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 →

Prime Numbers

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1153
Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members
Thanked: 146 times
by parallel_chase » Fri Jul 25, 2008 1:38 pm
How many integers between 0 and 1560 have a prime tens digit and a prime units digit.

A) 295
B) 252 OA
C) 236
D) 96
E) 76

I was able to solve this question by two methods.

First is through permutations, I am getting 232 as the answer. Took me less than 1 minute to solve this way.

Second, finding the pattern in counting the numbers from 1560. But that is very time consuming, took me around 3-4 minutes.

While posting the answers, kindly post the time it took you to solve and the explanation.

Thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 661
Joined: Tue Jul 08, 2008 12:58 pm
Location: France
Thanked: 48 times

by pepeprepa » Fri Jul 25, 2008 2:21 pm
Well, it depends on how you work, I chose the pattern and it was pretty fast, less 1', and with less error probability in my case. The only point is that I took 1 into account so it was wrong but the pattern was ok. The answer was noth there so it took me more time to correct it. Hope it helps even if I was wrong.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 139
Joined: Wed May 07, 2008 12:27 pm
Thanked: 8 times

by acecoolan » Fri Jul 25, 2008 2:58 pm
Isn't 252 the right answer

between 1- 100 = 16 numbers
between 100 - 1000 = 16 * 9 = 144 numbers
between 1000 - 1500 = 80 numbers
between 1500 - 1560 = 12 numbers

16 + 144 + 80 + 12 = 252

Am I doing something wrong?

How would you do this using permutations?

-A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1153
Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members
Thanked: 146 times

by parallel_chase » Fri Jul 25, 2008 3:16 pm
No you are not doing anything wrong, your answer is perfect.
I also did it by the same method but took me more than 3 minutes.

Now permutation method.

0,1,2,3,4,5,6,7,8,9

We have 4 primes numbers (2,3,5,7)

For two digits number 4*4 = 16

For three digits number 9*4*4 =144

For Four digits the number cannot exceed 1560
Therefore, 1*6*3*4 = 72
1 because first digit cannot have more than 1 options (1)
6 because second digit cannot have more than 6 options (0,1,2,3,4,5)
3 because third digit cannot have more than 3 prime number (2,3,5)
4 because we can have all the prime numbers.

16+144+72=232

Let me know if I am doing something wrong.

Thanks,
Last edited by parallel_chase on Fri Jul 25, 2008 3:23 pm, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 118
Joined: Sun Jun 01, 2008 1:47 pmFollowed by: 1 member
Thanked: 5 times

by ricky » Fri Jul 25, 2008 3:16 pm
I have done this way:

Since we need a only tens and units digit to be prime, we just need combinations of 2,3,5 and 7 starting from 10 till 1560.So it is pretty much clear that for every 100 numbers (starting from 0 to 100) we will have same number of combinations.So for first 100 numbers(0 to 100) we have 2^4 combinations i.e 16.

for all 15 such calculations(till 1500) we have 15*16 = 240 combinations.
In last 60 we have 12 prime number combnations.

Total = 240 + 12 = 254

:D or :shock: ?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1153
Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members
Thanked: 146 times

by parallel_chase » Fri Jul 25, 2008 3:20 pm
ricky wrote:I have done this way:

Since we need a only tens and units digit to be prime, we just need combinations of 2,3,5 and 7 starting from 10 till 1560.So it is pretty much clear that for every 100 numbers (starting from 0 to 100) we will have same number of combinations.So for first 100 numbers(0 to 100) we have 2^4 combinations i.e 16.

for all 15 such calculations(till 1500) we have 15*16 = 240 combinations.
In last 60 we have 12 prime number combnations.

Total = 240 + 12 = 254

:D or :shock: ?

Nicely Done!!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 572
Joined: Fri Feb 22, 2008 9:25 am
Thanked: 21 times

by reachac » Fri Jul 25, 2008 9:18 pm
parallel_chase wrote:No you are not doing anything wrong, your answer is perfect.
I also did it by the same method but took me more than 3 minutes.

Now permutation method.

0,1,2,3,4,5,6,7,8,9

We have 4 primes numbers (2,3,5,7)

For two digits number 4*4 = 16

For three digits number 9*4*4 =144

For Four digits the number cannot exceed 1560
Therefore, 1*6*3*4 = 72
1 because first digit cannot have more than 1 options (1)
6 because second digit cannot have more than 6 options (0,1,2,3,4,5)
3 because third digit cannot have more than 3 prime number (2,3,5)
4 because we can have all the prime numbers.

16+144+72=232

Let me know if I am doing something wrong.

Thanks,
You calculated
For Four digits the number cannot exceed 1560
Therefore, 1*6*3*4 = 72
That 3 in ur expression coreesponds to digits 2,3 and 5....means 10's digits can only be 2,3 or 5. However it is true only for numbers of form 15xx and not for others of the form 10xx, 11xx, 12xx, 13xx and 14xx. Hence u gettin the ans wrong.

u shud solve like
For Four digits the number cannot exceed 1560
Therefore, 1*6*4*4 - 1*1*1*4 = 92
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 661
Joined: Tue Jul 08, 2008 12:58 pm
Location: France
Thanked: 48 times

by pepeprepa » Sat Jul 26, 2008 12:36 am
acecoolan wrote:Isn't 252 the right answer

between 1- 100 = 16 numbers
between 100 - 1000 = 16 * 9 = 144 numbers
between 1000 - 1500 = 80 numbers
between 1500 - 1560 = 12 numbers

16 + 144 + 80 + 12 = 252

Am I doing something wrong?

How would you do this using permutations?

-A
Yours is the faster I think. Here what I did.

1-100: 16 numbers
So 15*16=240
1500-1560: 12
So 252
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1