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by sleepyjoe » Sun Jan 10, 2010 11:11 am
Please help.

Is the positive square root of a an integer?

(1) a = x, x is integer
(2) a = y4, y is integer

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient
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Source: — Data Sufficiency |
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by m-sand » Sun Jan 10, 2010 1:25 pm
sleepyjoe wrote:Please help.

Is the positive square root of a an integer?

(1) a = x, x is integer
(2) a = y4, y is integer

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient
IMO B
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by Inspired » Thu Jan 14, 2010 11:50 am
IMO E

Option 2: a=4y

if y = 2, then a= 8. square root of 8 is not an integer.
if y = 4, then a= 16. sqare root of a is 4 which is integer.

so, option 2 is not sufficient. Option 1 is also not sufficient.
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by Osirus@VeritasPrep » Thu Jan 14, 2010 12:35 pm
Inspired wrote:IMO E

Option 2: a=4y

if y = 2, then a= 8. square root of 8 is not an integer.
if y = 4, then a= 16. sqare root of a is 4 which is integer.

so, option 2 is not sufficient. Option 1 is also not sufficient.
Nah, if y = 2 then y^4 = 16.

2^3 = 8.

If y = 4, then a = 256 which is 16 squared

B is sufficient
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by akuma » Fri Jan 15, 2010 3:29 pm
sleepyjoe wrote:Please help.

Is the positive square root of a an integer?

(1) a = x, x is integer
(2) a = y4, y is integer

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient
(2)
no plug n chug needed if you know the algebra.

sqrt(y^4) = y^2
because (y^4)^(1/2) = y^2

now ask yourself, if y is an integer, wouldn't y^2 also be an integer? yes indeed.
in fact, if y is an integer then y^n is always an integer under these constraints (n is integer and n >= 0)
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