For how many integers, a, is it true that 2

Question

For how many integers, a, is it true that 2 < |a| < 9?

A 4
B 5
C 6
D 10
E 12

Chethan92 · Answer

|a| is always positive.
a can take 3,4,5,6,7,8 and -3,-4,-5,-6,-7,-8.
Total 12 values.

E is the answer.

KSBGC · Answer

Given,

2 < |a| < 9

**** |a| yields positive integers.

So, we must consider both positive and negative integers withing this range.

a = 3 , 4, 5, 6 , 7 , 8.

a = -3, -4, -5, -6, -7 , -8

Total: 12 integers.

E is the correct answer.

Archit3110 · Answer

2 < |a| < 9
lal = for both + & -ve (3,4,5,6,7,8)

total 12 IMO E

Lowpoint · Answer

To find the number of terms between two numbers in a set of consecutive integers we can use the formula:
Last Number - First Number - 1

So here it's 9-2-1 = 6. So there are a total of 6 numbers between 2 and 9.

We know that absolute values include positive and negative integers. So we need to double the result by multiplying the number of terms with 2 so 6*2 =12.

Answer: E

BrushMyQuant · Answer

We need to find For how many integers, a, is it true that 2 < |a| < 9?

As we have \|a\| in the equation so we will have two cases
-Case 1: a ≥ 0 => \|a\| = a => 2 < a < 9 => Possible integer values of a are from 3 to 8 => (8-3) + 1 => 6 values	-Case 2: a ≤ 0 => \|a\| = -a => 2 < -a < 9 Multiplying with -1 on all the sides and changing the sign of the inequality => -2 > a > -9 => -9 < a < -2 => Possible integer values of a are from -8 to -3 => 6 values

=> We have total 6 + 6 = 12 solutions

So, Answer will be E
Hope it helps!

Watch the following video to MASTER Absolute Values

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.

For how many integers, a, is it true that 2 < |a| < 9?

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

For how many integers, a, is it true that 2 < |a| < 9?

Prep Toolkit

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