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A boy multiplied 423 by a certain number and obtained 65589

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A boy multiplied 423 by a certain number and obtained 65589 [#permalink] New post 18 Mar 2005, 14:09
A boy multiplied 423 by a certain number and obtained 65589 as his answer. If both the 5s in the answer are wrong, but the other figures are right, find the correct answer.

(a) 62389
(b) 67889
(c) 60489
(d) 61389

Anirban
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Re: Find the right digits [#permalink] New post 18 Mar 2005, 14:33
anirban16 wrote:
A boy multiplied 423 by a certain number and obtained 65589 as his answer. If both the 5s in the answer are wrong, but the other figures are right, find the correct answer.

(a) 62389
(b) 67889
(c) 60489
(d) 61389

Anirban


(c) 60489.

Apparent observation of the results tell me that the multiplier should end with a three, and should be between 140 and 160.
The possible multiplicants therefore are 143, 153 and 163.
Trying to multiply (don't need to go all the way ... just check upto 2 digits - 153 and 163 don't give 89 as the last 2 digits). Multiply 423 with 143 to arrive at the answer.

Hope that helps.
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 [#permalink] New post 18 Mar 2005, 16:01
"C"....anyone knows a quicker way ?....I started with 3 as last digit for the multiplier and work backwards
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Re: Find the right digits [#permalink] New post 18 Mar 2005, 22:04
this is my approach.
lets get the sum of the divider= 4+2+3=9, which means 423 is divided by 3. so does the required number.
lets repeate the process.
(a) the sum is not multiple of 3.
(b) same.
(c) sum = 27
(d) sum = 27

lets do trial and error between C and D. so the answer is 60489.
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 [#permalink] New post 21 Mar 2005, 18:47
OA is C.
Unfortunatley there is no short cut. You may approximate.
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 [#permalink] New post 22 Mar 2005, 08:32
yea i dont think there is any shorter way of doing this
C here too
  [#permalink] 22 Mar 2005, 08:32
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A boy multiplied 423 by a certain number and obtained 65589

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