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# When 34, 36, and 38 are each divided by positive integer d, the remind

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Re: When 34, 36, and 38 are each divided by positive integer d, the remind [#permalink]
BrentGMATPrepNow wrote:
When 34, 36, and 38 are each divided by positive integer d, the remainders are 4, 0, and 2, respectively. When 41, 43, and 45 are each divided by positive integer k, the remainders are 5, 7, and 0, respectively. What is the value of d + k?

A) 12
B) 15
C) 18
D) 21
E) 24

Solution:

We see that d = 6 since 34/6 = 5 R 4, 36/6 = 6 R 0 and 38/6 = 6 R = 2. We see that k = 9 since 41/9 = 4 R 5, 43/9 = 4 R 7 and 45/9 = 5 R 0. Therefore, the value of d + k = 6 + 9 = 15.

(Note: One can come up with the value of d being 6 since d has to be a divisor of 36 and greater than 4 (recall that divisor is greater than remainder). This limits the value of d to be 6, 9, 12, 18, or 36. By simply dividing by 6, we see that d must be 6. Likewise, one can come up with the value of k being 9 since k has to be a divisor of 45 and greater than 7. This limits the value of k to be 9, 15, or 45. By simply dividing by 9, we see that k must be 9.)

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Re: When 34, 36, and 38 are each divided by positive integer d, the remind [#permalink]
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Re: When 34, 36, and 38 are each divided by positive integer d, the remind [#permalink]
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