How many positive two-digit numbers are odd, not divisible b

Expert replies

Previous Topic Next Topic

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Feb 25, 2019 5:53 am

Timer

00:00

Answers

Stats

Difficulty—

GMATH practice exercise (Quant Class 16)

How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits?

(A) 28
(B) 27
(C) 26
(D) 25
(E) 24

Answer: [spoiler]____(B)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

Source: Beat The GMAT — Problem Solving | Mon Feb 25, 2019 5:53 am

GMAT/MBA Expert

Brent@GMATPrepNow: 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 » Mon Feb 25, 2019 9:26 am

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 16)

How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits?

(A) 28
(B) 27
(C) 26
(D) 25
(E) 24

Answer: [spoiler]____(B)__[/spoiler]

After about 30 seconds, I recognized that I couldn't see a nice straightforward solution (one that doesn't involve considering multiple cases), so I had 3 options:
1) Keep searching for a nice straightforward solution
2) Guess and move on
3) List the possible outcomes

Since the answer choices are reasonably small, I can quickly list the outcomes and be finished in under 2 minutes (total)
So, let's do that.

We get: 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 79, 83, 85, 89, 91, 95, 97

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Feb 25, 2019 9:54 am

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 16)

How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits?

(A) 28
(B) 27
(C) 26
(D) 25
(E) 24

For any set of consecutive integers:
count = biggest - smallest + 1
Thus:
Number of two-digit integers between 10 and 99, inclusive = 99-10+1 = 90.

Of these 90 consecutive integers, 1 of every 3 will be a multiple of 3, implying that 2/3 will NOT be divisible by 3:
(2/3)(90) = 60.

Of these 60 remaining integers, exactly 1/2 will be ODD:
(1/2)(60) = 30.

Of these 30 remaining integers that are not divisible by 3 but are odd, three -- 11, 55 and 77 -- have repeated digits and thus must be subtracted from the total:
30-3 = 27.

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Feb 25, 2019 12:25 pm

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 16)

How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits?

(A) 28
(B) 27
(C) 26
(D) 25
(E) 24

$$?\,\,\,\,:\,\,\,\# N\,,\,\,N \in \left[ {10,99} \right]\,\,,\,\,{\rm{odd}}\,\,{\rm{,}}\,\,{\rm{not}}\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,{\rm{3}}\,,\,\,\,{\rm{not}}\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,11$$
$${\rm{I}}{\rm{.}}\,\,\,\,{\rm{odd}} \in \left[ {10,99} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{1 \over 2}\left( {99 - 10 + 1} \right) = 45\,\,{\rm{numbers}}$$

$${\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {{\rm{div}}\,\,{\rm{by}}\,\,3} \right)\,\,\,:\,\,\,\left\{ \matrix{
\,15 = 3 \cdot 5 + 0 \cdot 6 \hfill \cr
\,21 = 3 \cdot 5 + 1 \cdot 6 \hfill \cr
\,\,\, \ldots \hfill \cr
\,99 = 3 \cdot 5 + 14 \cdot 6 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,14 + 1 = 15\,\,{\rm{numbers}}$$
$${\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,3} \right)\,\,\,:\,\,\,45 - 15 = 30\,\,{\rm{numbers}}$$

$${\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,3} \right) \cap \,\,\left( {{\rm{div}}\,\,{\rm{by}}\,\,11} \right)\,\,\,:\,\,\,\left\{ {11,33,55,77,99} \right\} - \left\{ {33,99} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,3\,\,{\rm{numbers}}$$

$$?\,\, = \,\,{\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,3} \right) \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,11} \right) = \,\,30 - 3 = 27\,\,{\rm{numbers}}$$

The correct answer is (B).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review