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15 Jun 2021, 03:15
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Difficulty:
65%
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Question Stats:
57% (02:29) correct
43%
(02:14)
wrong
based on 210
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Which of the following exactly divides x, where x is the sum of the first 15 prime numbers?
(A) 11
(B) 21
(C) 31
(D) 41
(E) 51
(A) 11
(B) 21
(C) 31
(D) 41
(E) 51
15 Jun 2021, 05:03
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There's no way to find the sum of the first 15 primes without listing them and adding them up, which is too tedious for the GMAT to ever require. The first 15 primes are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
and these sum to 328 = 8*41, which is divisible by 41.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
and these sum to 328 = 8*41, which is divisible by 41.
15 Jun 2021, 08:26
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While I agree this is probably not a realistic problem, there is a nifty way to add up lists of numbers like this.
Break down into the different digits. We only have 2 digit numbers, and the tens digits (and accompanying units digits) are:
0: 2,3,5,7 [meaning the numbers 2, 3, 5, and 7]
1: 1,3,7,9 [meaning the numbers 11, 13, 17, and 19]
2: 3,9 [meaning the numbers 23 and 29]...etc.
3: 1,7
4: 1,3,7
We can add up all the units digits by groups: 17 + 20 + 12 + 8 + 11 = 68
Then we can add up the tens by how many numbers there are with each tens digit: 4(10) + 2(20) + 2(30) + 3(40) = 260
So the sum of 68 + 260= 328.
The factors would be... Well, start with 4:
Divide by 4: (300 + 28)/4 = 300/4 + 28/4 = 75 + 7 = 82
4*82 = 8*41
Break down into the different digits. We only have 2 digit numbers, and the tens digits (and accompanying units digits) are:
0: 2,3,5,7 [meaning the numbers 2, 3, 5, and 7]
1: 1,3,7,9 [meaning the numbers 11, 13, 17, and 19]
2: 3,9 [meaning the numbers 23 and 29]...etc.
3: 1,7
4: 1,3,7
We can add up all the units digits by groups: 17 + 20 + 12 + 8 + 11 = 68
Then we can add up the tens by how many numbers there are with each tens digit: 4(10) + 2(20) + 2(30) + 3(40) = 260
So the sum of 68 + 260= 328.
The factors would be... Well, start with 4:
Divide by 4: (300 + 28)/4 = 300/4 + 28/4 = 75 + 7 = 82
4*82 = 8*41
