If x is an integer, and 169

Question

If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

(A) 0
(B) 61
(C) 62
(D) 75
(E) 93

pushpitkc · Answer

x could take values -14,-15,-16,-17,17,16,15, and 14
The sum of all the values which satisfy this inequality is 0.
The reason for this is the negative numbers cancel out the positive terms.

0(Option A)  is the correct answer

sashiim20 · Answer

169 < x^2 < 324

(-13)^2  or  13^2 < x^2 < (-18)^2  or  18^2

Therefore  x  could be  = -14, 14,-15, 15,-16, 16,-17, 17

Sum of all possible values of  x = -14 + 14 -15 + 15 -16 + 16 -17 + 17 = 0

Answer (A)...

nvnt · Answer

Its 62, Option C.
Lower limit is 169 = 13^2, upper limit is 324 = 18^2.
So possible values between limits are 14,15,16,17 and sum of these is 62.

Skywalker18 · Answer

169 < x^2 < 324
=> 13^2 < x^2 < 18^2

X can take values 14, 15 , 16 , 17 and - 14 , -15 , -16 , -17
Sum = 0

Answer A

chetan2u · Answer

Hi...
 since x is an integer and it has an EVEN power, don't get into calculation ..
 ans is 0, as every positive value of x will have a corresponding similar negative value. these will cancel out when added. . 
so finally ans will be ZERO..
A

srikanth9502 · Answer

X can take 14,15,16,17 and -14,-15,-16,-17. So summation equals to zero.

mbaaspirant80 · Answer

If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

This question is logical and answering it should not take more than 30 sec.
169 < x^2 < 324, means 13<X<18 or -18<X<-13

means X will take same positive and negative values . Hence addition of all values = 0

JeffTargetTestPrep · Answer

We are given that 169 < x^2 < 324. That is, 13 < |x| < 18. If x is positive, x = 14, 15, 16, 17. If x is negative, x = -14, -15, -16, -17. We see that for every positive value of x, the opposite (or negative) is also a possibility. Thus, the sum of all values of x will be zero.

Answer: A

stonecold · Answer

Okay.
The possible values of x =>
14,-14
15,-15
16,-16
17,-17

Hence sum => Zero.

The presence of zero in the options signifies that this is a Novel question...

Best
Stone Cold

PV66 · Answer

X can also take a negative value since it is squared. So -14,14,-15,15,-16,16,-17,17, add all of them you get a 0.

Cheers,
PV66.

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

If x is an integer, and 169 < x^2 < 324, which of the following is the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions