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555-605 Level|   Geometry|      
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Bunuel
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A rectangle has sides x and y and diagonal z. What is the perimeter of 02 Jun 2018, 13:26
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

75% (01:35) correct 25% (01:34) wrong based on 127 sessions

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A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle?

(1) x - y = 7.
(2) z = 13.
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C
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Naren7
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A rectangle has sides x and y and diagonal z. What is the perimeter of 02 Jun 2018, 13:40
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Bunuel
A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle?

(1) x - y = 7.
(2) z = 13.
Answer?

Sent from my T1 7.0 using GMAT Club Forum mobile app
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A rectangle has sides x and y and diagonal z. What is the perimeter of 02 Jun 2018, 13:43
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Naren7
Bunuel
A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle?

(1) x - y = 7.
(2) z = 13.
Answer?

Sent from my T1 7.0 using GMAT Club Forum mobile app

The OA will be automatically revealed on Friday 8th of June 2018 01:26:09 PM Pacific Time Zone

Meanwhile you can attempt it and post a solution.
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A rectangle has sides x and y and diagonal z. What is the perimeter of 02 Jun 2018, 14:55
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Ans--> C

given - sides of rectangle are x and y. Diagonal is Z.

from Pythagoras theorem: x^2 + y^2 = z^2
perimeter of rectangle P = 2(x + y). So we need to find the value of P

1) X-Y = 7 insufficient because there will be infinite numbers of X and Y satisfying this equation.

2) Z= 13 insufficient because there will be infinite number of x and y for which x^2 + y^2 = 13^2. Remember it is not mentioned that x and y are integers

1 + 2
y = x-7 and z = 13
x^2 + (x-7)^2 = 13^2
x^2 + x^2 + 49 - 14x = 169
x^2 - 7x - 60 = 0
x = 12 , -5
x can not be negative hence x = 12
y = 5
P = 34 sufficient
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A rectangle has sides x and y and diagonal z. What is the perimeter of 02 Jun 2018, 17:30
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Bunuel
A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle?

(1) x - y = 7.
(2) z = 13.

From statement 1, we can have many combinations of both x and y. So we can't derive the exact value of 2(x+y). It's insufficient.

From statement 2, we can't derive the values of x and y. Though we know x^2 + y^2 = z^2, we can't derive (x+y) without knowing the individual values of both x and y. And we haven't given that both x & y are integers.

Combining both statements, we can derive individual values of x & y as x^2 + y^2 = 13^2 and y=x+7. Here in this equation, we have only one variable and we can easily find the value of x. Then y = x+7.

So, C is the answer.
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A rectangle has sides x and y and diagonal z. What is the perimeter of 21 Jun 2018, 07:03
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A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle?

(1) x - y = 7.
(2) z = 13.

1) not sufficient . we dont know individual value of x and y
2) x^2+Y^2=169. not sufficient

1 + 2

x^2+Y^2-2xy=169-2xy
(x-y)^2=169-2xy
2xy=169-49=120. xy=60

now, x^2+Y^2+2xy=169+2xy=169+120
we can find (x+y)^2 from here and therefore x+y as well.
now, we have x+y and x-y so we can find individual x and y. and therefore the permiter SUFFICIENT
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A rectangle has sides x and y and diagonal z. What is the perimeter of 19 Apr 2023, 04:39
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Bunuel KarishmaB

In a right angled triangle with a hypotenuse that fits one of the the Pythagorean triples, can we not presume that the legs will also fit the triple?

Because x and y form 90 degrees and the hypotenuse z = 13, I inferred that the legs were 5 and 12. Is this incorrect?
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A rectangle has sides x and y and diagonal z. What is the perimeter of 19 Apr 2023, 11:57
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achloes
A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle?

(1) x - y = 7.
(2) z = 13.

Bunuel KarishmaB

In a right angled triangle with a hypotenuse that fits one of the the Pythagorean triples, can we not presume that the legs will also fit the triple?

Because x and y form 90 degrees and the hypotenuse z = 13, I inferred that the legs were 5 and 12. Is this incorrect?

No, we cannot conclude that x = 5 and y = 12, or vice versa, unless we are given that the legs have integer lengths. In other words, the equation x^2 + y^2 = 13^2 does not necessarily imply that x = 5 and y = 12. If it were specified that x and y are integers, then indeed, the only solution would be either x = 5 and y = 12, or vice versa. However, without this constraint, the equation x^2 + y^2 = 13^2 would have infinitely many solutions for x and y. For example, if x = 1, then y = √168; if x = 3.2, then y = √(13^2 - 3.2^2); ...

Hope it helps.
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A rectangle has sides x and y and diagonal z. What is the perimeter of 19 Apr 2023, 22:17
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Dont really need to calculate.

From (i), I know x - y = 7
I need to find out perimeter - Clearly this information alone cannot help as there are infinite number of possibilities

From (ii), I know diagonal = 13
I need to find perimeter. This alone cannot help

Combining i and ii

if I know x - y, and I know what is x^2 + y^2 (diagonal, 13), then I can find out what is xy

and if I know xy, then I can find x + y by the formula x + y = SQRT((x - y)^2 + 4xy).

If I know what's x + y, doubling that would give me perimeter. So i and ii together can give me the correct answer
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