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Expert replies
by knight247 » Mon Aug 22, 2011 11:38 am
The digits of a positive integer having 3 digits when taken in order are in arithmetic progression and their sum is 18. The number obtained by reversing the digits is 396 less than the original number. Find the number
(A)468
(B)594
(C)792
(D)822
(E)864

OA is E

Detailed explanations would be appreciated. Thanks
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Source: — Problem Solving |

by vineeshp » Mon Aug 22, 2011 11:59 am
First digit is a, second digit is a + d and third digit is a + 2d. (Arithmetic progression)

a + a + d + a + 2d = 18 - eq 1

The actual number is
100 * a + 10 * (a + d) + a + 2d (Just like how 123 is 1 * 100 + 2 * 10 + 3)
=
Now the reversed number:
a + 2d takes the 100th place , a + d takes 10s place and a takes units place
= 100*(a + 2d) + 10 * (a + d) + a

Difference of above 2 is 396.
(100*(a + 2d) + 10 * (a + d) + a) - (100 * a + 10 * (a + d) + a + 2d) = -396
(I initially assumed reversed is greater than original by 396. was lazy to rewrite the whole equation. Hence I did it the easy way with a minus. :) )
100 * 2d - 2d = -396
198d = -396
d = -2.

3a + 3d = 18
3a + 3 * -2 = 18
3a = 24
a=8
hence numbers are 8 , 6 and 4.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by GMATGuruNY » Mon Aug 22, 2011 1:42 pm
knight247 wrote:The digits of a positive integer having 3 digits when taken in order are in arithmetic progression and their sum is 18. The number obtained by reversing the digits is 396 less than the original number. Find the number
(A)468
(B)594
(C)792
(D)822
(E)864

OA is E

Detailed explanations would be appreciated. Thanks
We can plug in the answer choices, which represent the 3-digit integer.

The sum of the digits must be 18.
Eliminate D (since 8+2+2≠18).

When the digits are taken in order, they must be in arithmetic progression.
Thus, the 3 digits must be equally spaced.
Eliminate B (since 4-5-9 is not equally spaced).
Eliminate C (since 2-7-9 is not equally spaced).

When the digits are reversed, the result must be 396 less than the original number.
Thus, the units digit must be smaller than the hundreds digit.
Eliminate A (since the units digit 8 is larger than the hundreds digit 4).

The correct answer is E.
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by czarczar » Tue Aug 23, 2011 9:21 am
knight247 wrote:The digits of a positive integer having 3 digits when taken in order are in arithmetic progression and their sum is 18. The number obtained by reversing the digits is 396 less than the original number. Find the number
(A)468
(B)594
(C)792
(D)822
(E)864

OA is E

I just tried with the answer choices and got E.

As 864-396 = 468 (Reverse of original number).
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by czarczar » Tue Aug 23, 2011 9:23 am
GMATGuruNY wrote:
knight247 wrote:The digits of a positive integer having 3 digits when taken in order are in arithmetic progression and their sum is 18. The number obtained by reversing the digits is 396 less than the original number. Find the number
(A)468
(B)594
(C)792
(D)822
(E)864

OA is E

Detailed explanations would be appreciated. Thanks
We can plug in the answer choices, which represent the 3-digit integer.

The sum of the digits must be 18.
Eliminate D (since 8+2+2≠18).

When the digits are taken in order, they must be in arithmetic progression.
Thus, the 3 digits must be equally spaced.
Eliminate B (since 4-5-9 is not equally spaced).
Eliminate C (since 2-7-9 is not equally spaced).

When the digits are reversed, the result must be 396 less than the original number.
Thus, the units digit must be smaller than the hundreds digit.
Eliminate A (since the units digit 8 is larger than the hundreds digit 4).

The correct answer is E.
Thanks sir!
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