GMAT Maths | Number Properties Q1

GMAT Sample Questions | Prime Factorization | Divisors

This GMAT sample question is a number theory, number properties practice question testing your understanding of factors/divisors of a number. You could get 2 to 4 questions testing concepts in number properties and number theory in the GMAT quant section.

Question 1: If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?

  1. 121
  2. 3267
  3. 363
  4. 33
  5. None of the above
 

Get to 705+ in the GMAT


Online GMAT Course
@ INR 6000

Video Explanation


GMAT Live Online Classes


Starts Sun, Mar 24, 2024


Explanatory Answer

Step 1 of solving this GMAT Number Properties Question: Prime factorize the given expression

a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311

Step 2 of solving this GMAT Number Properties Question: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33

112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should be a part of 'a'

33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.

Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.

The question is "what is the smallest possible value of 'a'?"
The smallest value that 'a' can take is 363

Choice C is the correct answer.



GMAT Online Course
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up

Already have an Account?

★ Login

GMAT Live Online Classes

Next Batch Mar 24, 2024

★ GMAT Live Info

GMAT Preparation Online | GMAT Number Properties Videos On YouTube


Other useful sources for Number Properties, Number Systems and Number Theory Sample Questions


GMAT Sample Questions | Topicwise GMAT Questions


Work @ Wizako

How to reach Wizako?

Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message