The product of three positive integers is 300. If one of them is 5 : Problem Solving (PS)

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92698

The product of three positive integers is 300. If one of them is 5 [#permalink]

20 Nov 2017, 11:08

Expert Reply

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

83% (01:10) correct

17% (01:22) wrong

based on 189 sessions

Hide Show timer Statistics

The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two?

A. 16
B. 17
C. 19
D. 23
E. 32

Show Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

_________________

New to the GMAT CLUB Forum?

Ultimate GMAT Quantitative Megathread

All You Need for Quant

GMAT Club's Complete Questions' Bank

My Signature Questions' Collection:

Bunuel's Signature Questions' Collection

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Signature Read More

L

chetan2u

RC & DI Moderator

Joined: 02 Aug 2009

Status:Math and DI Expert

Posts: 11109

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

21 Nov 2017, 09:46

1

Kudos

Expert Reply

Bunuel wrote:

The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two?

A. 16
B. 17
C. 19
D. 23
E. 32

Hi..
The logic behind it is that the factors closest would give least sum and max product.
Example \(16=4^2=4*4\)
So sum =4+4=8
Rest will keep increasing as we move outwards 2*8, so 2+8=10
1*16, so 1+16=17

Let's see the solution now..
300/5=60..
60~8^2
So look for factors close to 8.... 6*10
Sum =6+10=16

A
_________________

1. Absolute modulus:. 2. Fractions: 3. Percentage increase: 4. Combinations:

Signature Read More

S

animesh mohanty

Intern

Joined: 30 Nov 2016

Posts: 47

Location: India

Concentration: Finance, Strategy

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

20 Nov 2017, 11:14

we know that the product of the two remaining numbers is 60. the smallest number in the list is 16 which satisfies out condition by multiplying 10 and 6.

B

rulingbear

Manager

Joined: 03 May 2017

Posts: 63

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

20 Nov 2017, 11:18

1

Bookmarks

Bunuel wrote:

The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two?

A. 16
B. 17
C. 19
D. 23
E. 32

\(\frac{300}{5}= 60\). The closest factors of 60 are 10 and 6 and their sum is 16. A

B

SamriddhiPan

Intern

Joined: 15 Oct 2017

Posts: 6

Location: India

Concentration: Entrepreneurship, Marketing

Schools: Kellogg '20

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

21 Nov 2017, 02:49

Let a,b and c be the no.s
Given abc=500 and one of the nos is 5. Let a = 5
We know 500=5*60
For the sum of b and c to be minimum, their values have to be minimum too. Let's see -
Product Sum
60 = 15*4 19
30*2 32
10*6 16

Answer - A

L

Abhishek009

Board of Directors

Joined: 11 Jun 2011

Status:QA & VA Forum Moderator

Posts: 6075

Location: India

GPA: 3.5

WE:Business Development (Commercial Banking)

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

21 Nov 2017, 08:11

Bunuel wrote:

The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two?

A. 16
B. 17
C. 19
D. 23
E. 32

\(5*x*y = 300\)

So, \(xy = 60\)

Possible sets of x,y will be -

(1*60) , (2*30) , (3*20) , (4*15) , (5*12) , (6*10) , (10*6) , (12*5)................

Thus, the least possible value of the sum of the other two will be 10 + 6 = 16, answer must be (A)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Signature Read More

P

JeffTargetTestPrep

Target Test Prep Representative

Joined: 04 Mar 2011

Status:Head GMAT Instructor

Affiliations: Target Test Prep

Posts: 3043

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

22 Nov 2017, 13:15

Expert Reply

Bunuel wrote:

The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two?

A. 16
B. 17
C. 19
D. 23
E. 32

Since 300/5 = 60, we need to determine two numbers that multiply to 60. The possibilities are 1 x 60, 2 x 30, 3 x 20, 4 x 15, 5 x 12 and 6 x 10.

Of these products, we see that if we add each pair of factors, the sum that is a minimum is 10 + 6 = 16.

Answer: A
_________________

Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

Try 5-Day Full Access Trial For FREE
Perfect 5-Star Rating on GMAT Club
Conner Scored GMAT Focus 755 (100%)

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

Signature Read More

L

Nikhil

MBA Section Director

Joined: 22 May 2017

Affiliations: GMATClub

Posts: 12740

GRE 1: Q168 V154

GPA: 3.4

WE:Engineering (Education)

Re: The product of three positive integers is 300. If one of them is 5, wh [#permalink]

12 Jul 2018, 01:45

Expert Reply

The product of three positive integers is 300

Let the three positive integers be a, b and c

=> \(abc = 300\)

Given one of the integers is 5 => a = 5

=> \(bc = \frac{300}{a}\)

=> \(bc = \frac{300}{5} = 60\)

=> \(bc = 60\)

Now writing all the factor pairs of 60 we have

1 and 60 sum to 61
2 and 30 sum to 32
3 and 20 sum to 23
4 and 15 sum to 19
5 and 12 sum to 17
6 and 10 sum to 16

The least possible sum of b and c is 60

Hence option A
_________________

GMATClub Podcast - All episodes | Connect with me on LinkedIn!

Signature Read More

P

DavidTutorexamPAL

examPAL Representative

Joined: 07 Dec 2017

Posts: 1050

Re: The product of three positive integers is 300. If one of them is 5, wh [#permalink]

12 Jul 2018, 01:49

Bunuel wrote:

The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two?

A. 16
B. 17
C. 19
D. 23
E. 32

As this a question about a product, we'll first need to use factorization.
This is a Precise approach.

300 = 5 * 60 = 5 * 6 * 10 = 5 * 3 * 2 * 5 * 2.
So our two numbers have (together) the factors 2,2,3 and 5.
Let's try our answers, starting from the smallest:
Can we get (A) 16?
2*3 = 6 and 2*5 = 10.
Since 6 + 10 = 16, then yes, we can.

(A) is our answer.

*Note, in general, if two positive numbers a,b have a constant product then a+b is minimized when a = b = sqrt(ab). So a good guess is to try making a,b, as close to each other as possible, in this case by picking one small factor (2) and one large factor (3 or 5) for each.

G

CounterSniper

Director

Joined: 20 Feb 2015

Posts: 631

Concentration: Strategy, General Management

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

12 Jul 2018, 05:16

Bunuel wrote:

The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two?

A. 16
B. 17
C. 19
D. 23
E. 32

a*b*5=300
ab=60
The closer a and b are to 60/2 the lesser will be the sum
a=10 and b =6
least possible sum =16

D

BrushMyQuant

Tutor

Joined: 05 Apr 2011

Status:Tutor - BrushMyQuant

Posts: 1775

Location: India

Concentration: Finance, Marketing

Schools: XLRI (A)

GMAT 1: 700 Q51 V31

GPA: 3

WE:Information Technology (Computer Software)

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

09 Dec 2023, 02:44

Expert Reply

Top Contributor

The product of three positive integers is 300. If one of them is 5

Let the other two numbers be x and y
=> x * y * 5 = 300
=> xy = \(\frac{300}{5}\) = 60

What is the least possible value of the sum of the other two?

We need to find the minimum value of x + y

Sum of two numbers is minimum when either they are equal or are close to each other

\(\sqrt{60}\) between 7 and 8
So, we need to find numbers close to 7 and 8

60 can be written as 6 * 10
No other numbers apart from these two are closer to each other whose product = 60

=> Minimum sum = 6 + 10 = 16

So, Answer will be A
Hope it helps!
_________________

How to Solve :
All Quant Topics Theory || Units' Digit Problems || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot

GMAT Club Topic Wise Problems

Signature Read More

gmatclubot

Re: The product of three positive integers is 300. If one of them is 5 [#permalink]

09 Dec 2023, 02:44

GMAT Problem Solving (PS) Questions

The product of three positive integers is 300. If one of them is 5

GMAT Question Banks