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# If a and b are nonzero integers such that 2a = 5b, then each of the fo

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If a and b are nonzero integers such that 2a = 5b, then each of the fo  [#permalink]

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06 Oct 2015, 00:37
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55% (hard)

Question Stats:

65% (01:57) correct 35% (01:51) wrong based on 217 sessions

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If a and b are nonzero integers such that 2a = 5b, then each of the following must be true EXCEPT

A. 0 < b/a < 1
B. ab is positive.
C. On the number line, b lies between 0 and a.
D. The ratio of a to b is equivalent to 10/4.
E. a – b is positive.

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Re: If a and b are nonzero integers such that 2a = 5b, then each of the fo  [#permalink]

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06 Oct 2015, 01:12
5
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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

If a and b are nonzero integers such that 2a = 5b, then each of the following must be true EXCEPT

A. 0 < b/a < 1
B. ab is positive.
C. On the number line, b lies between 0 and a.
D. The ratio of a to b is equivalent to 10/4.
E. a – b is positive.

Since 2a = 5b, we can put a=5k, b=2k(k is a nonzero integer).
So b/a = 2k/5k = 2/5 ---> 0 < b/a = 2/5 < 1 is correct
ab = (5k)(2k)= 10 k^2. Since k^2>0, ab >0.
If k>0, 0<2k<5k(0<b<a). If k<0, 5k<2k<0(a<b<0). So "C" is also correct.
a/b=(5k)/(2k)= 5/2 = 10/4. So "D" is also correct.
a-b= 5k-2k=3k. If k>0, a-b is positive. If k<0, however, a-b is negative. So "E" is false. The answer is, therefore, E.
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Re: If a and b are nonzero integers such that 2a = 5b, then each of the fo  [#permalink]

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06 Oct 2015, 22:00
3
1

This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.

We're told that A and B are NONZERO INTEGERS and that 2A = 5b. We're told that each of the answer is always true EXCEPT for one of them...

Before we get to the actual work, it's important to note a few details:

1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.

Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...

A = 5
B = 2

AND

A = -5
B = -2

Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.

(2)(5) and (-2)(-5) both = +10. Answer B appears true.

Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0

5/2 = -5/-2
10/4 = 5/2

Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.

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Re: If a and b are nonzero integers such that 2a = 5b, then each of the fo  [#permalink]

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12 Aug 2017, 05:44
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Re: If a and b are nonzero integers such that 2a = 5b, then each of the fo   [#permalink] 12 Aug 2017, 05:44
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