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13 Jan 2016, 23:34
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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:
45%
(medium)
Question Stats:
65% (01:48) correct
35%
(01:34)
wrong
based on 1076
sessions
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Time
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Is rs a multiple of 25? (r and s are positive integers)
(1) r - s is a multiple of 5
(2) rs is a multiple of 5
(1) r - s is a multiple of 5
(2) rs is a multiple of 5
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14 Jan 2016, 00:26
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fattty
hi,
A good Q
again the Q stem first..
Is rs a multiple of 25..
1) both r and s are multiple of 5 or atleast one is multiple of 25
(1) r - s is a multiple of 5
this tells us two things..
A) r and s are multiple of 5, rs will be multiple of 25.. eg 35-20 etc
B) r and s are not multiples of 5, rs will not be multiple of 25 or for that matter even 5. For eg 37-27.
It is not possible that one is a multiple of 5 and other not, as in that case r-s will not be multiple of 5.....
insuff
(2) rs is a multiple of 5
both r and s can be multiples of 5.. or,
only one of them can be multiple of 5,..
insuff..
combined..
from 2 we know atleast one is muliple of 5, and from 1 we already know that either both are multiple of 5 or none..
therefore both r and s are multiple of 5..
suff
General Discussion
15 Jan 2016, 19:52
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Is rs a multiple of 25? (r and s are positive integers)
(1) r - s is a multiple of 5
(2) rs is a multiple of 5
In the original condition, there are 2 variables(r,s), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), rs=5's multiple becomes r=5's multiple. Then r-s=5's multiple becomes s=5's multiple. rs=5's multiple becomes multiple of rs=5*multiple of 5=multiple of 25, which is yes. Also, when it is multiple of s=5, r=5's multiple is derived from r-s=5's multiple. Then multiple of rs=5*multiple of 5=multiple of 25, which is yes and the answer is C. You cannot calculate them separately.
->For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
Is rs a multiple of 25? (r and s are positive integers)
(1) r - s is a multiple of 5
(2) rs is a multiple of 5
In the original condition, there are 2 variables(r,s), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), rs=5's multiple becomes r=5's multiple. Then r-s=5's multiple becomes s=5's multiple. rs=5's multiple becomes multiple of rs=5*multiple of 5=multiple of 25, which is yes. Also, when it is multiple of s=5, r=5's multiple is derived from r-s=5's multiple. Then multiple of rs=5*multiple of 5=multiple of 25, which is yes and the answer is C. You cannot calculate them separately.
->For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
