555

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Sep 22, 2013 2:33 am

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

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Source: Beat The GMAT — Problem Solving | Sun Sep 22, 2013 2:33 am

faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Sep 22, 2013 2:38 am

I can only get the pairs as 497 + 58 & 498 + 57

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Sun Sep 22, 2013 3:18 am

To get the units digit as 5, among the given digits only 8 and 7 can be used. 7+8 and 8+7, so option B to me.

I think you are right. What is the source and OA?

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Sep 22, 2013 3:24 am

Nope B is incorrect.

I just solved it.

The other two pairs are 457 + 98 & 458 + 97

OA is D.

Source - GMATPrep

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Sun Sep 22, 2013 3:52 am

I think today is not my day to get answers correct. Something wrong with me. Will get back refreshed at solving the questions.

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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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 » Sun Sep 22, 2013 3:56 am

faraz_jeddah wrote: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

Let the 5 digits be A, B, C, D and E, as follows:

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.

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Sep 22, 2013 4:39 am

For Units place: 7 + 8 = To make sum = _ _ 5

So Numbers:
_ _ 7
x _ 8

For Tens place: need to make sum as or _4_ --> 5 + 9 --> _ 5 5

So, numbers:
_ 5 7
x 9 8

We are only left with 4

So, numbers
4 5 7
x 9 8

However, 5 & 9 and 7 & 8 can swap possitions.. So total possible numbers

4 5 7
x 9 8
4 9 8
x 5 7

Answer[spoiler][D][/spoiler]

R A H U L

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8208; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: 555

by Scott@TargetTestPrep » Thu Nov 05, 2020 2:05 pm

faraz_jeddah wrote: ↑
Sun Sep 22, 2013 2:33 am
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

Solution:

Since the sum of the two integers is 555, the larger (three-digit) integer must be in the 400s.
If the larger integer is 457, then the smaller one is 555 - 457 = 98 (which is formed by the remaining two digits).

If the larger integer is 475, then the smaller one is 555 - 475 = 80 (which is NOT formed by the remaining two digits).

If the larger integer is 458, then the smaller one is 555 - 458 = 97 (which is formed by the remaining two digits).

If the larger integer is 485, then the smaller one is 555 - 485 = 70 (which is NOT formed by the remaining two digits).

If the larger integer is 459, then the smaller one is 555 - 459 = 96 (which is NOT formed by the remaining two digits).

If the larger integer is 495, then the smaller one is 555 - 495 = 60 (which is NOT formed by the remaining two digits).

If the larger integer is 478, then the smaller one is 555 - 478 = 77 (which is NOT formed by the remaining two digits).

If the larger integer is 487, then the smaller one is 555 - 487 = 68 (which is NOT formed by the remaining two digits).

If the larger integer is 479, then the smaller one is 555 - 478 = 76 (which is NOT formed by the remaining two digits).

If the larger integer is 497, then the smaller one is 555 - 497 = 58 (which is formed by the remaining two digits).

If the larger integer is 489, then the smaller one is 555 - 489 = 66 (which is NOT formed by the remaining two digits).

If the larger integer is 498, then the smaller one is 555 - 498 = 57 (which is formed by the remaining two digits).

Answer: D

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