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18 Sep 2018, 22:04
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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:
95%
(hard)
Question Stats:
32% (02:33) correct
68%
(01:51)
wrong
based on 88
sessions
History
Date
Time
Result
Not Attempted Yet
In the rectangle shown, if d = 10, what is x?
(1) The perimeter of the rectangle is 28.
(2) The area of the rectangle is 48.
Attachment:
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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18 Sep 2018, 22:24
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Bunuel
St1:- Perimeter of the rectangle=2(x+w)=28 or, x+w=14.....(1)
We have two symmetrical right angled triangles about the diagonal of the rectangle.
So , \(x^2+w^2=10^2\)---(2)
From (1) & (2), we have x=6 or 8.
No unique value of x.
Therefore insufficient.
St2:- Area of rectangle =x*w=48---(3)
From (1)&(3), we have
\((x+w)^2=x^2+w^2+2xw\)=100+96=196
Or, x+w=14.....(4)
From (2) & (4), we have x=6 or 8
No unique value of x.
Insufficient.
Combined, no new information to restrict the value of x.
Hence insufficient.
Ans. (E)
19 Sep 2018, 02:29
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Solution
Given:
- • The diagonal of a rectangle, d = 10
• x, w are the length and breadth of the rectangle
To find:
- • The value of x
Approach and Working:
- • We can write, \(d^2 = w^2 + x^2\)
• Implies, \(x^2 + w^2 = 10^2 = 100\) …………. (1)
With this understanding, let’s analyse the given statements
Analysing Statement 1
“Perimeter of the rectangle = 28”
- • Implies, 2(x + w) = 28
- o x + w = 14 => w = 14 – x ……. (2)
- o \(x^2 + (14 - x)^2 = 100\)
o \(2x^2 – 28x + 196 = 100\)
o \(x^2 – 14x + 48 = 0\)
o By factorization, we get, (x – 6) * (x – 8) =0
Therefore, Statement 1 is NOT sufficient to arrive at a unique answer
Analysing Statement 2
“Area of the rectangle = 48”
- • Implies, x*w = 48
- o \(w = \frac{48}{x}\) ……... (3)
- o \(x^2 + (\frac{48}{x})^2 = 100\)
o \((x + \frac{48}{x})^2 – 2*x*\frac{48}{x} = 100\)
o \((x + \frac{48}{x})^2 = 196\)
o Implies, \((x + \frac{48}{x}) = 14\)
o \(x^2 - 14x + 48 = 0\)
Therefore, Statement 2 is NOT sufficient to arrive at a unique answer
Combining Both Statements
- • From Statement 1, we got, x = 6 or 8
• From Statement 2, we got, x = 6 or 8
• Combining both, we get, x = 6 or 8
Therefore, both statements TOGETHER are NOT sufficient to arrive at a unique answer
Hence, the correct answer is option E.
Answer: E
19 Sep 2018, 02:56
Kudos
Bookmarks
Hi,
Its a 30-sec question, if we know the common pythogorean triplets asked in GMAT
Question: What is x ?
Given, it is a rectangle, so each vertex angle is 90 degree and also it is given that diagonal d = 10.
Since the questions is a Value DS question, we no need to do the algebra here, we just need to know the common pythogorean triplets.
6 – 8 – 10 is a very common pythogorean triplet, similarly 3 – 4 -5 , 12 – 5 -13 are common pythogorean triplets asked in GMAT.
So here,
x can be 6 and w can be 8 or
x can be 8 and w can be 6.
So there are two values of x.
Statement I is insufficient:
The perimeter of the rectangle is 28.
i.e., 2*(x+w) = 28
x+w = 14
Same reasoning,
x can be 6 and w can be 8 or
x can be 8 and w can be 6.
So not sufficient.
Statement II is insufficient:
The area of the rectangle is 48
i.e., x * w = 48
Same reasoning here too,
x can be 6 and w can be 8 or
x can be 8 and w can be 6.
Together also, same thing x can be 6 or 8. So not sufficient.
So the answer is E.
Its a 30-sec question, if we know the common pythogorean triplets asked in GMAT
Question: What is x ?
Given, it is a rectangle, so each vertex angle is 90 degree and also it is given that diagonal d = 10.
Since the questions is a Value DS question, we no need to do the algebra here, we just need to know the common pythogorean triplets.
6 – 8 – 10 is a very common pythogorean triplet, similarly 3 – 4 -5 , 12 – 5 -13 are common pythogorean triplets asked in GMAT.
So here,
x can be 6 and w can be 8 or
x can be 8 and w can be 6.
So there are two values of x.
Statement I is insufficient:
The perimeter of the rectangle is 28.
i.e., 2*(x+w) = 28
x+w = 14
Same reasoning,
x can be 6 and w can be 8 or
x can be 8 and w can be 6.
So not sufficient.
Statement II is insufficient:
The area of the rectangle is 48
i.e., x * w = 48
Same reasoning here too,
x can be 6 and w can be 8 or
x can be 8 and w can be 6.
Together also, same thing x can be 6 or 8. So not sufficient.
So the answer is E.
