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06 Sep 2019, 10:55
Kudos
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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:
35%
(medium)
Question Stats:
65% (01:27) correct
35%
(01:16)
wrong
based on 124
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of \(x^3 + y^3\) ?
(1) \(x + y = 7\)
(2) \(x^2 + y^2 = 25\)
(1) \(x + y = 7\)
(2) \(x^2 + y^2 = 25\)
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
07 Sep 2019, 01:42
Kudos
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What is the value of \(x^3+y^3\)?
\(x^3+y^3\) = (x+y)(\(x^2+y^2\)-2xy)
STATEMENT-(1) x+y=7
if x = 3, y=4 --- then \(x^3+y^3\) = 1728
if x = 2, y =5 ----then \(x^3+y^3\) = 1000
we cant get the definite value
hence INSUFFICIENT
STATEMENT-(2) \(x^2+y^2\)=25
if x = 3 y = 4 then \(x^3+y^3\) = 1728
if x = -3 y =4 then \(x^3+y^3\) = 37
we cant get definite value
hence, INSUFFICIENT
combining both STATEMENT-(1)&STATEMENT-(2)
we know x+y =7 and \(x^2+y^2\) = 25
we know \(x^3+y^3\) = (x+y)(\(x^2+y^2\)-2xy)
we need to find the value of xy
\((x+y)^2\)-2xy = \(x^2+y^2\)
49-2xy = 25
xy = 12
value of \(x^3+y^3\) = (x+y)(\(x^2+y^2\)-2xy) = 7*(25-2*12) = 7
SUFFICIENT
C is the correct answer
\(x^3+y^3\) = (x+y)(\(x^2+y^2\)-2xy)
STATEMENT-(1) x+y=7
if x = 3, y=4 --- then \(x^3+y^3\) = 1728
if x = 2, y =5 ----then \(x^3+y^3\) = 1000
we cant get the definite value
hence INSUFFICIENT
STATEMENT-(2) \(x^2+y^2\)=25
if x = 3 y = 4 then \(x^3+y^3\) = 1728
if x = -3 y =4 then \(x^3+y^3\) = 37
we cant get definite value
hence, INSUFFICIENT
combining both STATEMENT-(1)&STATEMENT-(2)
we know x+y =7 and \(x^2+y^2\) = 25
we know \(x^3+y^3\) = (x+y)(\(x^2+y^2\)-2xy)
we need to find the value of xy
\((x+y)^2\)-2xy = \(x^2+y^2\)
49-2xy = 25
xy = 12
value of \(x^3+y^3\) = (x+y)(\(x^2+y^2\)-2xy) = 7*(25-2*12) = 7
SUFFICIENT
C is the correct answer
05 Sep 2020, 04:26
Kudos
Bookmarks
We have to find \(x^3 + y^3\)
\(x^3 + y^3 = (x \space + \space y)^3 - 3xy(x \space + \space y)\)
If we get the value of x+ y and xy, we have sufficient data to get the answer
Statement 1: x + y = 7
With this information, we cannot calculate the value of \(x^3 + y^3\), as we do not have the value of xy.
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E
Statement 2: \(x^2 + y^2 = 25\)
We know that \(x^2 + y^2 = (x + y)^2 - 4xy\)
We do not get any information about x + y or xy from the above information.
Therefore Statement 2 Alone is Insufficient. Answer options could be C or E
Combining Both Statements:
We have x + y = 7 and \(x^2 + y^2 = 25\)
Since \(x^2 + y^2 = (x + y)^2 - 4xy\), we can get the value of xy.
Therefore Both Statements together are Sufficient.
Option C
Arun Kumar
\(x^3 + y^3 = (x \space + \space y)^3 - 3xy(x \space + \space y)\)
If we get the value of x+ y and xy, we have sufficient data to get the answer
Statement 1: x + y = 7
With this information, we cannot calculate the value of \(x^3 + y^3\), as we do not have the value of xy.
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E
Statement 2: \(x^2 + y^2 = 25\)
We know that \(x^2 + y^2 = (x + y)^2 - 4xy\)
We do not get any information about x + y or xy from the above information.
Therefore Statement 2 Alone is Insufficient. Answer options could be C or E
Combining Both Statements:
We have x + y = 7 and \(x^2 + y^2 = 25\)
Since \(x^2 + y^2 = (x + y)^2 - 4xy\), we can get the value of xy.
Therefore Both Statements together are Sufficient.
Option C
Arun Kumar
