x is a two-digit integer and y is a three-digit integer that is divi

Question

x is a two-digit integer and y is a three-digit integer that is divisible by x. If z is the value of the quotient y/x, is the units digit of z greater than 3?

(1) The units digit of x is 3.

(2) The units digit of y is the same as the units digit of x.

DavidTutorexamPAL · Answer

We'll first write things out as equations so we understand what we need to do.
This is a Precise approach.

Since y is divisible by x, then y = kx for some integer k.
Also, z = y/x --> y = zx. That is, the 'k' we wrote above us actually z meaning that z is an integer.
So all we know is that z is an integer and y = zx

(1) Without information on y this is insufficient. (As, for example, x=53, z=2 work as do x = 53, z=5)
Insufficient.

(2) Setting the units digit of z to 1 means this is always true (giving a NO) but if z = 5 and the units of digit of x is 5 it is also true (giving a YES)
Insufficient.

So the units digit of both x and y is 3. Then the units digit of z must be 1 (as 1*3 = 3 but 2*3, 3*3, ....9*3 are all different from 3).
Sufficient.

(C) is our answer.

WizakoBaskar · Answer

The data is sufficient if we can determine whether the units digit of z is greater than 3.
The answer is yes if z > 3
The answer is no if z <= 3

Statement 1 : The units digit of x is 3
Easiest approach. Look for a counter example
 Example : x = 13, y = 286; z = 22. Answer No.
 Counter Example : x = 13, y = 325; z = 25. Answer Yes.

Because z is the quotient of the division, the unit digit of the quotient could take any value from 0 to 9. 
Not sufficient

Statement 2 :The units digit of y is the same as the units digit of x.
Again let us look for a counter example
 Example : x = 13, y = 143; The unit digit of y and x are the same. z = 11. Answer No.
 Counter Example : x = 16, y = 256; The unit digit of y and x are the same. z = 16. Answer Yes.

We cannot answer conclusively using statement 2. Not sufficient.

Combine the 2 statements :The units digit of x is 3 and The units digit of y is the same as the units digit of x
Units digit of x and y are both 3.
If the unit digit of z = 1, the units digit of x and y will both be 3.
For any other value of the unit digit of z, the units digit of y will not be 3.

Unit digit of x is 3. Here are the results of multiplying x with different unit digits for z
If the unit digit of z = 2, the unit digit of y will be 6.
If the unit digit of z = 3, the unit digit of y will be 9.
If the unit digit of z = 4, the unit digit of y will be 2.
If the unit digit of z = 5, the unit digit of y will be 5.
If the unit digit of z = 6, the unit digit of y will be 8.
If the unit digit of z = 7, the unit digit of y will be 1.
If the unit digit of z = 8, the unit digit of y will be 4.
If the unit digit of z = 9, the unit digit of y will be 7.
If the unit digit of z = 0, the unit digit of y will be 0.

Therefore, if the unit digit of x and y are 3, the only value that the unit digit of z can take is 1.
Answer definite No.

Choice C.

EgmatQuantExpert · Answer

Solution

Given:

• x is a two-digit number.
• y is a three-digit number and, y is divisible by x.
• The quotient of y/x is z.

To find:

• We need to find if the units digit of x is greater than 3 or not.

Approach and Working:

Statement 1 :  The units digit of x is 3.

Since the units digit of x does not gives us any idea about the units digit of y, statement 1 is not sufficient to answer the question.

Statement 2 :  The units digit of y is the same as the units digit of x.

Since we don’t know the values of the units digit of both the numbers, x and y, statement 2 is not sufficient to answer the question.
 For example:  If the units digits of both, x and y is 2 then the units digits of z can be 6 or 1.

Combining both the statements together:

By combining both the statements, if the units of x and y is 3 then the units of z can only be 1 which is always less than 3.
Hence, we can find the answer by combining both the statements together.

Hence, option C is the correct answer.
   Answer: C

aryamanpanda · Answer

Bunuel ok messed up approach but tell me where i go wrong please. given: x - 2 digit . let x = 10A + B y - 3 digit . let y = 100C + 10D + E z - quotient of y/x = 10F + G we know xz = y need to find : G>3 ? YES/NO therefore (10A + B) * (10F + G) = 100C + 10D + E 100(AF) + 10(AG + BF) + (BG) = 100C + 10D + E comparing like terms we get -> AF = C -> AG + BF = D -> BG = E st1. : : B=3 we know BG = E therefore 3G = E --> G = E/3 . the largest value E can take is 9. therefore G(max) = 9/3 = 3 for all other values of E (0-8) , G<3 . Therefore G will always be lessed than 3 . \ Therefore SUFFICIENT. st2.: B = E we know BG = E --> G = E/B --> G = 1 . G<3 . Therefore SUFFICIENT IMO D

chetan2u · Answer

You are wrong in the colored portion..

You can not equate the terms the way you have done unless you know the values
for example x=23, y=115, so z=5..
Here F=0, so AF=C...2*0=1 ??

Checkmate22 · Answer

1) (x,y) = (13,130) No / (195,13) Yes / Not Sufficient
2) (x,y) = (13,143) No / (15,225) Yes / Not Sufficient
1+2) (x,y) = (13,143) No / (23,253) No / (23,483) No / Sufficient 
Logic = units digit of 3 will need to be multiplied by a units digit of 1 in order to result in a units digit of 3

C

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x is a two-digit integer and y is a three-digit integer that is divi

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