Let abcd be a general four-digit number. How many odd four-digits numbers abcd exist such that the four digits are all distinct, no digit is zero, and the product of a and b is the two-digit number cd?
(A) 4
(B) 6
(C) 12
(D) 24
(E) 36
Let abcd be a general four-digit number. How many odd four
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Condition:BTGmoderatorDC wrote:Let abcd be a general four-digit number. How many odd four-digits numbers abcd exist such that the four digits are all distinct, no digit is zero, and the product of a and b is the two-digit number cd?
(A) 4
(B) 6
(C) 12
(D) 24
(E) 36
a*b = integer cd
Since abcd must be odd and composed of 4 distinct digits, we get the following options for integer cd:
21, 31, 41, 51, 61, 71, 81, 91
13, 23, 43, 53, 63, 73, 83, 93
15, 25, 35, 45, 65, 75, 85, 95
17, 27, 37, 47, 57, 67, 87, 97
19, 29, 39, 49, 59, 69, 79, 89
Only the options in blue can be equal to the product of two distinct digits a and b:
Case 1: cd = 21, with the result that a=3 and b=7 or a=7 and b=3
In this case, abcd = 3721 or 7321
Case 2: cd = 63, with the result that a=7 and b=9 or a=9 and b=7
In this case, abcd = 7963 or 9763
Case 3: cd = 27, with the result that a=3 and b=9 or a=9 and b=3
In this case, abcd = 3927 or 9327
Total options for abcd = 6.
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
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