Carcass wrote:
If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2 : 1, then which one of the following is a possible value of (a + b + c)?
(A) 201
(B) 205
(C) 202
(D) 207
(E) 210
Given: a :
b = 3 :
4 and
b : c =
2 : 1
Both ratios share the variable
b.
To combine the ratios into one big ratio, we need to find a ratio that's equivalent to
2 : 1 so that both ratios share the same
b-value.
If
b : c =
2 : 1, we can multiply both sides of the given ratio by 2 to get the equivalent ratio:
b : c =
4 : 2
We now have: a :
b = 3 :
4 and
b : c =
4 : 2
We can all combined ratios to get: a :
b : c = 3 :
4 : 2
Since we're told a, b, c are three positive
integers, we know that a + b + c must be a multiple of 3 +
4 + 2
In other words,
a + b + c must be a multiple of 9Useful property: A number is divisible by 9 if and only if, the sum of its digits is divisible by 9.
When we check the answer choices, only answer choice D is such that the sum of its digits is divisible by 9 (i.e., 2 + 0 + 7 = 9, which is divisible by 9)
Answer: D
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Brent Hanneson - founder of Greenlight Test Prep