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 →

a and b are prime numbers

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

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] » Tue Mar 15, 2016 8:59 am
Hi jain2016,

This question requires a knowledge of PRIME numbers and a bit of 'brute force' to solve. We're looking for an answer that CANNOT be the sum of two prime numbers, so we could prove that 4 of the answers CAN be the sum of two prime numbers (so that we can eliminate those 4 answers):

A) 19 = 2 + 17
B) 25 = 2 + 23
C) 33 = 2 + 31
D) 46 = 3 + 43

Since those answers all CAN be the sum of two primes, there's only one answer left...

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 15, 2016 9:17 am
jain2016 wrote:If a and b are prime numbers, which of the following CANNOT be the sum of a and b?

A) 19
B) 25
C) 33
D) 46
E) 53
The GMAT LOVES testing whether or not people recognize that 2 is prime (many people believe 2 isn't prime because it's even).

Notice that only 1 of the answer choices is even (D). This is the trap answer for people who believe that ALL prime numbers are odd. These people will look at the other answer choices (which are all odd) and think "hmmm, the only way for 2 integers to add to a odd number is for 1 number to be odd and 1 number to be even. People who believe that all prime numbers are odd will automatically eliminate A, B, C and E and choose D.

As Rich has shown, A, B, C and D can all be rewritten as the sum of 2 primes. So, the answer is E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
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 » Thu Mar 17, 2016 10:06 pm
Another clue here: the only way to get an odd sum when summing two integers is to have Even + Odd. Since four of the answers are odd, and at least three of them MUST be possible, we know that the even number to test must be an even prime, or 2. Working from there

19 = 17 + 2
25 = 23 + 2
33 = 31 + 2

so those are all possible. Trying the next prime (3), we find

46 = 43 + 3

and we're set! Since all four of these can be represented as the sum of two primes, by elimination E must be the right answer.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Fri Dec 22, 2017 10:03 am
jain2016 wrote:If a and b are prime numbers, which of the following CANNOT be the sum of a and b?

A) 19

B) 25

C) 33

D) 46

E) 53
Since 2 + 17 = 19, A is not the answer.

Since 23 + 2 = 25, B is not the answer.

Since 31 + 2 = 33, C is not the answer.

Since 43 + 3 = 46, D is not the answer.

Thus, the answer is E.

Alternate Solution:

We see that all but one of the answer choices are odd numbers. Since the only even prime is 2, the only way the sum of two prime numbers is odd is if one of the numbers is 2. We can subtract 2 from the odd answer choices and see if we get a composite (i.e., non-prime) number:

Since 19 - 2 = 17 is prime, A is not the answer.

Since 25 - 2 = 23 is prime, B is not the answer.

Since 33 - 2 = 31 is prime, C is not the answer.

Since 53 - 2 = 51 is not prime, there is no way 53 is the sum of two prime numbers. Since we already found the answer, we don't even need to test the answer choice that is an even number.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1