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15 Mar 2018, 05:12
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The numbers x and y are positive integers such that x < y. If 6√6 = x√y, then XY could equal which of the following ?
A. 36
B. 48
C. 54
D. 96
E. 108
Sent from my Lenovo K53a48 using GMAT Club Forum mobile app
A. 36
B. 48
C. 54
D. 96
E. 108
Sent from my Lenovo K53a48 using GMAT Club Forum mobile app
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15 Mar 2018, 05:36
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SonalSinha803
IMO E
\(6\sqrt{6}\) can be expressed as \(2*3\sqrt{6}\)
Since x < y, we need to move one of the prime factors of 6 into the radical sign.
Hence two possibilities =
\(6\sqrt{6} = 2\sqrt{54}\) ( where 3 become 9 inside the sq root sign and 9 times 6 is 54.
similarly,
\(6\sqrt{6} = 3\sqrt{24}\)
Only the first gives a possible answer among the choices and hence X = 2 and Y = 54.
XY = 108.
Option E.
Please give kudos if you liked the explanation...
15 Mar 2018, 06:02
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I agree that it is this
IMO E
66√66 can be expressed as 2∗36√2∗36
Since x < y, we need to move one of the prime factors of 6 into the radical sign.
Hence two possibilities =
66√=254−−√66=254 ( where 3 become 9 inside the sq root sign and 9 times 6 is 54.
similarly,
66√=324−−√66=324
Only the first gives a possible answer among the choices and hence X = 2 and Y = 54.
XY = 108.
Option E.
IMO E
66√66 can be expressed as 2∗36√2∗36
Since x < y, we need to move one of the prime factors of 6 into the radical sign.
Hence two possibilities =
66√=254−−√66=254 ( where 3 become 9 inside the sq root sign and 9 times 6 is 54.
similarly,
66√=324−−√66=324
Only the first gives a possible answer among the choices and hence X = 2 and Y = 54.
XY = 108.
Option E.
