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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
Joined: 02 Sep 2009
Posts: 58335
If a is less than b, which of the following numbers is greater than a  [#permalink]

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27 Oct 2017, 00:18
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83% (01:05) correct 17% (01:33) wrong based on 103 sessions

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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

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

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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
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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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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.

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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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06 Feb 2019, 08:14
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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Posts: 169
Re: If a is less than b, which of the following numbers is greater than a  [#permalink]

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29 Apr 2019, 04:28
3
The average of two numbers will always lie in between the two.

a+b/2 = average
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Re: If a is less than b, which of the following numbers is greater than a   [#permalink] 29 Apr 2019, 04:28
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