There are x and y number of integers respectively in Set X and Set Y,

Question

There are x and y number of integers respectively in Set X and Set Y, where x<70. what is the value of positive integer y?

(1) 7x=8y
(2) There are exactly 0.4x common integers in two sets X and Y.

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vitaliyGMAT · Accepted Answer

Hi

1) 7x=8y
x is a multiple of 8 and y is a multiple of 7.
x = 8, 16, 24, 32 …., 64
y = 7, 14, 31, …, 56
If y=7 then x=8, if y=14 --> x = 16 and so on. Insufficient.

2) There are exactly 0.4x common integers in two sets X and Y.
That statement tells us that  \frac{2}{5}*x = integer . From that, x should be a multiple of 5. Insufficient.

1)&2) x is LCM (8, 5) = 40, 80 etc. and only one value to fit restriction x<70.
Hence x = 40 and y = 35. Sufficient.

C

Divyadisha · Answer

I would choose 'A' as the answer.

From statement 1, 7x=8y , i.e x = 8y/7. Since the set can not be in fraction 'y' should be factor of 7. Considering the given statement x<70, only one value for y is possible- 7. Sufficient
From statement 2, number of common integers can not be in fraction, and to make .4 an integer 'x' can hold many values- 5, 10, 15 and so on. Hence not sufficient.

Hope I have marked the right answer.

TheMechanic · Answer

I would go for A as well. But I have a doubt, couldn't there be a possibility that both the sets contain 0 numbers and in which case the Answer could be E. 
Let me know if there is anything else which hints or takes out the later possibility?

Nitish7 · Answer

I guess the answer will be C

Statement 1: 7x=8y which means x=8y/7 and question says x<70 we can say 8y/7 < 70 which means y< 490/8 hence Insufficient.
Statement 2: 0.4x common integers in two sets X and Y and as x<70 x can be 5,10,15,20,25....65 but no information about Y hence insufficient.

Combining both we can say X is a multiple of 5 and y will 7x/8 therefore y will be integer only when x is 40 80 and in the given question x<70 so when x=40 y =35.

Nitish7 · Answer

I guess the answer will be C

Statement 1: 7x=8y which means x=8y/7 and question says x<70 we can say 8y/7 < 70 which means y< 490/8 hence Insufficient.
Statement 2: 0.4x common integers in two sets X and Y and as x<70 x can be 5,10,15,20,25....65 but no information about Y hence insufficient.

Combining both we can say X is a multiple of 5 and y will 7x/8 therefore y will be integer only when x is 40 80 and in the given question x<70 so when x=40 y =35.

chetan2u · Answer

Explanation:-
 
Y is given as POSITIVE integer..
So both x and y are >0..

Let's see the statements

1) 7x=8y ..
This tells us that x is MULTIPLE of 8 and y is MULTIPLE of 7..
X can be 8,16,24,32,40,48,56,64..
Hence insufficient

2) 0.4x integers are common.. 
Since 0.4x has to be an integer..
X has to be multiple of 5
So 5,10..65 possible 
Hence insufficient

Combined 
X is MULTIPLE of 5 and 8, so minimum value is 5*8=40..
Next value 80>70..
So x =40
Sufficient

C

AnirudhaS · Answer

(1) x<70, and 7x=8y;
so the only possible values of x = 8,16,24,32,40,...
and corresponding values of y = 7,14,21,28,35...
Lots of possible solutions, therefore insufficient

(2) x<70 and common integers=0.4x=2x/5
So, for x=5,10,15,20,30,40,.. corresponding values of common integers = 2,4,6,8,10,12...
Again lots of possible solutions, therefore insufficient

(1)+(2)
x=40, (not 80 as x<70)
So y = 35
Sufficient

Answer:  C

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There are x and y number of integers respectively in Set X and Set Y,

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