More than one answer correct Questions

The new format of GRE has a set of questions that have more than one answer correct. The question may or may not specify the number of answers that are correct. You get credit only if you mark all the correct choices and none of the incorrect ones.

Here is an example.

What values of x will satisfy the inequality x^2 + 12x – 28 < 0?

a. -2 < x < 2

b. -14 < x < -12

c. -6 < x < 14

d. -2 < x < 14

e. x < -14

f. x < 2

Correct Answer: Choices A and B.

Explanation

Factorizing, we get (x + 14)(x – 2) < 0

If the expression in the left hand side of the inequality is less than 0,

either (x + 14) is positive and (x – 2) is negative or

(x + 14) is negative and (x – 2) is positive.

Case 1: (x + 14) is positive and (x – 2) is negative

i.e., (x + 14) > 0 and (x – 2) < 0

or x > -14 and x < 2

or -14 < x < 2

Case 2: (x + 14) is negative and (x – 2) is positive

i.e., (x + 14) < 0 and (x – 2) > 0

or x < -14 and x > 2. Such a number does not exist. Hence, infeasible solution

So, the range of values of x that satisfy the inequality is -14 < x < 2.

Shortcut to find the solution

If (x – a)(x – b) < 0 then x will lie between ‘a’ and ‘b’.

Now let us go to the choices

Choice A : -2 < x < 2. Lies within -14 < x < 2. Hence, satisfies.

Choice B : -14 < x < -12. Lies within -14 < x < 2. Hence, satisfies.

Choice C: -6 < x < 14. Lies outside -14 < x < 2. Does not satisfy.

Choice D: -2 < x < 14. Lies outside -14 < x < 2. Does not satisfy.

Choice E: x < -14. Lies outside -14 < x < 2. Does not satisfy.

Choice F: x < 2. Lies outside -14 < x < 2 for values of x < -14. Does not satisfy.

So, the answer choices that are correct are A and B.

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