If x and y are positive integers and y

Question

If x and y are positive integers and y<5x, the remainder is z when 5x is divided by y. What is the value of z?

(1) When y+1 is divided by 5, the remainder is 1.
(2) When y+1 is divided by 4, the remainder is 2.

KrishnakumarKA1 · Answer

Hi,

Answer has to be “E”.

There is not much information about “x”

Given:

x, y > 0 and integers

y < 5x
 
z = Rem When 5x is divided y.

Question: Value of “z”?

Statement I is insufficient:

When y+1 is divided by 5, the remainder is 1

i.e., y+1 could be 1,6, 11, 16, …..

So “y” values could be 0,5,10,15,20,25…(“y” can’t be zero as it is given y is positive).

Given y < 5x

Let’s say,

x = 7 and y = 5

then “y” is less than 5 < 35

then z = 0

But if

x = 7 and y = 15

then “y” is still less than 15 < 35

But we get different z, i.e., z = 5

So different values of “z”. Not sufficient.

Statement II is insufficient.

When y+1 is divided by 4, the remainder is 2.

Similar to statement I,

y+1 could be 2,6, 10, 14,18 …..

So “y” values could be 1,5,9,13,17,21,25…(“y” can’t be zero as it is given y is positive).

Given y < 5x

Let’s say,

x = 7 and y = 5

then “y” is less than 5 < 35

then z = 0

But if

x = 7 and y = 9

“y” is still less than 9 < 35

But z = 8

So different values of “z”. Not sufficient.

Together still insufficient:

Values could be still,

x = 7 and y = 5

then “y” is less than 5 < 35

then z = 0

OR

x = 7 and y = 5

then “y” is less than 5 < 35

then z = 0

x = 7 and y = 25

then “y” is less than 25 < 35

then z = 10

Still we are getting different values of “z”.

Together still not sufficient.

So the answer is E.

Hope this helps

Italiandrummer97 · Answer

We need to know:
A) The value of both y and 5x
Or
B)the value of the remainder.

No calculations needed, as in most DS questions.

POE:
1)No significant information given. Insufficient. Eliminate A and D.
2)Same as in 1. Insufficient. Eliminate B
1+2) We could be able to calculate the value of y, but we'd still be missing the value of 5x. Insufficient. Eliminate C.

Correct answer: E

Posted from my mobile device

user9123 · Answer

Does anyone have an algebraic way of solving this question?

SenseiA · Answer

Here’s how I solved it.

Fact 1: (y+1)/5 has a remainder of 1.

This means y is divisible by 5 i.e. the units digit is 5 or 0
Test 1: If y is 5, z is definitely 0 because 5 definitely goes in 5x without a remainder
Test 2: If y is 20, we need to know what x is to know the remainder Z, since we will have a 1/4 to account for (5/20)
INSUFFICIENT! Knock out A & D

Fact 2: (y+1)/4 leaves a remainder of 2.

This means the y could be 1, since (1+1)/4 leaves a remainder of 2. y could also be 5, 9, 13, 17,21,25, etc (keeping adding 4)
Test 1: y=5, as shown above, this gives a z of 0
Test 2: y=25, uncertain for the same reasons as the 20 test in fact 1. 
INSUFFICIENT! Knock out B

Combined:
5 and 25 fit both test cases and are obviously not sufficient as proven.
Still insufficient together.

Answer is E!

Ekland · Answer

Saw this question in target test prep and wondered how one could do the this question in 2 minutes?
TIPS pls?
Any tips to be able to do it two minutes?

Ekland · Answer

I've found out that GMAT rewards flexibility.

When the solution seems too iterative as you begin and you are not some savant with ESP, quickly try ALGEBRA.

I TRIED ALGEBRA AND THE SOLUTION HAPPENED FASTER THAN I HAD IMAGINED.

Stem is  5x =yq+z 
find  z

1)   y = 5t 
substitute (1) into stem to get  5x=5tq+z 
two equations with 5 unknowns. Also no identity found.  NOT SUFFICIENT

2)   y=4h+1 
substitute (2) into stem to get  5x=4hq+q+z 
same situation as in (1) above
 NOT SUFFICIENT

Both)   5x=5tq+z 
  5x=4hq+q+z 
leading to  5t=4h-1 
Since there's no unique values for  t  and  h , do we cannot get unique  q  or z  which is the variable we want to find.
 user9123 
 E

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If x and y are positive integers and y<5x, the remainder is z when 5x

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