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05 Feb 2024, 02:30
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Difficulty:
65%
(hard)
Question Stats:
58% (02:04) correct
42%
(02:10)
wrong
based on 194
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If x = 343y, where y is a positive integer, and x/196 is a terminating decimal, what is the smallest possible value of y?
A. 1
B. 3
C. 5
D. 7
E. 9
A. 1
B. 3
C. 5
D. 7
E. 9
05 Feb 2024, 03:10
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343=7*7*7
196=2*2*7*7
Hence as per given conditions
343y/196= 7*7*7*y/2*2*7*7
Since we have to find the smallest value for y, lets start with substituting from options ,so let y=1
therefore we have
7*7*7*1/2*2*7*7 we are left with 7/4 which is a terminating decimal evaluating to 1.75 and thus sufficient
196=2*2*7*7
Hence as per given conditions
343y/196= 7*7*7*y/2*2*7*7
Since we have to find the smallest value for y, lets start with substituting from options ,so let y=1
therefore we have
7*7*7*1/2*2*7*7 we are left with 7/4 which is a terminating decimal evaluating to 1.75 and thus sufficient
05 Feb 2024, 13:34
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Correct option should be A
We can write x = 343y as x = \(7^{3}\)y and 196 is \(14^{2}\) which is \(7^{2}\)*4
So, if we divide x by 196 we get \(\frac{7y}{4}\) which again equals 1.75y.
Any number when divided by 4 gives us a terminating decimal. Hence, if this is always true that 1.75y is always a terminating decinmal, smallest value of y would be 1.
Hence, correct option is A
We can write x = 343y as x = \(7^{3}\)y and 196 is \(14^{2}\) which is \(7^{2}\)*4
So, if we divide x by 196 we get \(\frac{7y}{4}\) which again equals 1.75y.
Any number when divided by 4 gives us a terminating decimal. Hence, if this is always true that 1.75y is always a terminating decinmal, smallest value of y would be 1.
Hence, correct option is A
