An odd number added to itself an odd number of times yields

Question

An odd number added to itself an odd number of times yields

(A) an odd number
(B) an even number
(C) a prime number
(D) a positive number
(E) a perfect square

The OA is A.

I did it for a particular number, but is there any way to prove it in general?

Jay@ManhattanReview · Answer

Vincen wrote:An odd number added to itself an odd number of times yields

(A) an odd number
(B) an even number
(C) a prime number
(D) a positive number
(E) a perfect square

The OA is A.

I did it for a particular number, but is there any way to prove it in general?

Say an odd number is 3, and it is added 5 times (odd number of times) to itself (3).

Thus, the result = 3 + 3 + 3 + 3 + 3 = 15, and odd number.

An algebraic approach:

Say an odd number is n and it is added m times, where m is also an odd number.

Thus, the result = n + n + n + ... m times = m*n = Odd * Odd = Odd.

The question is not drafted well. The correct should be: An odd number added to itself an odd number of times must yield

Otherwise, except option B, all the options can also be correct, though not always. For example, if 1 is added 3 times, the result is a prime and a positive number. Similarly, if 3 is added 3 times, the result is a perfect square number.

Thus, except B, all option could be correct; however, only A must be correct.

Hope this helps!

-Jay

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
_________________
Manhattan Review GMAT Prep

Locations: New York | Barcelona | Manila | Melbourne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

EconomistGMATTutor · Answer

Vincen wrote:An odd number added to itself an odd number of times yields

(A) an odd number
(B) an even number
(C) a prime number
(D) a positive number
(E) a perfect square

The OA is A.

I did it for a particular number, but is there any way to prove it in general?

Hi Vincen,
Let's take a look at your question.

The question states that,
An odd number added to itself an odd number of times.
We know that an odd number can be represented as 2n + 1 in general.

An odd number added to itself 3 times:
(2n+1)+(2n+1)+(2n+1) = 3(2n + 1)

An odd number added to itself 5 times:
(2n+1)+(2n+1)+(2n+1)+(2n+1)+(2n+1) = 5(2n + 1)
...
An odd number added to itself an odd number of times let's say for (2n+3) times
(2n+1)+(2n+1)+(2n+1)+(2n+1)+...+(2n+1) = (2n+3)(2n+1)

We know that (2n+3) is an odd number and (2n+1) is an odd number.
The product of two odd numbers is an odd number always.
Therefore, (2n+3)(2n+1) is an odd number.

Option A is correct.

I am available if you'd like any followup.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Scott@TargetTestPrep · Answer

Vincen wrote: ↑Fri Sep 29, 2017 5:52 pm An odd number added to itself an odd number of times yields (A) an odd number (B) an even number (C) a prime number (D) a positive number (E) a perfect square The OA is A. I did it for a particular number, but is there any way to prove it in general? 1 added to itself 3 times is: 1 + 1 + 1 = 3 3 added to itself 5 times is: 3 + 3 + 3 + 3 + 3 = 15 Thus, we see the result must be an odd number. Answer: A

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

An odd number added to itself an odd number of times yields

GMAT/MBA Expert

GMAT/MBA Expert

Re: An odd number added to itself an odd number of times yields

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER