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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Number properties

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sat Sep 19, 2015 10:56 am
Hi sud21,

There is a pattern involving prime factorization that can help on this question. While it's a relatively rare pattern, the GMAT might slip in into your Test in 1 question (when you're scoring at a sufficiently high level).

For a positive integer to have EXACTLY 6 factors, the prime-factorization of that number will yield 2 DIFFERENT primes, one of which shows up TWICE.

For example:
12 = (2)(2)(3) = 2 different primes, one of which shows up twice.

Factors of 12: 1,12, 2,6, 3,4

We can use this pattern to quickly find the various integers that fit this pattern (and 'leapfrog' all of the integers that don't). Since the two Facts "hint" at the fact that we're going to be dealing with 2-digit numbers, I'm going to limit my work to those.....

Start with the prime that shows up twice:
(2^2)(3) = 12
(2^2)(5) = 20
x7 = 28
x11 = 44
x13 = 52
x17 = 68
X19 = 76
Etc.

(3^3)(2) = 18
(3^3)(5) = 45
x7 = 63
x11 = 99

(5^2)(2) = 50
(5^2)(3) = 75

(7^2)(2) = 98

1) A and (A+1) each have exactly 6 factors.

IF...
A = 44, (A+1) = 45, then the answer to the question is 44

IF...
A = 75, (A+1) = 76, then the answer to the question is 75
Fact 1 is INSUFFICIENT

2) A < 76

Here, A can be any integer from 1 to 75, inclusive.
Fact 2 is INSUFFICIENT

Combined, we have enough information in our prior work to prove that A could be 44 or 75.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Tue Sep 22, 2015 3:36 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

What is the value of the positive integer a?

(1) a and (a+1) each have exactly 6 factors.
(2) a < 76

In the original condition there is 1 variable (a) and thus we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D has high probability of being the answer. In order to have 6 factors, we must have (p^2)q while p and q are distinct prime numbers.

--> number of factors = (2+1)(1+1)=6
In case of 1), a=44=(2^2)11, a+1=45=(3^2)5, a=75=3(5^2), a+1=76=(2^2)19....the answer is not unique and therefore the condition is not sufficient
In case of 2), the answer is not unique and therefore the condition is not sufficient.
Using both 1) & 2) together, a=44=(2^2)11, a+1=45=(3^2)5, a=75=3(5^2), a+1=76=(2^2)19....the answer is still not unique, and therefore the conditions are not sufficient. Therefore the answer is E.


Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously 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.
Unlimited Access to over 120 free video lessons - try it yourself (https://www.mathrevolution.com/gmat/lesson)
See our Youtube demo (https://www.youtube.com/watch?v=R_Fki3_2vO8)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Sep 25, 2015 1:32 am
[email protected] wrote:For a positive integer to have EXACTLY 6 factors, the prime-factorization of that number will yield 2 DIFFERENT primes, one of which shows up TWICE.

Max@Math Revolution wrote: In order to have 6 factors, we must have (p^2)q while p and q are distinct prime numbers.
Not quite right, p� would also have exactly six factors. (2�, for instance: 1, 2, 4, 8, 16, 32.)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1