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Remainder of (63*7*37*41*71*41)/10
Now using concept 2, let’s write the numbers in form of multiples of 10
Remainder of (60+3)*7*(30+7)*(40+1)*(70+1)*(40+1)/10
Remainder of 3*7*7*1*1*1/10
Remainder of 147/10 = 7
Now remember, we had canceled off 10 so to get the actual remainder so we need to multiply by 10: 7*10 = 70.... | deepmind/aqua_rat |
S is a set containing 10 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
A) The median of S is prime.
B) The median of T is prime
C) The median of S is equal to the median of T.
D) The sum of the terms in S is pri... | deepmind/aqua_rat |
(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to ... | deepmind/aqua_rat |
S is a set containing 6 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
A) The median of S is prime.
B) The median of T is prime
C) The median of S is equal to the median of T.
D) The sum of the terms in S is prim... | deepmind/aqua_rat |
(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to ... | deepmind/aqua_rat |
Two travelers set out on a long odyssey. The first traveler starts from city X and travels north on a certain day and covers 1 km on the first day and on subsequent days, he travels 2 km more than the previous day. After 3 days, a second traveler sets out from city X in the same direction as the first traveler and on h... | deepmind/aqua_rat |
The total distance covered by traveler 1 is the summation of the AP.
Sum of an AP = (n/2)(2a1 + (n-1)d)
Total distance travelled by traveller 1 in (n + 3) days = n+3/2[2(1)+(n+3−1)(2)]
The above term simplifies as (n + 3)2
The total distance covered by the second traveler = 12 + 13 + 14 + ... + n terms
Total distance t... | deepmind/aqua_rat |
If a, q, and c are consecutive even integers and a < q < c, all of the following must be divisible by 4 EXCEPT
A)a + c
B)q + c
C)ac
D)(bc)/2
E)(abc)/4
Correct Answer:B)q + c
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated b... | deepmind/aqua_rat |
E - aqc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'q' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - q + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2... | deepmind/aqua_rat |
In how many different ways can change be provided for a one dollar bill using pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents), if at least one of each type of coin must be included?
A)39
B)42
C)60
D)65
E)66
Correct Answer:C)60
Rationale: I. Case I = Four Quarters = this is impossible, bec... | deepmind/aqua_rat |
(4 ways) we could have 1-4 nickels
Subcase 3 = 1 Q, 4 D (65 cents)
(6 ways) we could have 1-6 nickels
Subcase 4 = 1 Q, 3 D (55 cents)
(8 ways) we could have 1-8 nickels
Subcase 5 = 1 Q, 2 D (45 cents)
(10 ways) we could have 1-10 nickels
Subcase 6 = 1 Q, 1 D (35 cents)
(12 ways) we could have 1-12 nickels
Case IV allow... | deepmind/aqua_rat |
Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, ... | deepmind/aqua_rat |
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1... | deepmind/aqua_rat |
Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, ... | deepmind/aqua_rat |
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1... | deepmind/aqua_rat |
If n is a positive integer and n^2 is divisible by 264, then the largest positive integer that must divide n is
A)6
B)12
C)24
D)36
E)48
Correct Answer:E)48
Rationale: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 ... | deepmind/aqua_rat |
Now, ask yourself: if n=48, is n divisible by 48? No. So, n is not always divisible by 48.
E | deepmind/aqua_rat |
The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits M of the larger integer?
A)M=2
B)M=5
C)M=8
D)10
E)11
Correct Answer:A)M=2
Rationale: Really hard. But let's start with few concepts:
1. ... | deepmind/aqua_rat |
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only c... | deepmind/aqua_rat |
Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum V in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her origina... | deepmind/aqua_rat |
The sum of these two probabilities is 0.008 + 0.096 = 0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.
The correct answer is A.
This problem illustrates the power of diversification in financial investments. All else be... | deepmind/aqua_rat |
A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight, in kg, of the heaviest box ?
A)60
B)61
C)64
D)Can't be determined
E)None
Correct Answ... | deepmind/aqua_rat |
Subtracting equation 2 from equation 1, we get, b1 + b3 + b5 = 173.
We know that b1 + b3 = 112, So b5 = 173 - 112 = 61 = Desired answer.
Answer : B | deepmind/aqua_rat |
A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% sunflower. If a customer purchases a mix of the two types of birdseed that is 50% sunflower, what percent of the mix is Brand A?
A)40%
B)45%
C)50 %
D)55 %
E)60 %
Correct Answer:E)60 %
R... | deepmind/aqua_rat |
Here is a pictorial representation :
Brand A= 60%------------------------10% or 0.10 above average, A times-----------------Total below = + 0.10 A
----------------------------------------------------------------------------------------Average = 50% or 0.50
Brand B = 35 %--------------------------15% or 0.15 below avera... | deepmind/aqua_rat |
The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits Q of the larger integer?
A)Q=2
B)Q=5
C)Q=8
D)Q=10
E)11
Correct Answer:A)Q=2
Rationale: Really hard. But let's start with few concepts:
1... | deepmind/aqua_rat |
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only c... | deepmind/aqua_rat |
Tanya prepared 4 different letters to 3 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?
A)1/24
B)1/8
C)1/4
D)1/... | deepmind/aqua_rat |
Event 1 - E1
We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the f... | deepmind/aqua_rat |
However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result.
If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 an... | deepmind/aqua_rat |
Of the 14,210 employees of the anvil factory, 3/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
A) 14.3%
B) 16.67%
C) 33%
D) 28.6%
E) 49.67%
Correct Answer:A) 14.3%
Rationale: The exam gives us a number that is easily divisible by 7 to piq... | deepmind/aqua_rat |
Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either p... | deepmind/aqua_rat |
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