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

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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 26 Oct 2017, 23:18
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (01:05) correct 16% (01:42) wrong based on 63 sessions

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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, 01:19
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
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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, 13:08
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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Re: If a is less than b, which of the following numbers is greater than a  [#permalink]

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New post 06 Feb 2019, 07:14
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


Testing choices, a=4, b=5
A) 9/2 = 4.5, looks good
B) 20/2 = 10, not <b
C) 25-16=9, not <b
D) 20, not <b
E) 5-4 = 1, not >a

Thinking about it logically, adding a+b together and then dividing by two means the number will be halfway between a and b, so regardless of what value we pick it will be <b and >a.
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Re: If a is less than b, which of the following numbers is greater than a   [#permalink] 06 Feb 2019, 07:14
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If a is less than b, which of the following numbers is greater than a

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