GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Aug 2019, 02:50

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

| (|a| + 4)*(|b| - 3) | = 16. How many pairs of integers (a,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
G
Joined: 30 Sep 2017
Posts: 232
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
| (|a| + 4)*(|b| - 3) | = 16. How many pairs of integers (a,  [#permalink]

Show Tags

New post 05 Aug 2019, 11:18
2
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

25% (02:05) correct 75% (02:17) wrong based on 51 sessions

HideShow timer Statistics

| (|a| + 4) * (|b| - 3) | = 16. How many pairs of integers (a,b) can satisfy this equation ?

A. 10
B. 14
C. 16
D. 18
E. 20

Hit +1 kudo if this is a good question
Manager
Manager
avatar
G
Joined: 30 Sep 2017
Posts: 232
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
| (|a| + 4)*(|b| - 3) | = 16. How many pairs of integers (a,  [#permalink]

Show Tags

New post Updated on: 21 Aug 2019, 13:21
1
(|a|+4) ≥4 but (|b|-3) can be negative or positive in any combination in order to satisfy | (|a| + 4) * (|b| - 3) | = 16.

(|a|+4) can take three values: 4, 8 and 16. Correspondingly, (|b|-3) must pair with following values: 4, +/-2, +/-1. Note that (|b|-3) = -4 is not possible because |b|≥0.

|(|a| + 4) * (|b| - 3)|
=|4*4|... a=0,b=+/-7, number of solution=1*2=2
=|8*2|...a=+/-4,b=+/-5, number of solution=2*2=4
=|8*-2|...a=+/-4,b=+/-1, number of solution=2*2=4
=|16*1|...a=+/-12,b=+/-4, number of solution=2*2=4
=|16*-1|...a=+/-12,b=+/-2, number of solution=2*2=4

Thus, total number of pairs of integers (a,b) that satisfy the equation = 2+4+4+4+4=18
Answer is (D)

Originally posted by chondro48 on 05 Aug 2019, 11:40.
Last edited by chondro48 on 21 Aug 2019, 13:21, edited 1 time in total.
CrackVerbal Quant Expert
User avatar
S
Joined: 12 Apr 2019
Posts: 218
Re: | (|a| + 4)*(|b| - 3) | = 16. How many pairs of integers (a,  [#permalink]

Show Tags

New post 07 Aug 2019, 03:58
3
1
In a question on Absolute values, remember that you need to think about the input values that the can be put inside the ‘Mod’ and not the output. The output is anyways going to be positive, since the absolute value function is a distance function.

In this question also, note that you can plug in both positive and negative values for a and b, without affecting the dynamics of the equation.
The question also gives us that elbow space to try only integer values, otherwise, this could have been a more difficult question.

The product of the expression inside the modulus should give us a +16 or a -16. So, essentially, we have to look for the factors of 16.

16 can be written as a product of 2 integral factors in the following ways:
16 = 16 * 1
16 = 8 * 2
16 = 4 * 4
16 = 2 * 8
16 = 1 * 16.

Let’s take the first case. As per this, |a| + 4 = 16 and |b| - 3 = 1. For the above equations, there will be two values of a and b, which will satisfy the individual equations i.e. a = 12 or -12 and b = 4 or – 4.

So, this case gives us 4 pairs.
Similarly, cases 2, 4 and 5 will give us 4 pairs.

For case 4, |a| + 4 = 4 and |b| - 3 = 4. Only one value of a i.e. a=0 satisfies the first equation, while, the second equation will be satisfied by two values of b i.e. b = 7 or -7.
So, case 4 gives us 2 pairs i.e. (0, 7) and (0,-7).

Therefore, the total number of integral pairs of (a,b) is 18.
The correct answer option is D.

Hope this helps!
_________________
GMAT Club Bot
Re: | (|a| + 4)*(|b| - 3) | = 16. How many pairs of integers (a,   [#permalink] 07 Aug 2019, 03:58
Display posts from previous: Sort by

| (|a| + 4)*(|b| - 3) | = 16. How many pairs of integers (a,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne