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If a is less than b, which of the following numbers is greater than a

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 42250

Kudos [?]: 132495 [0], given: 12323

If a is less than b, which of the following numbers is greater than a [#permalink]

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New post 27 Oct 2017, 00:18
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

84% (00:46) correct 16% (01:26) wrong based on 38 sessions

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Kudos [?]: 132495 [0], given: 12323

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P
Joined: 25 Feb 2013
Posts: 537

Kudos [?]: 245 [0], given: 33

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
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If a is less than b, which of the following numbers is greater than a [#permalink]

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New post 27 Oct 2017, 02:19
Bunuel wrote:
If a is less than b, which of the following numbers is greater than a and less than b ?

(A) (a + b)/2
(B) ab/2
(C) b^2 – a^2
(D) ab
(E) b – a


given \(b>a\). we need to find \(x\) where \(a<x<b\)

(A) \(\frac{(a + b)}{2}\) ----this is the mid-point of \(a\) & \(b\) in a number line. Hence has to be between \(a\) & \(b\). Correct

(B) \(\frac{ab}{2}\) ------ if \(a=2\) & \(b = 4\), then \(\frac{ab}{2}=b\). Does not satisfy the condition

(C) \(b^2 – a^2\)--------- again if \(a=1\) and \(b=4\), then \(b^2-a^2=15>b\). Does not satisfy the condition

(D) \(ab\) ------ if \(a=2\) & \(b = 4\), then \(ab=8>b\). Does not satisfy the condition

(E) \(b – a\) ------if \(a=-1\) and \(b=1\), then \(b-a=2>b\). Does not satisfy the condition

Option A

Kudos [?]: 245 [0], given: 33

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Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 900 [0], given: 5

Re: If a is less than b, which of the following numbers is greater than a [#permalink]

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New post 30 Oct 2017, 14:08
Bunuel wrote:
If a is less than b, which of the following numbers is greater than a and less than b ?

(A) (a + b)/2
(B) ab/2
(C) b^2 – a^2
(D) ab
(E) b – a


Let’s take a = 3 and b = 4 and test each answer choice:

A) (a + b)/2 = (3 + 4)/2 = 3.5

We see that (a + b)/2 is greater than a and less than b.

We could stop here, but let’s double-check the remaining answer choices.

B) ab/2 = 3(4)/2 = 6

We see that ab is greater than b.

C) b^2 - a^2 = 16 - 9 = 7

We see that b^2 - a^2 is greater than b.

D) ab = 3(4) = 12

We see that ab is greater than b.

E) b - a = 4 - 3 = 1

We see that b - a is less than a.

The only answer choice that produced a value between a and b is A.

Answer: A
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Kudos [?]: 900 [0], given: 5

Re: If a is less than b, which of the following numbers is greater than a   [#permalink] 30 Oct 2017, 14:08
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If a is less than b, which of the following numbers is greater than a

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