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Inequalities

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Inequalities

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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

which of the above options is the correct answer based on your calculation?
i don't seem to get any right Embarassed

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GMAT/MBA Expert

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The question stem should read as follows:

Quote:
If a is less than b, which of the following expressions MUST BE greater than a but less than b?

(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a
Test a=0 and b=1 in the answer choices:

(A) (a + b)/2 --> (0+1)/2 = 1/2.
(B) ab/2 --> (0*1)/2 = 0.
(C) b² - a² --> 1² - 0² = 1.
(D) ab --> 0*1 = 0.
(E) b - a --> 1-0 = 1.

Eliminate B, C, D and E, which do not yield values between a=0 and b=1,

The correct answer is A.

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Hello Roland. I hope you're well.

You can pick two numbers and try option by option. Let's take a=1 and b=2. Now,

$$Option\ E:\ b-a=2-1=1,$$ this is not greater than a. INCORRECT.

$$Option\ D:\ ab=1\cdot2=2,$$ this is not less than b. INCORRECT.

$$Option\ C:\ b^2-a^2=2^2-1^2=4-1=3,$$ this is not less than b. INCORRECT.

$$Option\ B:\ ab/2=1\cdot2/2=1,$$ this is not greater than a. INCORRECT.

$$Option\ A:\ (a+b)/2=(1+2)/2=3/2=1,5,$$ this is greater than a and less than b. CORRECT.

So, the correct option is A.

I hope this can help you.

I'm available if you'd like any follow up.

Regards.

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