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23 Jun 2016, 02:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
71% (01:06) correct
29%
(01:20)
wrong
based on 295
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X and Y are the lengths of two non-hypotenuse sides of a right triangle, is the area of the triangle an integer?
(1) X is a prime number.
(2) Y is an odd integer.
(1) X is a prime number.
(2) Y is an odd integer.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
23 Jun 2016, 02:26
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Area of a right angle triangle is 1/2*non-hypotenuse side 1*non-hypotenuse side 2
so, we need both the sides information to reach the answer.
Therefore Statement 1 and 2 alone are not helpful. A,B,D are out.
Combining Statement 1 and 2, we are sure that both non-hypotenuse sides are integers. But, we have to see that one of them has to be even as the formula of area of a triangle has a 1/2 multiplied by two non-hypotenuse side. If X=2 then area will be integer otherwise for all other prime numbers it will be odd and the area will be non-integer.
Hence, the answer will be E.
P.S. Don't forget to give Kudos.
so, we need both the sides information to reach the answer.
Therefore Statement 1 and 2 alone are not helpful. A,B,D are out.
Combining Statement 1 and 2, we are sure that both non-hypotenuse sides are integers. But, we have to see that one of them has to be even as the formula of area of a triangle has a 1/2 multiplied by two non-hypotenuse side. If X=2 then area will be integer otherwise for all other prime numbers it will be odd and the area will be non-integer.
Hence, the answer will be E.
P.S. Don't forget to give Kudos.
23 Jun 2016, 03:11
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Quote:
Area = 1/2(LxB) = 1/2 (X x Y)
Statement 1) X is a prime no. i.e 2,3,5,7,11 and so on. Except for 2 all prime no.s are odd.
If X=2 => Area=1/2(2xY) = Area = Y ... We dont know whether Y is an integer or not - Insufficient.
Statement 2) Y is an odd Interger ... We dont know whether X is an or not - Insufficient.
Statement 1) & 2) combined
Area = (Prime no. x Odd no.)/2
If X = 2 => Area = (2 x Odd no.)/2 => Area = Odd Integer ... True
If X = 3,5,7 and so on for prime no. => Area = (Odd x Odd)/2 = Even/2 .. Not true
Choice E) is the correct ans. Statement 1) & 2) combined are not sufficient to ans the question.
Good luck
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