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# If a and b are positive numbers, is a < b?

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Manager
Joined: 01 Sep 2016
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GMAT 1: 690 Q49 V35
If a and b are positive numbers, is a < b?  [#permalink]

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Updated on: 17 Jun 2017, 02:10
3
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:00) correct 33% (01:58) wrong based on 109 sessions

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If a and b are positive numbers, is a < b?

(1) a < b/2 + 2
(2) a < b/2 -2

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Originally posted by bkpolymers1617 on 17 Jun 2017, 01:45.
Last edited by Bunuel on 17 Jun 2017, 02:10, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If a and b are positive numbers, is a < b?  [#permalink]

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17 Jun 2017, 02:45
Given a and b are positive numbers, we need to find out if a < b?

(1) a < b/2 + 2
Equation can be re-written as a-2 < b/2
For values a = b = 10 statement a<b is false as a=b
Similarly, for values a = 3,b=3.2 statement a<b is true
Hence, not sufficient.

(2) a < b/2 - 2
Equations can be rewritten as a+2 < b/2
If a=b=any value, the equation a+2 < b/2 will not stand.
If a>b for any positive number, the equation a+2 < b/2 will not stand.
Only when a<b, this statement stands.

Hence this statement alone is sufficient.(Option B)
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Re: If a and b are positive numbers, is a < b?  [#permalink]

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17 Jun 2017, 03:09
If a and b are positive numbers, is a < b?

(1) a < b/2 + 2. If b = 2 and a = 2, then answer is NO but if b = 4 and a = 1, then the answer is YES. Not sufficient.

(2) a < b/2 - 2. Notice that b/2 is less than b, so b/2 - 2 is even less. So, even if b/2 - 2 is greater than a, then so must be b alone. Sufficient.

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Re: If a and b are positive numbers, is a < b?  [#permalink]

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17 Jun 2017, 03:18
S1 -> if b = 2 then a < 3 so it can be 2 but if b = 4, a < 6 so it can be 5 and can be 1. Insufficient

S2 -> b = 2 then a < -1, if b = 4 a < 0. Sufficient.

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Re: If a and b are positive numbers, is a < b?  [#permalink]

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17 Jun 2017, 07:38
Top Contributor
bkpolymers1617 wrote:
If a and b are positive numbers, is a < b?

(1) a < b/2 + 2
(2) a < b/2 - 2

Target question: Is a < b?

Given: a and b are positive numbers

Statement 1: a < b/2 + 2
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 0 and b = 2, in which case a < b
Case b: a = 2.5 and b = 2, in which case a > b
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: a < b/2 - 2
Since b is POSITIVE, we know that b/2 < b
We can also say that b/2 - 2 < b/2
We can COMBINE these inequalities to get: a < b/2 - 2 < b/2 < b
If we ignore the middle parts, we see that a < b
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: If a and b are positive numbers, is a < b?  [#permalink]

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15 Oct 2018, 06:17
Bunuel wrote:
If a and b are positive numbers, is a < b?

(1) a < b/2 + 2. If b = 2 and a = 2, then answer is NO but if b = 4 and a = 1, then the answer is YES. Not sufficient.

(2) a < b/2 - 2. Notice that b/2 is less than b, so b/2 - 2 is even less. So, even if b/2 - 2 is greater than a, then so must be b alone. Sufficient.

Dear brunel
Any tips in deciding the numbers to test the inequalities? i am taking too much in agreeing on the numbers to test the DS questions. thanks in advance
Re: If a and b are positive numbers, is a < b?   [#permalink] 15 Oct 2018, 06:17
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