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Is r*s a multiple of 25? (r and s are positive integers)

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Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 13 Jan 2016, 23:34
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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
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Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 14 Jan 2016, 00:26
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2
fattty wrote:
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


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 25or even .. eg 37-27 etc
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
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Re: Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 15 Jan 2016, 19:52
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.
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Re: Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 15 Jan 2016, 19:52
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.
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Re: Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 23 Jan 2016, 19:44
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Hi fattty,

This question can be solved by TESTing VALUES and Number Properties.

We're told that R and S are POSITIVE INTEGERS. We're asked if (R)(S) is a multiple of 25? This is a YES/NO question.

1) R - S is a multiple of 5

This Fact tells us that EITHER both variables are multiples of 5 OR both variables are NOT multiples of 5.

IF....
R = 6
S = 1
(6)(1) = 6 and the answer to the question is NO.

IF....
R = 10
S = 5
(10)(5) = 50 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

(2) (R)(S) is a multiple of 5

This Fact tells us that AT LEAST ONE of the two variables is a multiple of 5.

IF....
R = 5
S = 4
(5)(4) = 20 and the answer to the question is NO.

IF....
R = 10
S = 5
(10)(5) = 50 and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know that...
R - S is a multiple of 5
(R)(S) is a multiple of 5

From Fact 2, we know that AT LEAST one of the two variables is a multiple of 5. From the Fact 1, we know that IF one of the variables is a multiple of 5, then the other one MUST be also. Combining these two Facts proves that BOTH variables are multiples of 5; when you multiply two multiples of 5 together, you end up with a larger number that is a multiple of 25. Thus, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

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Re: Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 19 May 2016, 19:10
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1. r-s = multiple of 5.
we can have 2 multiples of 5, then rs will be divisible by 25
or we can have r=7 and s=2. in this case - no.

2. rs=multiple of 5.
r=1, s=5 -> not multiple of 25.
r=5, s=5 -> multiple of 25
2 alone not sufficient.

1+2
rs multiple of 5
r-s is a multiple of 5
it must be true that both r and s are multiple of 5.

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Re: Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 02 Oct 2016, 00:30
Still not clear. Can someone please elaborate this for me.

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Re: Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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New post 02 Oct 2016, 01:08
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AmritaSarkar89 wrote:
Still not clear. Can someone please elaborate this for me.

TIA


Let me try helping you out.

We are asked if rs = 25 * k , where k is a positive integer. ( r and s both are given as positive integers)

Now,

Statement 1 : r - s = 5k' ; This is possible when r= 10 and s = 5, in that case rs will be a multiple of 5. But it is possible when r = 7 and s =2, in that case rs will not be a multiple of 5. Hence, insufficient.

Statement 2 : rs is a multiple of 5. It may happen rs = 10 ( Not a multiple of 25) or rs = 25 ( A multiple of 5) Hence, insufficient.

Combining, for rs to be a multiple of 5, we need to have atleast one of r or s a multiple of 5. And we have seen in statement 1 that when one is a multiple of 5 the other should also be a multiple of 5 to get the difference a multiple of 5. Hence, Sufficient.
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Re: Is r*s a multiple of 25? (r and s are positive integers)  [#permalink]

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