 (B) 77 (C) 267 (D) 15 (E) 99<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and ... | 64,947 |
<|im_start|>user
What work together in pairs to bend or straighten a joint?
Answer choice: (A) muscles (B) nerve fibers (C) collagen bands (D) cartilage tissues<|im_end|>
<|im_start|>assistant
<think>
</think>
Muscles work together in pairs to bend or straighten the joint.
The answer is A<|endoftext|> | 1,616 |
<|im_start|>user
A computer program produces a sequence a1, a2, a3, ... such that a1=a2=1 and ak=a(k-1)*3-1 for 2 < k < n for some n. If n=9, what is a6?
Answer Choices: (A) 35 (B) 37 (C) 39 (D) 41 (E) 43<|im_end|>
<|im_start|>assistant
<think>
</think>
a1=1
a2=1
a3=1*3-1=2
a4=2*3-1=5
a5=5*3-1=14
a6=14*3-1=42-1=41
41... | 78,310 |
<|im_start|>user
12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
Answer Choices: (A) 6 (B) 8 (C) 10 (D) 20 (E) 40<|im_end|>
<|im_start|>assistant
<think>
</think>
we have 1 litre = 1000cm³ (thanks Bunuel... | 78,206 |
<|im_start|>user
22 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
Answer Choices: (A) 33 (B) 32 (C) 60 (D) Data inadequate (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</thin... | 95,226 |
<|im_start|>user
An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability N that the sum of the 2 numbers on the balls will be even?
Answer Choices: (A) 25% (B) 37.5% (C) 50% (D) 62.5% (E) 75%<|im_end|>
<|im_start|>assistant
<think>
</thi... | 87,297 |
<|im_start|>user
In adaptive radiation, what is the name of the initial species that then subsequently becomes multiple other ones?
Answer choice: (A) pioneer (B) father (C) founder (D) Mother<|im_end|>
<|im_start|>assistant
<think>
</think>
In some cases, a population of one species disperses throughout an area, and... | 11,251 |
<|im_start|>user
For how many integers n is 3^n = n^3?
Answer Choices: (A) None (B) One (C) Two (D) Three (E) More than Three<|im_end|>
<|im_start|>assistant
<think>
</think>
draw a graph with n^3and 2^n, you'll seemore than 3 intercepts between the 2 curves, and
The answer is E<|endoftext|> | 57,470 |
<|im_start|>user
The price of an item is discounted 2 percent on day 1 of a sale. On day 2, the item is discounted another 12 percent, and on day 3, it is discounted an additional 25 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Answer Choices: (A) 66% (B) 67.5% (C) 69% (D) 70% ... | 52,878 |
<|im_start|>user
Bookman purchased 55 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 460, how many paperback copies were sold?
Answer Choices: (A) 10 (B) 11 (C) 12... | 32,317 |
<|im_start|>user
With a slope of 4, with a straight line in the xy- plane which has a point with x-coordinate of the point 14 and y-coordinate 19, find the y-intercept.
Answer Choices: (A) -19 (B) 18 (C) -37 (D) 50 (E) 37<|im_end|>
<|im_start|>assistant
<think>
</think>
Eq of line = Y = MX +C
M = 4
X= 14
Y= 19
C= Y -... | 23,271 |
<|im_start|>user
Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is?
Answer Choices: (A) 33 (B) 76 (C) 85 (D) 22 (E) 99<|im_end|>
<|im_start|>assistant
<think>
</think>
Since the numbers are co-prime, they ... | 21,751 |
<|im_start|>user
If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
Answer Choices: (A) 100 (B) 110 (C) 121 (D) 132 (E) 143<|im_end|>
<|im_start|>assistant
<think>
</think>
(a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)
Therefore... | 50,711 |
<|im_start|>user
Many glasses eventually crystallize, rendering them brittle and this?
Answer choice: (A) opaque (B) powdered (C) soft (D) molten<|im_end|>
<|im_start|>assistant
<think>
</think>
Many glasses eventually crystallize, rendering them brittle and opaque. Modifying agents such as TiO 2 are frequently added... | 2,743 |
<|im_start|>user
The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is:
Answer Choices: (A) 89.25 km/hr. (B) 77 km/hr. (C) 90.25 km/hr. (D) 94.25 km/hr. (E) 96.25 km/hr.<|im_end|>
<|im_start|>assistant
<think>
</think>
Let t... | 25,689 |
<|im_start|>user
The unit digit in the product (124 * 812 * 816 * 467) is:
Answer Choices: (A) 2 (B) 7 (C) 6 (D) 8 (E) 1<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Unit digit in the given product = Unit Digit in (4*2*6*7) = 6
The answer is C<|endoftext|> | 39,611 |
<|im_start|>user
Find the greatest number that will divide 205, 626 and 588 leaving 5, 6 and 8 as remainders respectively
Answer Choices: (A) 19 (B) 17 (C) 13 (D) 9 (E) 20<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Answer will be HCF of (205-5, 626-6, 588-8)
HCF of (200, 626, 580) = 20
Option E
The... | 30,043 |
<|im_start|>user
There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
Answer Choices: (A) 4 (B) 5 (C) 6 (D) 7 (E) 8<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation :
GIVEN:
RED + GREEN + BLUE ... | 20,541 |
<|im_start|>user
If a: b :: 3 : 7, then what is (5a+6b): (a-b)?
Answer Choices: (A) 57:11 (B) -57:4 (C) 11 : 10 (D) -11 : 10 (E) -1 : 10<|im_end|>
<|im_start|>assistant
<think>
</think>
a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-1]= [5*(3/7)+6]/[(3/7)-1]= -57/4
B
The answer... | 74,196 |
<|im_start|>user
Double strands of what wrap around histone proteins to form nucleosomes, which are coiled into a chromatin fiber?
Answer choice: (A) bacteria (B) ribosomes (C) dna (D) chromatids<|im_end|>
<|im_start|>assistant
<think>
</think>
Figure 10.4 Double-stranded DNA wraps around histone proteins to form nuc... | 8,310 |
<|im_start|>user
Find the sum of prime numbers lying between 60 and 75.
Answer Choices: (A) 199 (B) 201 (C) 211 (D) 272 (E) NOne<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol.
Required sum = ( 61 + 67 + 71 + 73)
= 272.
The answer is D<|endoftext|> | 51,306 |
<|im_start|>user
The greatest number of 5 digits = 99999.
Answer Choices: (A) 137 (B) 143 (C) 77 (D) 88 (E) 11<|im_end|>
<|im_start|>assistant
<think>
</think>
The answer is B<|endoftext|> | 44,360 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Every object is made of one or more materials. A material is a type of matter. Wood, glass, metal, and plastic are common materials.
A material has different properties. A material's properties tell you how it looks, feels, ... | 747 |
<|im_start|>user
One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is?
Answer Choices: (A) 5:4 (B) 5:6 (C) 5:0 (D) 5:4 (E) 4:5<|im_end|>
<|im_start|>assistant
<think>
</think>
36 * 5/18 = 12.5
20:25 => 4:5
The answer is E<|endoftext|> | 88,835 |
<|im_start|>user
When 28 is divided by the positive integer r, the remainder is 1. What is the sum of all the possible values of r for which this is true?
Answer Choices: (A) 2 (B) 3 (C) 9 (D) 30 (E) 39<|im_end|>
<|im_start|>assistant
<think>
</think>
The only possible values of the form 28=rp+1 are 3,9 or 27
The sum... | 58,852 |
<|im_start|>user
Jim bought edging to go around a circular garden with a radius of 6 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
Answer Choices: (A) 28.84' additional edging (B) 48.84' additional edging (C) 38.84' additional edging (D) 18.84' additional edging ... | 30,065 |
<|im_start|>user
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was ... | 74,776 |
<|im_start|>user
If two numbers are in the ratio 2:3. If 14 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Answer Choices: (A) A) 12 (B) B) 18 (C) C) 20 (D) D) 24 (E) E) 28<|im_end|>
<|im_start|>assistant
<think>
</think>
2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 14] = 3[3x + 14]... | 76,758 |
<|im_start|>user
A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Answer Choices: (A) 8.7 days (B) 2.0 days (C) 6.6 days (D) 7.7 days (E) 4.8 days<|im_end|>
<|im_start|>assistant
<think>
</think>
C = 1/2 - 1... | 70,730 |
<|im_start|>user
A and B together can do a piece of work in 3 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
Answer Choices: (A) 0.28 days (B) 0.45 days (C) 0.55 days (D) 0.25 days (E) 0.15 days<|im_end|>
<|im_start|>assistant
<think>
</think>
B = 1/2 – 1/20 =0.28 days
The ans... | 19,469 |
<|im_start|>user
Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 5.5 km apart, if they walk in the same direction?
Answer Choices: (A) 11 hrs (B) 14 hrs (C) 15 hrs (D) 17 hrs (E) None<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol.
to be ... | 53,301 |
<|im_start|>user
The sum of all the integers d such that -26 < d < 24 is
Answer Choices: (A) 0 (B) -2 (C) -25 (D) -49 (E) -51<|im_end|>
<|im_start|>assistant
<think>
</think>
Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 d= -49.
D is
The answer is D<|en... | 46,200 |
<|im_start|>user
If a, b and c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is
Answer Choices: (A) equilateral (B) isosceles (C) right-angled (D) obtuse-angled (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation :
We know that (a + b + c)2 = a2 + b2 + c2 +... | 19,576 |
<|im_start|>user
Find the average of first 8 multiples of 5?
Answer Choices: (A) 10 (B) 15 (C) 12.5 (D) 22.5 (E) 21<|im_end|>
<|im_start|>assistant
<think>
</think>
average = (5+10+15+20+25+30+35+40)/8 = 22.5
The answer is D<|endoftext|> | 64,766 |
<|im_start|>user
Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
Answer Choices: (A) 16.39 (B) 16.33 (C) 16.35 (D) 16.3 (E) 16.32<|im_end|>
... | 5,051 |
<|im_start|>user
A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 7/11. How many tennis balls did the retailer order originally.
Answer Choices: (A) 17.5 (B... | 63,505 |
<|im_start|>user
In how many different ways can the letters of the word ‘CAN’ be arranged?
Answer Choices: (A) 6 (B) 12 (C) 8 (D) 2 (E) 4<|im_end|>
<|im_start|>assistant
<think>
</think>
A
6
The word SMART has 3 distinct letters.
Number of arrangements = 3!
= 3 × 2 × 1 = 6
The answer is A<|endoftext|> | 28,319 |
<|im_start|>user
If x is an integer and 2.134 × 10^x is less than 220,000, what is the greatest possible value for x?
Answer Choices: (A) 7 (B) 6 (C) 5 (D) 4 (E) 3<|im_end|>
<|im_start|>assistant
<think>
</think>
x is an integer and 2.134 × 10x is less than 220,000, what is the greatest possible value for x?
for 2.13... | 70,160 |
<|im_start|>user
A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
Answer Choices: (A) 33809 (B) ... | 29,750 |
<|im_start|>user
What system in the human body makes white blood cells that protect the body from diseases?
Answer choice: (A) cardiovascular system (B) renal system (C) reproductive system (D) lymphatic system<|im_end|>
<|im_start|>assistant
<think>
</think>
The lymphatic system also plays an important role in the i... | 1,324 |
<|im_start|>user
Find the probability that a leap year selected at random will not have 53 Sundays or Mondays.
Answer Choices: (A) 6/7 (B) 5/7 (C) 4/7 (D) 3/7 (E) 2/7<|im_end|>
<|im_start|>assistant
<think>
</think>
There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Sundays, 52 Mondays and 2 days.
Th... | 16,423 |
<|im_start|>user
Each of the integers from 1 to 14 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?
Answer Choices: (A) 19 (B) 12 (C) 11 (D) 10 (E) 8<... | 36,366 |
<|im_start|>user
Chemical and physical changes in a system may be accompanied by an increase or a decrease in the disorder of the system, corresponding to an increase or decrease in what?
Answer choice: (A) enthalpy (B) vibration (C) entropy (D) volume<|im_end|>
<|im_start|>assistant
<think>
</think>
Chemical and phy... | 5,267 |
<|im_start|>user
What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9?
Answer Choices: (A) 397 (B) 401 (C) 403 (D) 405 (E) 399<|im_end|>
<|im_start|>assistant
<think>
</think>
A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, ... | 7,805 |
<|im_start|>user
If log 27 = 1.431, then the value of log 9 is:
Answer Choices: (A) 0.934 (B) 0.945 (C) 0.954 (D) 0.958 (E) 0.965<|im_end|>
<|im_start|>assistant
<think>
</think>
log 27 = 1.431
log (33 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
The answer is C<|endoftext... | 52,321 |
<|im_start|>user
Solve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0
Answer Choices: (A) If x>y (B) If x>=y (C) If x<y (D) If x<=y (E) x=y or relationship cannot be established<|im_end|>
<|im_start|>assistant
<think>
</think>
Solution:-
X=+1,-1 and Y= -1,-3
Comparing we ge... | 8,726 |
<|im_start|>user
Sarah's seafood restaurant gets a delivery of fresh seafood every day, 6 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total c... | 20,872 |
<|im_start|>user
By selling 99 pencil, a trader gains the cost of 33 Pencil. Find his gain percentage?
Answer Choices: (A) 26 1/3% (B) 51 1/3% (C) 33 1/3% (D) 53 1/3% (E) 34 1/3%<|im_end|>
<|im_start|>assistant
<think>
</think>
C
33 1/3%
Let the CP of each pencil be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 p... | 87,956 |
<|im_start|>user
In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
Answer Choices: (A) 40% (B) 80% (C) 58% (D) 50% (E) 60%<|im_end|>
<|im_start|>assistant
<think>
</think>
Number of students passed = 60% of 140 = 60/100 * 140 ... | 33,213 |
<|im_start|>user
What group of gases are unusually unreactive?
Answer choice: (A) noble gases (B) volcanic gases (C) greenhouse gases (D) halogens<|im_end|>
<|im_start|>assistant
<think>
</think>
Nonmetals tend to gain electrons in chemical reactions and have a high attraction to electrons within a compound. The most... | 4,427 |
<|im_start|>user
Which of the following integers is NOT a divisor of x if x = (21)(3^7) + (23)?
Answer Choices: (A) 2 (B) 5 (C) 9 (D) 10 (E) 25<|im_end|>
<|im_start|>assistant
<think>
</think>
(21)(3^7) is divisible by 3 but 23 is not divisible by 3.
Therefore (21)(3^7) + 23 is not divisible by 3 and thus not divisib... | 86,758 |
<|im_start|>user
If 3^x*4^y = 19,683 and x – y = 9, then x = ?
Answer Choices: (A) 8 (B) 9 (C) 10 (D) 11 (E) 12<|im_end|>
<|im_start|>assistant
<think>
</think>
Since 19,683 is an odd number, it is not a multiple of 4.
This means that y must equal zero.
Since x - y = 9 and y = 0, then x = 9.
The answer is B<|endoftex... | 60,454 |
<|im_start|>user
Chemical elements and water are recycled through what cycle?
Answer choice: (A) biogeochemical (B) biogenic (C) evaporation (D) dynamical<|im_end|>
<|im_start|>assistant
<think>
</think>
Chemical elements and water are recycled through biogeochemical cycles. The cycles include both biotic and abiotic... | 9,572 |
<|im_start|>user
Lanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
Answer... | 45,907 |
<|im_start|>user
Two trains of length 150 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Answer Choices: (A) 22 sec (B) 77 sec (C) 76 sec (D) 21.5 sec (E) 66 sec<|im_end|>
<|im_start|>assistant
<t... | 70,634 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Some animals have a backbone. The backbone is made of many bones in an animal's back. An animal's backbone helps connect the different parts of its body. In the drawings below, each animal's backbone is colored orange.
Other... | 6,211 |
<|im_start|>user
If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. Line L does pass the origin.
2.Line L must passes through the first quadrant.
3.The slope of L is negative
Answer Choices: (A) I only (B) II only (C) III only (D) I and II (E) II a... | 92,340 |
<|im_start|>user
In a triangle, one side is 6 Cm and another side is 4 Cm. which of the following can be the perimeter of the triangle?
Answer Choices: (A) 18. (B) 25. (C) 30. (D) 32. (E) 34.<|im_end|>
<|im_start|>assistant
<think>
</think>
Given : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > ... | 57,740 |
<|im_start|>user
What is at the top of the mesosphere?
Answer choice: (A) Troposphere (B) mesopause (C) Stratosphere (D) Mesosphere<|im_end|>
<|im_start|>assistant
<think>
</think>
At the top of the mesosphere is the mesopause. Temperatures here are colder than anywhere else in the atmosphere. They are as low as -100... | 1,293 |
<|im_start|>user
The reciprocal of the hcf and lcm of two are 1/13 and 1/312 .if one of the number is 24 then other no. is
Answer Choices: (A) 126 (B) 136 (C) 146 (D) 156 (E) 169<|im_end|>
<|im_start|>assistant
<think>
</think>
reciprocal of the hcf and lcm of two are 1/13 and 1/312
so, HCF = 13 , LCM = 312
LCM * HCF... | 46,530 |
<|im_start|>user
Let d > c >e > a. If c is twice as far from a as it is from d, and e is twice as far from c as it is from a, then (d - e)/(d - a) = ?
Answer Choices: (A) 2/9 (B) 1/3 (C) 2/3 (D) 7/9 (E) 3/2<|im_end|>
<|im_start|>assistant
<think>
</think>
Draw a number line and label with x and y. You would have:
Bef... | 37,644 |
<|im_start|>user
The cost of 20 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
Answer Choices: (A) Rs 42 (B) Rs 56 (C) Rs 58.50 (D) Rs 64.75 (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation :
Let the required cost be ... | 3,129 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Informal writing is typically used in casual situations or when communicating with someone you know well. Informal language often expresses familiarity and tends to sound more like speech. It uses more conversational languag... | 607 |
<|im_start|>user
As x increases from 151 to 152, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x
Answer Choices: (A) II only (B) II,III only (C) I,II only (D) I only (E) III only<|im_end|>
<|im_start|>assistant
<think>
</think>
On Increasing the value of x from 151 to 152
I) x−1/x will increase as... | 66,589 |
<|im_start|>user
If one positive integer is greater than another positive integer by 3, and the difference of their cubes is 63, what is their sum?
Answer Choices: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1<|im_end|>
<|im_start|>assistant
<think>
</think>
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
The two numbers are 1 and 4.
The answer i... | 38,707 |
<|im_start|>user
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 14^a and y = 9^b, which of the following is a possible units digit of xy?
Answer Choices: (A) 1 (B) 6 (C) 5 (D) 7 (E) 8<|im_end|>
<|im_start|>assistant
<think>
</think>
Only Units digit of X and Y contribute to the Units ... | 24,173 |
<|im_start|>user
In a 1000 m race, A beats B by 60 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Answer Choices: (A) 154 m (B) 176 m (C) 268 m (D) 129 m (E) 218 m<|im_end|>
<|im_start|>assistant
<think>
</think>
By the time A covers 1000 m, B covers (1000 - 60) = 940 m.
By the time B c... | 6,296 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
When writing, make sure to avoid vague pronoun references. A vague pronoun reference occurs when a pronoun could refer to more than one possible antecedent.
When Lisa and Kim finally landed, she breathed a sigh of relief.
Th... | 4,868 |
<|im_start|>user
If 893 × 78 = p, which of the following is equal to 893 × 79?
Answer Choices: (A) p + 1 (B) p + 78 (C) p + 79 (D) p + 893 (E) p + 894<|im_end|>
<|im_start|>assistant
<think>
</think>
Since 893 × 78 = p and 79=78+1, we have 893 × 79 = 893 ×(78+1)=893×78 + 893 ×1 = p + 893.
The answer is D<|endoft... | 16,565 |
<|im_start|>user
A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?
Answer Choices: (A) 100 (B) 102 (C) 104 (D) 108 (E) 90<|im_end|>
<|im_start|>assistant
<think>
</think>
The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number ... | 81,100 |
<|im_start|>user
The average age of a husband and his wife was 26 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
Answer Choices: (A) 11 (B) 18 (C) 21 (D) 287 (E) 27<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Sum of the pr... | 96,414 |
<|im_start|>user
Which number can we add to 897326 to get a number exactly divisible by 456?
Answer Choices: (A) 58 (B) 66 (C) 74 (D) 82 (E) 90<|im_end|>
<|im_start|>assistant
<think>
</think>
897326 / 456 = 1967 with a remainder of 374.
We need to add 456 - 374 = 82
The answer is D<|endoftext|> | 43,371 |
<|im_start|>user
If k is an integer and 0.00010101 x 10^k is greater than 1000, what is the least possible value of k?
Answer Choices: (A) 6 (B) 7 (C) 8 (D) 9 (E) 10<|im_end|>
<|im_start|>assistant
<think>
</think>
0.00010101 * 10^k > 1000
We need to move the decimal point to the right 7 places to get 1010.1
This is ... | 17,119 |
<|im_start|>user
The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Answer Choices: (A) 19002 (B) 1902... | 80,257 |
<|im_start|>user
A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets... | 75,417 |
<|im_start|>user
If a sum of money doubles itself in 10 years at simple interest, the ratepercent per annum is
Answer Choices: (A) 10 (B) 12.5 (C) 13 (D) 13.5 (E) 14<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 10) = 10
Option A
The answer ... | 57,856 |
<|im_start|>user
In a school there are 20 balls for every 200 players. If the school has 600 players, how many balls are required?
Answer Choices: (A) 34 (B) 45 (C) 60 (D) 36 (E) 14<|im_end|>
<|im_start|>assistant
<think>
</think>
20/200=x/600
x=60
The answer is C<|endoftext|> | 31,221 |
<|im_start|>user
In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?
Answer Choices: (A) 80 (B) 86 (C) 92 (D) 94 (E) 96<|im_end|>
<|im_start|>assistant
<think>
</think>
Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Q... | 50,417 |
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