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If a, b, c are three positive integers such that a and b are in the ra
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22 Nov 2021, 08:33
22 Nov 2021, 08:33
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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
(A) 201
(B) 205
(C) 202
(D) 207
(E) 210
Re: If a, b, c are three positive integers such that a and b are in the ra
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22 Nov 2021, 09:03
22 Nov 2021, 09:03
\(a:b = 3:4\)
\(b:c = 2:1 = 4:2\)
Therefore, \(a:b:c = 3:4:2\)
Now, we can write as \(a = 3k, b = 4k,\) and \(c = 2k\)
\(a + b + c = 3k + 4k + 2k = 9k\)
\(k\) will be an integer
Check all options and see which one is divisible by 9.
In this case, only 207 is divisible by 9. (Use Divisibility Test of 9 for ease)
Hence, Answer is D
\(b:c = 2:1 = 4:2\)
Therefore, \(a:b:c = 3:4:2\)
Now, we can write as \(a = 3k, b = 4k,\) and \(c = 2k\)
\(a + b + c = 3k + 4k + 2k = 9k\)
\(k\) will be an integer
Check all options and see which one is divisible by 9.
In this case, only 207 is divisible by 9. (Use Divisibility Test of 9 for ease)
Hence, Answer is D
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Re: If a, b, c are three positive integers such that a and b are in the ra
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22 Nov 2021, 09:37
22 Nov 2021, 09:37
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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
(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 9
Useful 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
