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
555
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- faraz_jeddah
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- faraz_jeddah
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I can only get the pairs as 497 + 58 & 498 + 57
A good question also deserves a Thanks.
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- vinay1983
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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?
I think you are right. What is the source and OA?
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!
- faraz_jeddah
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Nope B is incorrect.
I just solved it.
The other two pairs are 457 + 98 & 458 + 97
OA is D.
Source - GMATPrep
I just solved it.
The other two pairs are 457 + 98 & 458 + 97
OA is D.
Source - GMATPrep
A good question also deserves a Thanks.
Messenger Boy: The Thesselonian you're fighting... he's the biggest man i've ever seen. I wouldn't want to fight him.
Achilles: That's why no-one will remember your name.
Messenger Boy: The Thesselonian you're fighting... he's the biggest man i've ever seen. I wouldn't want to fight him.
Achilles: That's why no-one will remember your name.
- vinay1983
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I think today is not my day to get answers correct. Something wrong with me. Will get back refreshed at solving the questions. ![Sad :(](./images/smilies/sad.png)
![Sad :(](./images/smilies/sad.png)
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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Let the 5 digits be A, B, C, D and E, as follows: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
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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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]
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]
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Solution:faraz_jeddah wrote: ↑Sun Sep 22, 2013 2:33 amEach 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
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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