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Ratio of larger to smaller number is 6:1. So larger number must be 6 times the smaller number, and it should also be a multiple of 6.

So we have only two options to look at: 12 and 18

If larger=12, smaller=2. But 12+2 is not equal to 21

If larger=18, smaller=3. 18+3=21

Hence answer is E
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Bunuel
If the ratio of two numbers is 6 and their sum is 21, what is the value of the larger number?

(A) 1
(B) 5
(C) 12
(D) 17
(E) 18

We can let n = the larger number and m = the smaller number; thus:

n : m = 6x : x

Since their sum is 21, we know that n + m = 21, or:

6x + x = 21

7x = 21

x = 3

Thus, the larger number is 3(6) = 18.

Answer: E
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