GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 09 Jul 2020, 03:36 ### 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

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.  # How many multiples of 4 are there between 12 and 96, inclusive?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 65133
How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

5
1
71 00:00

Difficulty:   15% (low)

Question Stats: 74% (00:45) correct 26% (00:56) wrong based on 1125 sessions

### HideShow timer Statistics

How many multiples of 4 are there between 12 and 96, inclusive?

(A) 21
(B) 22
(C) 23
(D) 24
(E) 25

Problem Solving
Question: 11
Category: Arithmetic Properties of numbers
Page: 63
Difficulty: 550

The Official Guide For GMAT® Quantitative Review, 2ND Edition

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 65133
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

82
145
marcusaurelius wrote:
How many multiples of 4 are there between 12 and 96, inclusive?

21
22
23
24
25

My answer was 21 and that's incorrect.

$$# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1$$.

In the original case: $$\frac{96-12}{4}+1=22$$.

If the question were: how many multiples of 5 are there between -7 and 35, not inclusive?

Last multiple of 5 IN the range is 30;
First multiple of 5 IN the range is -5;

$$\frac{30-(-5)}{5}+1=8$$.

OR:
How many multiples of 7 are there between -28 and -1, not inclusive?
Last multiple of 7 IN the range is -7;
First multiple of 7 IN the range is -21;

$$\frac{-7-(-21)}{7}+1=3$$.

Hope it helps.
_________________
Manager  Joined: 27 Jul 2010
Posts: 127
Location: Prague
Schools: University of Economics Prague
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

8
1
Thanks Bunuel. One day, after my GMAT is over, and that day will come soon, you should bake a cake for you ##### General Discussion
Intern  Joined: 06 Aug 2011
Posts: 49
Concentration: Entrepreneurship, Finance
GPA: 3.87
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

1
1
Why add one to the final result? I can count from 12-96 by four and come up with 22 that way, but I want to know the logic behind it.
Math Expert V
Joined: 02 Sep 2009
Posts: 65133
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

10
9
Stoneface wrote:
Why add one to the final result? I can count from 12-96 by four and come up with 22 that way, but I want to know the logic behind it.

Set of consecutive multiples of 4 is an evenly spaced set (arithmetic progression).

If the first term of arithmetic progression is $$a_1$$ and the common difference of successive members is $$d$$, then the $$n_{th}$$ term of the sequence is given by:

$$a_ n=a_1+d(n-1)$$ --> $$n=\frac{a_n-a_1}{d} + 1$$.

Hope it helps.
_________________
Manager  Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

5
1
My approach would be this way:
12/4 = 3;
96/4 = 24;

Since both are inclusive, I will go with (Last - First + 1) concept:
24 - 3 + 1
= 22;

Ans is (B)
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17059
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

1
1
Hi All,

This is an example of a "fencepost" problem, since you have to include the "posts" (the numbers 12 and 96) in your calculation. There are a couple of different ways to approach these types of prompts, depending on what you're given and how comfortable you are with the 'technical aspects' of the math.

Here, we have a pretty easy situation: we're asked for all the multiples of 4 between 12 and 96, INCLUSIVE (meaning we have to include the 12 and the 96).

(4)(25) = 100, so there are 25 positive multiples of 4 when dealing with all positive integers from 1 to 100.

(4)(24) = 96, so there are 24 positive multiples of 4 when dealing with all positive integers from 1 to 96, INCLUSIVE.

We now have to remove the multiples of 4 that DO NOT fit the given range....

There are two: 4 and 8

24 - 2 = 22 total multiples of 4

GMAT assassins aren't born, they're made,
Rich
_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11052
Location: United States (CA)
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

marcusaurelius wrote:
How many multiples of 4 are there between 12 and 96, inclusive?

A. 21
B. 22
C. 23
D. 24
E. 25

We can determine the number of multiples of 4 from 12 to 96, inclusive, by using the following formula:

(largest multiple of 4 - smallest multiple of 4)/4 + 1

(96 - 12)/4 + 1 =84/4 + 1 = 21 + 1 = 22

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern  B
Joined: 15 Jul 2018
Posts: 11
Location: Nigeria
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

Is there a difference in the equation, when the numbers are not inclusive?
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17059
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

Hi TestTaker9,

To answer your immediate question: YES - the equation would change IF we were NOT including 12 and 96. Since both of those numbers are multiples of 4, we would have to subtract 2 from the total. As an alternative, you could recalculate using the lower-most and upper-most multiples of 4 that would be in the range of what you were looking for. In your hypothetical, that would be 16 and 92.

GMAT assassins aren't born, they're made,
Rich
_________________
Intern  B
Joined: 18 Jun 2016
Posts: 22
Concentration: Accounting, Accounting
WE: Accounting (Education)
How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

Total multiples of 4 to 96 =96/4=24
4 has two multiples up to 12 which are 4 & 8.
So, multiples of 4 for 12 to 96 inclusive= 24-2=22 (Ans. B)

Posted from my mobile device
Intern  B
Joined: 09 Feb 2019
Posts: 6
Location: India
Concentration: Statistics, Economics
Schools: Rotman '22
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

1
Since all the numbers will be in ap
So the first number will be 12 and last is 96.
An=a+(n-1)d
96=12+(n-1)4
21=n-1
N=22

Posted from my mobile device
Intern  B
Joined: 09 Feb 2019
Posts: 6
Location: India
Concentration: Statistics, Economics
Schools: Rotman '22
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

1
1
Since all the numbers will be in ap
So the first number will be 12 and last is 96.
An=a+(n-1)d
96=12+(n-1)4
21=n-1
N=22

Posted from my mobile device
Senior Manager  G
Joined: 10 Aug 2018
Posts: 280
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)
Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

### Show Tags

TestTaker9 wrote:
Is there a difference in the equation, when the numbers are not inclusive?

Yes there will be a difference then.
The range would be 16 to 92
and in between there are 76 numbers out of which 19 will be divisble by 4 and +1, 20 would be the answer.
_________________
On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES.

" I CAN AND I WILL" Re: How many multiples of 4 are there between 12 and 96, inclusive?   [#permalink] 18 Aug 2019, 23:47

# How many multiples of 4 are there between 12 and 96, inclusive?  