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# If xy/5 is an integer, is x divisible by 5?

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Math Expert
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If xy/5 is an integer, is x divisible by 5?  [#permalink]

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25 Dec 2016, 02:39
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35% (medium)

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66% (01:09) correct 34% (01:04) wrong based on 113 sessions

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If xy/5 is an integer, is x divisible by 5?

(1) y is divisible by 3.
(2) y is divisible by 10.

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Re: If xy/5 is an integer, is x divisible by 5?  [#permalink]

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25 Dec 2016, 04:22
Let's understand that rule for divisibility of 0 here before start answering the question. 0 is divisible by any number, however, we can not divide any number with 0. Another rule, even number which is divisible by 5 will also be divisible by 10.
Option 1:
If xy/5 is an integer, is x divisible by 3?
X value can be anything 3,6 and 9.... To divide the product xy by 5, y must have to be divided by 5. Sufficient.
Option 2:
y is divisible by 10. X can be any value 2,3,4,5.... Some of them divide by 5 and some of them not... Not sufficient.

Answer is A.... I hope I am right...
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Re: If xy/5 is an integer, is x divisible by 5?  [#permalink]

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25 Dec 2016, 04:31
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Bunuel wrote:
If xy/5 is an integer, is x divisible by 5?

(1) y is divisible by 3.
(2) y is divisible by 10.

(1) y is divisible by 3.

Say $$y=15$$. $$\frac{x*15}{5} = 3*x$$ This does not give us any information about divisibility of x by 5. (Had it been said "y is diisible only by 3"). Insufficient.

(2) y is divisible by 10

$$y=10a$$

$$\frac{x*10a}{5} = x*2a$$ Again, no info about divisibility of x by 5. Insufficient

(1) & (2) togather. Combination of two won't give us addiional infomation.

$$\frac{x*30a}{5} = x*6a$$ Insufficient.

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If xy/5 is an integer, is x divisible by 5?  [#permalink]

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03 Jan 2018, 00:46
Case 1 ->
y = 30
x = 1

NO, x is not divisible by 5

Case 2 -->
y=30
x=5
YES, x is divisible by 5

Use the above test case to reject A,B,C

and then off-course -> Smash that E

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Re: If xy/5 is an integer, is x divisible by 5?  [#permalink]

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03 Jan 2018, 03:48
Bunuel wrote:
If xy/5 is an integer, is x divisible by 5?

(1) y is divisible by 3.
(2) y is divisible by 10.

A few ways to solve this:

Using logic:
Since we know xy is divisible by 5, The only way to know for sure whether x is divisible by 5 or not is either information about x, or knowing that y definitely isn't divisible by 5 (in which case x definitely will be). Neither statement gives us any of these: (1) doesn't rule out y being divisible by 5 as well, and (2) tells us y is - which tells us nothing about x. Combining them doesn't help, for the same reason that (2) is insufficient. Not enough data.

Using the alternative method of using numbers:
(1) say y=3 > 3x/5 > x must be divisible by 5. But say y equals 30 > 30x/5 > x could equal 1 - insufficient!
2) As discussed, in 30x/5 we can't know whether x is or isn't divisible by 5. Insufficient!
Combined: once again, 30x/5 fits the criteria and can go both ways. Insufficient!
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Re: If xy/5 is an integer, is x divisible by 5?  [#permalink]

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07 Jan 2018, 13:54
Bunuel wrote:
If xy/5 is an integer, is x divisible by 5?

(1) y is divisible by 3.
(2) y is divisible by 10.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations,C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):

x = 5, y = 30 : Yes
x = 1, y = 30 : No

Since the answer is not unique, both conditions together are not sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: If xy/5 is an integer, is x divisible by 5?   [#permalink] 07 Jan 2018, 13:54
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