GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 11:58 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # M10-12

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59587

### Show Tags

1
8 00:00

Difficulty:   15% (low)

Question Stats: 83% (01:26) correct 17% (01:47) wrong based on 92 sessions

### HideShow timer Statistics

If $$X$$ is a positive integer, what is the remainder of $$\frac{X}{8}$$?

(1) The remainder of $$\frac{X}{16}$$ is 2.

(2) The remainder of $$\frac{X}{24}$$ is 10.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59587

### Show Tags

1
1
Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$X = 16N + 2$$ where $$N$$ is an integer. Thus, the remainder of $$\frac{X}{8}$$ is 2.

Statement (2) by itself is sufficient. From S2 it follows that $$X = 24N + 10 = (24N + 8) + 2$$ where $$N$$ is an integer. Thus, the remainder of $$\frac{X}{8}$$ is 2.

_________________
Intern  Joined: 25 Jul 2013
Posts: 3

### Show Tags

I'd appreciate if you could explain what you did for st 2.. how did you get x/8 ?
Manager  Joined: 07 Dec 2009
Posts: 86
GMAT Date: 12-03-2014

### Show Tags

1
1
Split 24N + 10 ==> (24N+8) + 2

It can further be written as 8(3N+1) + 2. When this is divided by 8 the remainder is 2.
Manager  B
Joined: 27 Aug 2014
Posts: 66

### Show Tags

Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$X = 16N + 2$$ where $$N$$ is an integer. Thus, the remainder of $$\frac{X}{8}$$ is 2.

Statement (2) by itself is sufficient. From S2 it follows that $$X = 24N + 10 = (24N + 8) + 2$$ where $$N$$ is an integer. Thus, the remainder of $$\frac{X}{8}$$ is 2.

Hi

I think I am missing some concept here. I framed equations like this:
Stem=X=8a+R; To find R=X-8a
Stmt1=X=16b+2
Stmt2=X=24c+10

Hence got E as cant find a or X from any of the stmts. I knw logically what I did is not wrong but dont know how to proceed from here. Read something about primes but how does the concept come about? Pls elaborate. Thanks.
Math Expert V
Joined: 02 Aug 2009
Posts: 8281

### Show Tags

3
3
sinhap07 wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$X = 16N + 2$$ where $$N$$ is an integer. Thus, the remainder of $$\frac{X}{8}$$ is 2.

Statement (2) by itself is sufficient. From S2 it follows that $$X = 24N + 10 = (24N + 8) + 2$$ where $$N$$ is an integer. Thus, the remainder of $$\frac{X}{8}$$ is 2.

Hi

I think I am missing some concept here. I framed equations like this:
Stem=X=8a+R; To find R=X-8a
Stmt1=X=16b+2
Stmt2=X=24c+10

Hence got E as cant find a or X from any of the stmts. I knw logically what I did is not wrong but dont know how to proceed from here. Read something about primes but how does the concept come about? Pls elaborate. Thanks.

Hi,
NOTE:-
whatever is the remainder by an integer, the remainder will remain teh same if div by its factors..
only thing to check is if the R is further div by that factor

what you should have done after making your statements..
Stmt1=X=16b+2
we do not require X or a, we are interested in R..
so what does x/8 mean..
(16b+2)/8=16b/8 + 2/8..
16b is div by 8 so will not leave any remainder but 2/8 will leave a remainder of 2..
suff

Stmt2=X=24c+10

same way ( 24c+10)/8= 3c +10/8..
when 10 is div by 8, it will give us 2 as remainder ..
again suff

D

_________________
Manager  B
Joined: 27 Nov 2015
Posts: 120

### Show Tags

could someone explain to me how does it follow from statement 1 that

that X=16N+2X=16N+2 where N is an integer?
Math Expert V
Joined: 02 Aug 2009
Posts: 8281

### Show Tags

nausherwan wrote:
could someone explain to me how does it follow from statement 1 that

that X=16N+2X=16N+2 where N is an integer?

hi
I. (1) The remainder of $$\frac{X}{16}$$ is 2...
it can be written as -- when x is divided by 16, the remainder is 2...
we do not know the quotient(Q) here but just know the remainder..
how do I write it in a equation-
x = 16a + 2..
a is the quotient and 2 is the remainder..
say a is 5.. so x= 5*16 +2 = 82..
I can write it as-- the remainder of 82/16 is 2..

so x=16n+2 is just another way of writing -- The remainder of $$\frac{X}{16}$$ is 2
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59587

### Show Tags

1
nausherwan wrote:
could someone explain to me how does it follow from statement 1 that

that X=16N+2X=16N+2 where N is an integer?

Divisibility and Remainders on the GMAT

Theory on remainders problems

Tips on remainders

Cyclicity on the GMAT

Units digits, exponents, remainders problems

Hope it helps.
_________________
Intern  Joined: 02 Aug 2016
Posts: 7

### Show Tags

why did you consider N as an integer.it was not given in the question?
Manager  G
Joined: 12 Jun 2016
Posts: 205
Location: India
WE: Sales (Telecommunications)

### Show Tags

Another approach - Write out few of the Numbers and check

S1: The Remainder of $$\frac{X}{16}= 2$$
This means X = 2, 18, 34...
Remainders when divided by 8 in all the cases = 2
Suff

S2: The Remainder of $$\frac{X}{24}= 10$$
This means X = 10, 34, 58...
Remainder when X is divided by 8 in all cases = 2
Suff

_________________
My Best is yet to come!
Intern  B
Joined: 09 Jan 2018
Posts: 1

### Show Tags

I think this is a high-quality question and I don't agree with the explanation. what if we take x=14 for statement 1.
then 14/16 gives rem as 2
but 14/8 gives rem as 6.
so the correct answer should be B.
Math Expert V
Joined: 02 Sep 2009
Posts: 59587

### Show Tags

muditsingh0616 wrote:
I think this is a high-quality question and I don't agree with the explanation. what if we take x=14 for statement 1.
then 14/16 gives rem as 2
but 14/8 gives rem as 6.
so the correct answer should be B.

14 divided by 16 gives the remainder of 14, not 2. From (1) x could be 2, 18, 34, 50, 66, ... Each of these values gives a remainder of 2 when divided by 8, so (1) is sufficient.
_________________
Intern  B
Joined: 06 Oct 2018
Posts: 29

### Show Tags

Don't see how S) 1 is sufficient.

x/16 gives remainder 2.

Hence X = 16q + 2

if q=0,
x= 16(0) + 2
=2

if q=1
x= 16 + 2
= 18

lets take x=2. 2/8 gives 0 remainder 8.
lets take x=18 18/8 gives 2 remainder 2.

Insufficient.

S) 2 on the other hand..

X = 24p + 10

if p=0
x= 10

p=1
x = 34

10/8 gives remainder 2
34/8 gives remainder 2.

Statement 2 works, but 1 doesn't.
Intern  Joined: 28 Feb 2019
Posts: 4
GMAT 1: 650 Q49 V31 ### Show Tags

PierTotti17 wrote:
Don't see how S) 1 is sufficient.

x/16 gives remainder 2.

Hence X = 16q + 2

if q=0,
x= 16(0) + 2
=2

if q=1
x= 16 + 2
= 18

lets take x=2. 2/8 gives 0 remainder 8.
lets take x=18 18/8 gives 2 remainder 2.

Insufficient.

S) 2 on the other hand..

X = 24p + 10

if p=0
x= 10

p=1
x = 34

10/8 gives remainder 2
34/8 gives remainder 2.

Statement 2 works, but 1 doesn't.

PierTotti17 All is good in what you wrote, except, 2/8 gives a remainder of 2, not 8. Hence 1 is sufficient as well.
Senior Manager  P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 440

### Show Tags

Easy to prove sufficiency with number picking, just plug in 2, 18 for St 1) you will get remainder 2 both times when dividing by 8.
St 2) must give the same remainder... you get 2 when dividing by 8 as well, plug in 2 and 34.
This is because both 16 and 24 are multiples of 8 so they all share the same remainder when dividing X. As chetan2u mentioned the only thing is to make sure remainder/divisor is in the most reduced form.
Manager  B
Joined: 26 Aug 2017
Posts: 52
Location: Singapore
Concentration: Strategy, General Management
Schools: HBS '21
WE: Management Consulting (Consulting)

### Show Tags

My two cents' worth here, probably a rehash of what the experts have expounded on above:

In both statements, the divisors 16, 24 (in relation and including the divisor '8' in the stem) are all multiples of the smallest of the divisors: '8'.

If so, we can possibly infer that all outcomes when divided by the divisors (=8K) would yield the same remainder; without calculating, I would pick 'D'.

Here are some numbers to try out e.g. 2,4,8 as divisors; the same numerator X=17 is tested.
17/2 with R=1
17/4 with R=1
17/8 with R=1

Each statement is sufficient on its own, hence D. Re: M10-12   [#permalink] 29 Nov 2019, 01:37
Display posts from previous: Sort by

# M10-12

Moderators: chetan2u, Bunuel  