Each of the digits 7,5,8,9 and 4 is used only once to form a three digit integer and a two digit integer. If the sum of the integers is 555, how many such pairs of integers can be formed.
A.One
B.Two
C.Three
D.Four
E.Five
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
GMATPrep Exam 3 Q12
This topic has expert replies
-
divyeshbatra
- Newbie | Next Rank: 10 Posts
- Posts: 5
- Joined: Mon Aug 04, 2014 7:06 am
In order to make 555, we need _ _ 7 + _ 8 or _ _ 8 + _ 7
Now by hit and trial I get one pair as ( 497,58)
flipping the units and tens' digit I get ( 498,57) , (458,97), (457,98) and (497,58)
Thus 4 combinations.
Now by hit and trial I get one pair as ( 497,58)
flipping the units and tens' digit I get ( 498,57) , (458,97), (457,98) and (497,58)
Thus 4 combinations.
-
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
Let the 5 digits be A, B, C, D and E, as follows:Each of the digits 7,5,8,9,4 is used only once to form a 3-digit integer and a 2 digit integer. If the sum of the integers is 555, how many such pairs of integers can be formed?
A - One
B - Two
C - Three
D - Four
E - Five
ABC
XDE
555
To yield a sum of 555, A=4:
4BC
XDE
555
Given the remaining digits 5, 7, 8, and 9, it is not possible that C+E = 5.
Thus, to yield a units digit of 5, C+E=15.
Implication:
Either C=7 and E=8 or C=8 and E=7.
Total options = 2.
For the tens place, only the digits 5 and 9 remain.
Thus, either B=5 and D=9 or B=9 and D=5.
Total options = 2.
To combine the options above, we multiply:
2*2 = 4.
The correct answer is D.
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
