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19 Jul 2018, 11:22
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D
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What is the difference between the number of chocolates with Alice and Bob, if each of them has at least one chocolate and Alice has 25% more chocolates than Bob?
(1) Together Alice and Bob have less than 30 but more than 20 chocolates.
(2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
(1) Together Alice and Bob have less than 30 but more than 20 chocolates.
(2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
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
19 Jul 2018, 19:32
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What is the difference between the number of chocolates with Alice and Bob, if each of them has at least one chocolate and Alice has 25% more chocolates than Bob?
A=1.25B=5B/4
(1) Together Alice and Bob have less than 30 but more than 20 chocolates.
So 20<A+B<30........20<B+5B/4<30........20<9B/4<30.........
Since B is an integer, Only possibility of 9B/4 is 27....B=27*4/9=12
A = 1.25*12=15
Difference=15-12=3
Sufficient
(2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
Straight way a+B=27
\(a^2-b^2=27(a-b)..................(a-b)(a+b)=27(a-b).....................(a+b)=27\)
We know total is 9B/4=27.....B=12
Sufficient
D
A=1.25B=5B/4
(1) Together Alice and Bob have less than 30 but more than 20 chocolates.
So 20<A+B<30........20<B+5B/4<30........20<9B/4<30.........
Since B is an integer, Only possibility of 9B/4 is 27....B=27*4/9=12
A = 1.25*12=15
Difference=15-12=3
Sufficient
(2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
Straight way a+B=27
\(a^2-b^2=27(a-b)..................(a-b)(a+b)=27(a-b).....................(a+b)=27\)
We know total is 9B/4=27.....B=12
Sufficient
D
Ashu9876
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26 Mar 2023, 23:35
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Sol. Let’s assume,
Bob – x chocolates
Alice – 5x/4 chocolates (25% more than Bob)
Difference between the number of chocolates they have = x/4
St. (1) Together Alice and Bob have less than 30 but more than 20 chocolates.
20< 5x/4+x<30
20< 9x/4<30
80< 9x<120
Possible values for x = 9, 10, 11, 12
Since value of x must be divisible by 4 as x/4 is integer, only 12 satisfy the condition and hence difference between number of chocolates they have = 3
Statement (1) is sufficient. BCE eliminated
St. (2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
(5x/4)^2-(x)^2=27 (x/4)
25x/16-x=27
Above equations can be solved and hence sufficient to find the value of x.
Hence statement (2) is also sufficient. “A” eliminated and correct answer is D.
Bob – x chocolates
Alice – 5x/4 chocolates (25% more than Bob)
Difference between the number of chocolates they have = x/4
St. (1) Together Alice and Bob have less than 30 but more than 20 chocolates.
20< 5x/4+x<30
20< 9x/4<30
80< 9x<120
Possible values for x = 9, 10, 11, 12
Since value of x must be divisible by 4 as x/4 is integer, only 12 satisfy the condition and hence difference between number of chocolates they have = 3
Statement (1) is sufficient. BCE eliminated
St. (2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
(5x/4)^2-(x)^2=27 (x/4)
25x/16-x=27
Above equations can be solved and hence sufficient to find the value of x.
Hence statement (2) is also sufficient. “A” eliminated and correct answer is D.
