BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Which of the following MUST yield an integer when . . . .

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

Which of the following MUST yield an integer when . . . .

by Vincen » Wed Jan 03, 2018 11:53 am
Which of the following MUST yield an integer when divided by 5?

A. The sum of five consecutive positive integers.
B. The square of a prime number.
C. The sum of two odd integers.
D. The product of three consecutive odd numbers.
E. The difference between a multiple of 8 and a multiple of 3.

The OA is the option A.

How can I show that the correct answer is option A? Experts, could you give me some help, please?
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

by EconomistGMATTutor » Wed Jan 03, 2018 12:51 pm
Hello Vincen.

Let's take a look at your question.

The sum of five consecutive positive integers is:

n + (n+1) + (n+2) + (n+3) + (n+4) = 5n + 10 = 5(n+2).

So, it is multiple of 5. Therefore, it MUST yield an integer when divided by 5.

Hence, there is no need to try the rest of the options.

The correct answer is A.

I hope this explanation may help you.

Regards.

------------------------------------------------------------------------------------------------------------------------------------------------------
If you want we can prove that the rest of the options are incorrect.

Option 2: The square of a prime number is not always divisible by 5. We can choose 3, then 3^2=9.

Option 3: The sum of two odd integers is not always divisible by 5. We can choose 3 and 5, then 3+5=8.

Option 4: The product of three consecutive odd numbers is not always divisible by 5. We can choose 17, 19 and 21.

Option 5: The difference between a multiple of 8 and a multiple of 3 is not always divisible by 5. We can choose 24-3=21.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top
User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Mon Aug 12, 2019 5:46 pm
Vincen wrote:Which of the following MUST yield an integer when divided by 5?

A. The sum of five consecutive positive integers.
B. The square of a prime number.
C. The sum of two odd integers.
D. The product of three consecutive odd numbers.
E. The difference between a multiple of 8 and a multiple of 3.

The OA is the option A.

How can I show that the correct answer is option A? Experts, could you give me some help, please?
The sum of 5 consecutive integers will always be divisible by 5. If we denote the integers by n, n + 1, ... , n + 4; then the sum is 5n + 10, which is divisible by 5 regardless of the number we choose for n. (Note: In fact, the sum of k consecutive positive integers is always divisible by k. So the sum of 5 consecutive positive integers is divisible by 5.)

Alternate Solution:

We can rule out every answer choice except A:

- The square of a prime number is not divisible by 5 unless the prime we choose is 5.
- The sum of two odd integers need not be divisible by 5 (for instance, 1 + 3 = 4 is not divisible by 5).
- The product of three odd integers need not be divisible by 5 (for instance, 9 x 11 x 13 is not divisible by 5).
- The difference between a multiple of 8 and a multiple of 3 need not be divisible by 5 (for instance, 16 - 3 = 13 is not divisible by 5).

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1