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

 It is currently 02 Apr 2020, 12:18

### 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

# The sum of three integers is 40. The largest integer is 3

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62456
The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

28 Jan 2014, 00:57
12
00:00

Difficulty:

5% (low)

Question Stats:

86% (02:19) correct 14% (02:44) wrong based on 664 sessions

### HideShow timer Statistics

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

The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?

(A) 1,104
(B) 972
(C) 672
(D) 294
(E) 192

Problem Solving
Question: 62
Category: Algebra Simultaneous equations
Page: 69
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 62456
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

28 Jan 2014, 00:57
4
6
SOLUTION

The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?

(A) 1,104
(B) 972
(C) 672
(D) 294
(E) 192

The middle number = x;
The largest integer is 3 times the middle integer = 3x;
The smallest integer is 23 less than the largest integer = 3x-23.

The sum of three integers is 40 --> x + 3x + 3x - 23 = 40 --> x=9 --> the product ((3x-23)*x*3x) is a multiple of 9. The only multiple of 9 among the options is B (9 + 7 + 2 = 18 = (a multiple of 9), which implies that 972 IS a multiple of 9).

_________________
##### General Discussion
Intern
Joined: 10 Apr 2012
Posts: 38
Concentration: Finance
Schools: Goizueta '19 (I)
WE: Analyst (Commercial Banking)
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

28 Jan 2014, 03:29
2
Set up the values as in the given question:

Let the middle value be denoted by the value 'n'. the sequence as per question is therefore:

3n-23;n;3n for the smallest, middle and largest integers respectively.
So 3n-23+n+3n=40
n=9.

After substitution, the value of the three numbers will be 4;9;27 in the same order above.

Their product =972.

Manager
Joined: 29 Apr 2012
Posts: 69
Location: United States
GMAT Date: 10-22-2012
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

28 Jan 2014, 10:05
Cosmas wrote:
Set up the values as in the given question:

Let the middle value be denoted by the value 'n'. the sequence as per question is therefore:

3n-23;n;3n for the smallest, middle and largest integers respectively.
So 3n-23+n+3n=40
n=9.

After substitution, the value of the three numbers will be 4;9;27 in the same order above.

Their product =972.

I did the same way.
Agree with B...
IMO:B
Manager
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

28 Jan 2014, 20:57
2
1
Let us assume 3 different integers to be x, y and z, in ascending order.

Given that x + y + z = 40;
We are give that z = 3y & x = z - 23 (or) x = 3y - 23;(just to keep a single variable for calculation)

3y - 23 + y + 3y = 40;
7y = 63;
y = 9;

From here, we can determine that z = 27 & x = 4;

Since we are asked to find the product, we can find xyz: 4 * 9 * 27 = 972;

Ans is (B).
Manager
Joined: 20 Dec 2013
Posts: 220
Location: India
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

29 Jan 2014, 02:28
1
a+b+c=40 (1)
Let a<b<c
Therefore,c=3b and a=c-23.
Replacing, a and b in (1)
we get c=27
a=4 and b=9
a*b*c=4*9*27=972
Ans. B
Intern
Joined: 06 Jan 2014
Posts: 35
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

30 Jan 2014, 10:37
1
When you guys post questions from the Official Review...How do you know the difficulty level?

The difficulty is crazy low, but its a 600 Level Question?

and yah, I got 972 as well

A+B+C=40

A+B+3B=40
3B-23+B+3B=40
7B=63

$$\frac{7B}{7}$$ $$=$$ $$\frac{63}{7}$$

$$B=9$$

The rest is history

I represent my three numbers as three different variables because it shows how they can be non or interrelated when I started the problem, I had no idea about the relationship(s) of the numbers and never assume they are "n" related, besides being integers.
Manager
Joined: 04 Oct 2013
Posts: 150
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

02 Feb 2014, 06:09
The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?

(A) 1,104
(B) 972
(C) 672
(D) 294
(E) 192

Let the numbers be $$x_1$$, $$x_2$$ and $$x_3$$

Given that, $$x_3 = 3*x_2$$ Or, $$x_2 = x_3/3$$ & $$x_1 = x_3 -23$$

Since,$$x_1+ x_2 + x_3 = 40$$

Or,$$x_3-23 +\frac{x_3}{3} + x_3=40$$

Or, $$3* x_3+x_3 + x_3*3=(40 + 23)*3$$

Or, $$7x_3=189$$

Or, $$x_3=27$$

Substituting the value of $$x_3$$, $$x_1= x_3-23=4$$ & $$x_2=x_3/3=9$$

So, $$x_1*x_2*x_3=4*9*27=972$$

Current Student
Joined: 10 Mar 2013
Posts: 452
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A\$)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

27 Jul 2015, 09:08
1
L + M + S = 40
3M + M + 3M - 23= 40
7M=63, M=9 -> L=27 -> S=4 ---> 4*27*9 ~ 100*9 = 900 (B)
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16331
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

27 Jul 2015, 16:54
3
Hi All,

This prompt is built on a few Number Properties, so you can actually solve it with a bit of 'brute force' math (without the need of any lengthy equations or calculations:

We're given a few facts to work with:
1) The SUM of 3 integers is 40
2) The largest integer = 3(middle integer)
3) The largest integers = 23 + smallest integer

We're asked for the PRODUCT of the three integers.

First, notice how all 3 answers are POSITIVE, that means that our 3 integers are likely all positive. From the given information, we can see that the largest integer will be considerably bigger than each of the other two.

From the first fact, we know that the largest integer is 3 TIMES the middle integer, so the largest integer MUST be a multiple of 3. Here, we can start brute-forcing the work by 'playing around' with multiples of 3...

IF...
the largest number is 21, then the other two numbers are 7 and -2; the sum is 26, which is TOO LOW. Let's try something bigger....

IF....
the largest number is 24, then the other two numbers are 8 and 1; the sum is 33, which is TOO LOW. We have to go bigger...

IF....
the largest number is 27, then the other two numbers are 9 and 4; the sum IS 40, so these MUST be the 3 numbers

The answer to the question will be the product of 27, 9 and 4. You can organize this math in variety of ways, but you might find it easiest to look at it this way....

(27x4)(9) = (108)(9) --> something MORE than 900 but LESS than 1,000. You might also notice that since one of the numbers is 9, the product MUST be a multiple of 9 (and there's only one answer that fit's THAT description).

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Current Student
Joined: 12 Aug 2015
Posts: 2537
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

29 Jul 2016, 09:34
Here is my approach =>
let x,y,z be the three integers in decreasing order
here x+y+z=40
x+x/3+x-23=40
=> 7x=63*9=> x=27
so y=27/3=9
z=27-23=4
hence the product = 27*9*4
also as the only option that is a multiple of three is B => Smash it
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9937
Location: United States (CA)
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

14 Aug 2017, 14:23
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?

(A) 1,104
(B) 972
(C) 672
(D) 294
(E) 192

We can create the following 3 equations in which a = the smallest integer, b = the middle integer, and c = the largest integer:

a + b + c = 40

and

c = 3b

c/3 = b

and

c - 23 = a

Thus:

c - 23 + c/3 + c = 40

2c + c/3 = 63

Multiplying by 3, we have:

6c + c = 189

7c = 189

c = 27, so a = 27 - 23 = 4 and b = 27/3 = 9.

Thus, the product of the 3 integers is 4 x 9 x 27 = 972.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 01 Mar 2019
Posts: 4
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

27 Jun 2019, 02:40
Bunuel wrote:
SOLUTION

The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?

(A) 1,104
(B) 972
(C) 672
(D) 294
(E) 192

The middle number = x;
The largest integer is 3 times the middle integer = 3x;
The smallest integer is 23 less than the largest integer = 3x-23.

The sum of three integers is 40 --> x + 3x + 3x - 23 = 40 --> x=9 --> the product ((3x-23)*x*3x) is a multiple of 9. The only multiple of 9 among the options is B (9 + 7 + 2 = 18 = (a multiple of 9), which implies that 972 IS a multiple of 9).

Hi,

How do we know that the product ((3x-23)*x*3x) is a multiple of 9?

Doesn't the -23 mean that the product is whatever -23?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16331
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

12 Dec 2019, 13:16

Once you know that one of the three integers is 9 (in this case, that's the "middle number") which is a multiple of 9.... then the product of that number and two other INTEGERS will ALSO be a multiple of 9. While you're correct that the "-23" means that (3X - 23) is NOT a multiple of 9, that does not matter - again, since we're multiplying two integers by 9, the resulting product WILL be a multiple of 9.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
VP
Joined: 18 Dec 2017
Posts: 1254
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: The sum of three integers is 40. The largest integer is 3  [#permalink]

### Show Tags

08 Feb 2020, 23:08
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?

(A) 1,104
(B) 972
(C) 672
(D) 294
(E) 192

x,y,z be the three numbers in increasing order.

z=3y
x=z-23
x=3y-23

x+y+z=40
3y-23+y+3y=40
y=9
z=27
x=4

Product of x,y, and z = 972

Option B.
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Why You Don’t Deserve A 700 On Your GMAT

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
Re: The sum of three integers is 40. The largest integer is 3   [#permalink] 08 Feb 2020, 23:08
Display posts from previous: Sort by