If n is a three-digit positive integer, what is the tens digit of n?

Question

(1) Dividing n by 4 gives the same remainder as does dividing n by 25.
(2) Dividing n by 16 gives the same remainder as does dividing n by 25.

chetan2u · Accepted Answer

IMPORTANT :-
 when can two numbers leave same remainder - when we are looking at the numbers after their LCM or x*LCM, where x is a positive integer

(1) Dividing n by 4 gives the same remainder as does dividing n by 25.
so the numbers should be immediately after the LCM of 4 and 25, which is 100..
and remainder of 4 can be 0,1,2,3.... so numbers can be 100,101,102,103
next will be 2*100, 201,202,203
 so in all cases the TEN's digit will be 0 
sufficient

(2) Dividing n by 16 gives the same remainder as does dividing n by 25.
so the numbers should be immediately after the LCM of 16 and 25, which is 400..
and remainder of 16 can be 0,1,2,3...15, so numbers can be 400,401,402,403,....410,411,..415
next will be 2*400, 801,802,803...810,811...815
 so in all cases the TEN's digit will be 0 or 1 
insufficient

a

CAMANISHPARMAR · Answer

Question Stem:- n is a three-digit positive integer. To find - what is the  tens digit  of n
Important points:-
Its a value question.

STATEMENT 1:-

First find LCM 4 & 25 ---> 100. Check which all three digit numbers will give same remainder when divided by 100. e.g. 101, 102, 103, 201, 202, 203 ...... 901, 902, 903 etc. These are different numbers but look what the question stem is asking? Its asking for tens digit hence we have a definite value, its 0. hence statement 1 is sufficient.

We are down to A vs D.

Statement 2:-
Repeat the same process, First find LCM 16 & 25 ---> i.e. 400. Check which all three digit numbers will give same remainder when divided by 400. e.g. 401, 402, 403, .....414,415......... 801, 802, 803....814, 815.... etc. These are not only different numbers but this time we don't even have a tens digit which has a definite value, it can be 0 or 1. hence statement 2 is insufficient.

Hence the correct answer is A

Masterscorp · Answer

Nice question but it should be moved to the DS section

CAMANISHPARMAR · Answer

Thanks, I have already informed the administrators to do the needful but they have not moved it yet

Thanks again!!

Bunuel · Answer

Moved to DS forum. Thank you.

CAMANISHPARMAR · Answer

Thanks  Bunuel

GyMrAT · Answer

Given n is a three digit number, required is tens digit of n.

Statement 1:
Let  r  be remainder, then
 n = 4k + r ,  0<=r<4 
 n = 25q + r ,  0<=r<25

Hence  0<=r<4 ,  r = 0,1,2,3

LCM of  4  &  25  is  100 , hence  n = 100p + r

So r will be units digit of a multiple of 100, hence the tens digit of n will be 0.

Statement 1 is sufficient.

Statement 2:
Let  z  be remainder, then
 n = 16x + z ,  0<=z<16 
 n = 25y + z ,  0<=z<25

Hence  0<=z<16 ,  z = 0,1,2,3,4,....15

LCM of  16  &  25  is  400 , hence  n = 400w + z

So if  z<10 ,  z  will be units digit of a multiple of  400 , hence the tens digit of  n  will be  0 .
& if  z>=10 , then last digit of 2 digit number  "z" , will be the units digit of a multiple of  400  & the tens digit will be  1 .

Hence 2 values for the remainder.

Statement 2 is Insufficient.

Answer A.

Thanks,
GyM

Shobhit7 · Answer

St.1: Divisors 4 and 25.
Possible Remainders 0 to 3.
LCM of 4 and 25 is 100

For Remainder 0: 
Common no. 100, 200 to 900
(Adding LCM to first common no.)

For Remainder 1: 101 to 901
For Remainder 2: 102 to 902
For Remainder 3: 103 to 903

In all of the above, tens digit is 0. SUFFICIENT.

St.2: Divisors 16 and 25.

So, with divisor 16, Remainders range is from 0 to 15.

Hence, tens digit can be either 0 or 1. INSUFFICIENT.

Therefore, Ans A

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samstthomas · Answer

Hi, for the statement A, if I chose the number as 150. The remainder is 2 when divisible by 4 and 25. In which, case the there are two outcomes isnt it? Please clarify

CAMANISHPARMAR · Answer

My dear friend, what is the remainder when 150 is divided by 25?

bumpbot · Answer

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If n is a three-digit positive integer, what is the tens digit of n?

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GMAT Data Sufficiency (DS) Questions

If n is a three-digit positive integer, what is the tens digit of n?

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