If x + 5 2 and x - 3

Question

If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

(A) -3 and 10
(B) -3 and 4
(C) 2 and 7
(D) 3 and 4
(E) 3 and 10

Bunuel · Answer

If x + 5 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?

(A) -3 and 10
(B) -3 and 4
(C) 2 and 7
(D) 3 and 4
(E) 3 and 10

x + 5 > 2 --> x>-3;
x - 3 < 7 --> x<10.

Therefore, the value of x must be between -3 and 10 (-3<x<10).

Answer: A.

ScottTargetTestPrep · Answer

Let’s isolate x in each inequality. x + 5 > 2 x > -3 Next we simplify x – 3 < 7. x – 3 < 7 x < 10 We know that x is greater than -3 and less than 10. The answer is A.

adiagr · Answer

x+5 > 2
taking 5 on other side, we get: x > 2-5; x > -3
 
x - 3 < 7

taking -3 on other side, we get: x > 3+7; x > 10

x lies between -3 and 10

Option A is correct answer.

kamranko · Answer

x+5>2 ==>x>-3 x-3<7 ==> x<10 -3

Alvarito · Answer

there's something I still dont get, how is possible for X to be -3.

If you replace: X+5>2 ==> -3+5>2 ==> 2>2 ¿2 is not higher than 2? the right answer should be "=" not ">" the same for the another.

Anisha1637 · Answer

the two inequalities clearly suggests that x>-3 and x<10 
therefore the valuve of x will be between -3 and 10  (A)

CrackverbalGMAT · Answer

When the word ‘And’ used in conjunction with two inequalities, we need to find a range that satisfies both inequalities – in short, we have to find a common range.

x + 5 > 2. Subtracting 5 from both sides, the inequality can be rewritten as x > -3.
x – 3 < 7. Adding 7 to both sides, the inequality can be rewritten as x < 10.

Note that adding / subtracting the same number to / from both sides of an inequality does not change the inequality sign.

Since we are looking for a range that will satisfy both, we can say that -3<x<10. Therefore, x has to be between -3 and 10.

The correct answer option is A.

Hope that helps!
Aravind B T

CrackverbalGMAT · Answer

Hello Alvarito,

As you have observed, the range of x that satisfies both the inequalities is -3<x<10.

-3<x means the number -3 is lesser than x ; in other words,  x is more than -3 . You cannot take x = -3.

Additionally, the question is very clear in what it asks: the value of x is  between  which pairs of numbers. When you use the word ‘between’ you do not consider the extremities.

Try to work on leveraging language clues.

Hope that helps!
Aravind B T

totaltestprepNick · Answer

A https://www.youtube.com/watch?v=L0oj0UIFKa8 Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

If x + 5 > 2 and x - 3 < 7, the value of x must be between

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