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X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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Question Stats: 70% (01:06) correct 30% (01:10) wrong based on 158 sessions

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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.

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X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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4
1
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.

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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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Quote:
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.

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.

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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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Bunuel wrote:
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.

Area= 1/2*b*h

(1) X is a prime number.
X can be 2, 3 or any other prime number. We have no information about Y. Not sufficient.

(2) Y is an odd integer.
No information about X . Not sufficient.

Combining both statement is not sufficient.

if X is 2 and Y is any odd integer. Then 1/2*b*h is an integer.

If X is 3 (or any prime number other than 2) and Y is any odd integer. Then 1/2*x*y is not an integer.

E is the answer
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Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl  [#permalink]

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If x, y are the legs then x*y*(1/2) = Area. Test some numbers:

1) x = prime number
x=2 or 3,
2*y*(1/2) or 3*y*(1/2) or ... no info about y, insufficient

2) y = odd integer
y=3, 3*x*(1/2) ? ... no info about x, insufficient

1+2)
take the examples from above
when x = 2, we get 2*3/2 = 3, Yes
x = 3, we get 3*3/2 = 4.5, no
Both together are insufficient, E Re: X and Y are the lengths of two non-hypotenuse sides of a right triangl   [#permalink] 27 Feb 2019, 17:08
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