BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
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
Is it a prime number?
Source: Beat The GMAT — Data Sufficiency |
IMO Bpepeprepa wrote:If x is a positive integer, is x! + (x+1) a prime number?
1) x<10
2) x is even
The thing is to do this question in 2' time.
1) x<10
x=2 --> 2!+(2+1)=5 is prime
x=3 --> 3!+(3+1)=10 is not prime
We cannot state anything.
2) x is even
x=2 --> 2!+(2+1)=5 is prime
x=4 --> 4!+(4+1)=29 is prime
x=6 --> 6!+(6+1)=727 is prime
Ok it seems pretty cool with x even, and at this moment I stopped and took B which seems logic. What I would like to know is what can give you a clue that you have to go on? This trap is hard to forecast...
Because x=8 --> 8!+(8+1)=8*7*6*5*4*3*2 + 9
Both terms are multiple of 3 so the result is a multiple of 3 so the result is not a prime.
Insufficient
1)and2)
Now it's ok we have example/counter-example for x=2 and x=8 for example.
OA:E
1) x<10
x=2 --> 2!+(2+1)=5 is prime
x=3 --> 3!+(3+1)=10 is not prime
We cannot state anything.
2) x is even
x=2 --> 2!+(2+1)=5 is prime
x=4 --> 4!+(4+1)=29 is prime
x=6 --> 6!+(6+1)=727 is prime
Ok it seems pretty cool with x even, and at this moment I stopped and took B which seems logic. What I would like to know is what can give you a clue that you have to go on? This trap is hard to forecast...
Because x=8 --> 8!+(8+1)=8*7*6*5*4*3*2 + 9
Both terms are multiple of 3 so the result is a multiple of 3 so the result is not a prime.
Insufficient
1)and2)
Now it's ok we have example/counter-example for x=2 and x=8 for example.
OA:E
Chase, till which number did you go ?
Indeed, with the statement 1) x<10, I think I should have been till 12 to see what happens above it. But it's already a lot of calculation for one question...
Indeed, with the statement 1) x<10, I think I should have been till 12 to see what happens above it. But it's already a lot of calculation for one question...
Yeah went till 12 but miscalculated 8! which landed B as an answer.pepeprepa wrote:Chase, till which number did you go ?
Indeed, with the statement 1) x<10, I think I should have been till 12 to see what happens above it. But it's already a lot of calculation for one question...
This was a huge blunder. Thanks for these wonderful questions, keeps us on our feet.
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
- GMAT Score:780
This is only for interest, and won't be much help on the GMAT:
There is no formula for generating prime numbers, which should make you a bit suspicious that the information in the above question is insufficient. Some formulas appear to always generate primes for small values of x, as when you plug even values of x into the above problem, but no formula generates primes for all x. Fermat (incorrectly) thought the following:
2^(2^x) + 1
would generate primes for all x, and if you plug in x = 1, 2, 3 and 4 you do get a prime each time (5, 17, 257 and 65,537 are all prime). These numbers are called Fermat primes. However, for x = 5, you do not get a prime (you do get a very large number, in the billions, so don't try to prove it isn't a prime!). In fact, to date, the only values of x for which the above formula is known to generate primes are exactly the values above: 1, 2, 3 and 4. This illustrates that it is sometimes dangerous to guess that a pattern will continue only because it holds true for a small number of values.
There is no formula for generating prime numbers, which should make you a bit suspicious that the information in the above question is insufficient. Some formulas appear to always generate primes for small values of x, as when you plug even values of x into the above problem, but no formula generates primes for all x. Fermat (incorrectly) thought the following:
2^(2^x) + 1
would generate primes for all x, and if you plug in x = 1, 2, 3 and 4 you do get a prime each time (5, 17, 257 and 65,537 are all prime). These numbers are called Fermat primes. However, for x = 5, you do not get a prime (you do get a very large number, in the billions, so don't try to prove it isn't a prime!). In fact, to date, the only values of x for which the above formula is known to generate primes are exactly the values above: 1, 2, 3 and 4. This illustrates that it is sometimes dangerous to guess that a pattern will continue only because it holds true for a small number of values.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
