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For positive integers a, b, and c, b is 120% greater than a, and c is
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29 Oct 2020, 10:51
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For positive integers a, b, and c, b is 120% greater than a, and c is 25% less than the sum of a and b. Which of the following could be the value of |a – c| ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
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Re: For positive integers a, b, and c, b is 120% greater than a, and c is
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29 Oct 2020, 13:08
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Sajjad1994 wrote:
For positive integers a, b, and c, b is 120% greater than a, and c is 25% less than the sum of a and b. Which of the following could be the value of |a – c| ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Since a, b and c are integers, |a - c| will also be an integer
b = 120% greater than a = 2.2a
c = 75% (a + b) = 0.75 (a + 2.2a) = 0.75 * 3.2a = 2.4a
|a - c| = |a - 2.4a| = |-1.4a| = 1.4a
a has to be multiples of 5, so that the difference is an integer.
a = 5 gives 1.4a = 7. Higher multiples of a will give values of multiples of 7 which are not among the options
Option B
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Re: For positive integers a, b, and c, b is 120% greater than a, and c is
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05 Nov 2020, 12:38
Expert Reply
Sajjad1994 wrote:
For positive integers a, b, and c, b is 120% greater than a, and c is 25% less than the sum of a and b. Which of the following could be the value of |a – c| ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Solution:
Since b is 120% greater than a, b = 2.2a. Then, the sum of a and b is a + b = a + 2.2a = 3.2a. Since c is 25% less than the sum of a and b, c = 3/4 * 3.2a = 2.4a. Thus:
|a - c|
|a - 2.4a|
|-1.4a|
|1.4a|
|14a/10| = |7a/5|
7/5 * |a|
Notice that since a and c are integers, |a - c| is also an integer. No matter what the value of a is, the expression 7/5 * |a| is a multiple of 7. We see that the only multiple of 7 among the answer choices is 7.
Answer: B