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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:55) correct 30% (01:49) wrong based on 202 sessions

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If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which of the following cannot be the value of a – b?

A. –5
B. –3
C. 2
D. 7
E. 8

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Math Expert V
Joined: 02 Aug 2009
Posts: 7978
Re: If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which  [#permalink]

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Bunuel wrote:
If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which of the following cannot be the value of a – b?

A. –5
B. –3
C. 2
D. 7
E. 8

Hi

If we look at a-b, b is infinite on the upper side since b>=2...
And B is being subtracted, so the minimum value will be infinite..
this itself should tell us that the largest value should be the answer ..

But let's see why 8 should be the answer..
Max value of a and min value of b should give us max value..
a has max value of 5 and min value of b is -2..
So a-b=5-(-2)=5+2=7..
So any value beyond 7 will be wrong..

Therefore 8 is not possible..

E
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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4009
If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which  [#permalink]

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Top Contributor
Bunuel wrote:
If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which of the following cannot be the value of a – b?

A. –5
B. –3
C. 2
D. 7
E. 8

Here's an approach that uses a nice rule that essentially says: "if two inequalities are arranged so that the inequality symbols are facing the same direction, we can ADD them to create a new inequality.

We have: 5 ≥ a > 1, which we'll rewrite as 1 < a ≤ 5
Now, for the time being, let's focus on the fact that a ≤ 5

We're also told that b ≥ – 2
To get the inequality facing the same way as the above inequality (in red), let's take b ≥ – 2 and multiply both sides by -1
When we do this, we get: -b ≤ 2

Great, we now have:
a ≤ 5
-b ≤ 2

Since the inequality symbols are facing the same direction, we can ADD the inequalities to create a new inequality.
When we do so, we get: a - b ≤ 7
This means that a - b CANNOT equal 8

So, the correct answer is E

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Re: If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which  [#permalink]

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_________________ Re: If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which   [#permalink] 15 Oct 2018, 07:38
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