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03 Jun 2020, 23:55
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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)!
Difficulty:
15%
(low)
Question Stats:
79% (01:04) correct
21%
(01:11)
wrong
based on 122
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of rectangle ABCD?
(1) The length of side AB is 2 units more than the length of side BC.
(2) The length of the diagonal AC is 10 units.
(1) The length of side AB is 2 units more than the length of side BC.
(2) The length of the diagonal AC is 10 units.
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
yashikaaggarwal
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04 Jun 2020, 00:35
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IMO C
Statement 1 : l=b+2
Area = l*b = (b+2)*b =? (Insufficient)
Statement 2: 10^2=l^2+b^2
100=l^2+b^2 =? (Insufficient)
1&2 together.
100 = l^2+b^2
100 = (b+2)^2+b^2
100 = b^2+4+4b+b^2.
96 = 2b^2+4b
48 = b^2+2b => 48 = b(b+2)
6*8 = b(l)
Length = 8 and breadth= 6.
Area of rectangle = 6*8= 48 (sufficient)
Posted from my mobile device
Statement 1 : l=b+2
Area = l*b = (b+2)*b =? (Insufficient)
Statement 2: 10^2=l^2+b^2
100=l^2+b^2 =? (Insufficient)
1&2 together.
100 = l^2+b^2
100 = (b+2)^2+b^2
100 = b^2+4+4b+b^2.
96 = 2b^2+4b
48 = b^2+2b => 48 = b(b+2)
6*8 = b(l)
Length = 8 and breadth= 6.
Area of rectangle = 6*8= 48 (sufficient)
Posted from my mobile device
04 Jun 2020, 00:42
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Bunuel
Solution
Step 1: Analyse Question Stem
- • We need to find the area of rectangle ABCD.
- o Area of a rectangle \(= length * breadth = AB*BC\)
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The length of side AB is 2 units more than the length of side BC.
- • \(AB = BC + 2\)
• So, \(Area = AB*BC = (BC+2)*BC\)
• However, we don’t know BC so we cannot find the area.
Statement 2: The length of the diagonal AC is 10 units.
- • It means, \(AB^2 + BC^2 = 10^2\)
• But we cannot find AB and BC from here and hence we cannot find AB*BC
Step 3: Analyse Statements by combining.
From statement 1: \(AB – BC = 2\)
From statement 2: \(AB^2 + BC^2 =10^2\)
On combining the two statements, we can write,
- • \((AB – BC)^2 = 4 ⟹ AB^2 + BC^2 – 2AB*BC = 4 ⟹10^2 - 2AB*BC = 4\)
Thus, the correct answer is Option C.
