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

Redeem

how many integers between 0 and 1560...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 120
Joined: Thu Sep 02, 2010 8:56 am
Location: India
Thanked: 7 times
GMAT Score:730

how many integers between 0 and 1560...

by euro » Fri Oct 01, 2010 10:42 am
[Q] How many integers between 0 and 1560 have a prime tens digit and a prime units digit?

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

OA is [spoiler](B)[/spoiler] But can't figure out how?
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1031
Joined: Thu Jul 03, 2008 1:23 pm
Location: Malibu, CA
Thanked: 716 times
Followed by:255 members
GMAT Score:750

by Brian@VeritasPrep » Fri Oct 01, 2010 11:00 am
Great question, euro - here's how I'd look at this one:

1) Determine how many prime digits there are (2, 3, 5, 7 --> there are 4 of them)

2) Determine how many numbers meet the requirements per hundred: There are 4 potential tens digits and 4 potential units digits so there are 16 potential numbers (4x4) per hundreds digit. (e.g. 22, 122, 222, 322....)

3) So there are 16 possibilities per fresh set of 100, and there are 15 hundreds/hundreds-and-thousands digits that have "full sets" (0-14).

4) The 16th set of 100 is truncated at 60 (1500 - 1560), so we need to account for the fact that 7 as a tens digit doesn't work on that one. Therefore there are 3 potential tens digits and 4 potential units digits, so there are 3*4 = 12 potential numbers in that set.

Therefore, our number is going to be 15*16 + 12 = 252.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
Top
Post new topic Post Reply
• Page 1 of 1