• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Is at least one of 3 consecutive integers a multiple of 5?

This topic has 1 expert reply and 2 member replies

GMAT/MBA Expert

Max@Math Revolution Legendary Member
Joined
24 Jul 2015
Posted:
1312 messages
Followed by:
25 members
Upvotes:
19
GMAT Score:
Most Active Expert

Is at least one of 3 consecutive integers a multiple of 5?

Post Thu Mar 08, 2018 1:17 am
[GMAT math practice question]

Is at least one of 3 consecutive integers a multiple of 5?

1) The sum of the integers is divisible by 5
2) The product of the integers is divisible by 5

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $79 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
GMATinsight Legendary Member
Joined
10 May 2014
Posted:
1058 messages
Followed by:
23 members
Upvotes:
205
Post Fri Mar 09, 2018 6:23 am
Max@Math Revolution wrote:
[GMAT math practice question]

Is at least one of 3 consecutive integers a multiple of 5?

1) The sum of the integers is divisible by 5
2) The product of the integers is divisible by 5
Question : Is at least one of 3 consecutive integers a multiple of 5?

Statement 1: The sum of the integers is divisible by 5

For any Arithmetic Progression (Sequence in which terms are equally spaced)

Mean = Median = (First Term+Last Term)/2


The addition of 3 consecutive integers = 3* Middle Term = Multiple of 5 (As given in statement)

i.e. Middle term must be a multiple of 5 for this to be true

SUFFICIENT

Statement 2: The product of the integers is divisible by 5

For product of Integers to be a multiple of 5, one of those 3 consecutive integers must be a multiple of 5

SUFFICIENT

Answer: option D

_________________
Bhoopendra Singh & Sushma Jha - Founder "GMATinsight"
Testimonials e-mail: info@GMATinsight.com I Mobile: +91-9999687183 / +91-9891333772
To register for One-on-One FREE ONLINE DEMO Class Call/e-mail
One-On-One Private tutoring fee - US$40 per hour & for FULL COURSE (38 LIVE Sessions)-US$1000

  • +1 Upvote Post
  • Quote
  • Flag
Post Fri Mar 09, 2018 7:48 am
I think that the correct option is D.

(1) The sum of the integers is divisible by 5.

Let's take 3 consecutive integers k, k+1 and k+2. Hence $$\frac{k+k+1+k+2}{5}=\frac{3k+3}{5}=\frac{3\left(k+1\right)}{5}=T\ \ \Leftrightarrow\ \ 3\left(k+1\right)=5\cdot T,\ $$ where T is an integer.
Now, since 3(k+1) is a multiple of 5, then k+1 must be multiple of 5. Therefore, one of the 3 integers is multiple of 5. SUFFICIENT.

(2) The product of the integers is divisible by 5.

We have that $$k\cdot\left(k+1\right)\cdot\left(k+2\right)=5\cdot T,\ $$ where T is an integer. Therefore, one of the 3 integers must be multiple of 5. SUFFICIENT.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Max@Math Revolution Legendary Member
Joined
24 Jul 2015
Posted:
1312 messages
Followed by:
25 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post Sun Mar 11, 2018 5:23 pm
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Write the 3 consecutive integers as n-1, n, n+1.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since ( n - 1 ) + n + ( n + 1 ) = 3n is divisible by 5, and 3 and 5 are prime numbers, n is a multiple of 5, since 3 is not divisible by 5.
Condition 1) is sufficient.

Condition 2)
Since (n-1)n(n+1) is divisible by 5 and 5 is a prime number, one of n-1, n and n+1 is a multiple of 5.
Condition 2) is sufficient.

Therefore, D is the answer.

Answer: D

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $79 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 GMATGuruNY 103 first replies
2 Brent@GMATPrepNow 43 first replies
3 Rich.C@EMPOWERgma... 34 first replies
4 Jay@ManhattanReview 29 first replies
5 Scott@TargetTestPrep 11 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

152 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

139 posts
3 image description Scott@TargetTestPrep

Target Test Prep

104 posts
4 image description Max@Math Revolution

Math Revolution

86 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

86 posts
See More Top Beat The GMAT Experts