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

 It is currently 15 Oct 2019, 19:38

### 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

# If a, b, c and d are positive integers, is d odd?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58340
If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

26 Sep 2016, 03:19
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:33) correct 30% (01:52) wrong based on 247 sessions

### HideShow timer Statistics

If a, b, c and d are positive integers, is d odd?

(1) a/b=2c

(2) a/c=d+1

_________________
Intern
Joined: 27 Oct 2013
Posts: 22
Schools: Erasmus '17
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

29 Sep 2016, 19:49
5
a/b = 2c

eg 10/5 = 2
8/4 = 2
with more examples u vl see tht , a has to be even n b caould be anything ..

now a = 2bc.

Sub. it in second eq. a/c = d+1
== 2bc/c = d+1

== 2b = d+1

hence d+1 is even . therefore d == odd.
HENCE C
##### General Discussion
Retired Moderator
Joined: 26 Nov 2012
Posts: 576
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

26 Sep 2016, 05:23
3
Bunuel wrote:
If a, b, c and d are positive integers, is d odd?

(1) a/b=2c

(2) a/c=d+1

Stat 1: a/b = 2c...here 2c will always be even...i.e. a and b have to be even...even / even will yield even...but no data about d...insuffficient

Stat 2: a/c=d+1

Now d can be odd or even..

suppose d = odd then d+1 = even and if d = even => d+1 = odd....Insufficient.

Both : a and c are even from stat 1 and when both even we have to get even result i.e. d+1 must be even...in such case d has to be odd..

IMO option C.
Intern
Joined: 23 Apr 2016
Posts: 21
Location: Finland
GPA: 3.65
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

29 Sep 2016, 14:04
3
msk0657: Stat 1: a/b = 2c...here 2c will always be even...i.e. a and b have to be even...even / even will yield even

>> Not necessarily 12/3 = 4, we just know from this statement that a is even, but we dont know if b is even or not ...

Second statement does not give any new information as well ... a/c = d+1

IMHO, combining statement 1 and 2 also does not tell anything about d
from 1 we know that a is even, so combining 1& 2
if c is even then d is even
if c is odd then is odd ...can't conclude...Hence E for me.
Current Student
Joined: 26 Jan 2016
Posts: 98
Location: United States
GPA: 3.37
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

29 Sep 2016, 14:18
We actually do not know that C is even. Take the example 10/5=2 Here C could be 1.

Statement 1 and 2 insuff. But look at them together

Lets take 10/5=2 So we have a=10, b=5, and C=1. If we apply that to statement 2 we see that 10/1=d+1 and D=9 odd

From Statement 1 we know that A is even. If we say that C is even (we just said it was odd and we got D was odd) we get even/even=even+1 odd

Either way D is still odd

C for me
Intern
Joined: 14 May 2014
Posts: 16
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

29 Sep 2016, 21:40
3
C for me.
from (1) we have a/c=2b => a/c even
from (2) we have d=a/c-1= an even -1 = an odd
Manager
Joined: 24 Oct 2013
Posts: 129
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

01 Oct 2016, 06:29
I go with C

Both statements combined together we get value of 2b = d + 1

d = 2b-1 => definitely odd number
Manager
Joined: 26 Mar 2016
Posts: 69
Location: Greece
GMAT 1: 710 Q51 V34
GPA: 2.9
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

09 Oct 2016, 05:05
3
(1) a/b=2c clearly insufficient.

(2) a/c=d+1 , d could take any value even or odd. Not sufficient.

(1)+(2) , from statement (1) we know that a/c=even=2b, therefore d+1=even => d=odd.

Ans. C
_________________
+1 Kudos if you like the post
Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1348
Location: Malaysia
If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

27 Feb 2017, 00:36
Bunuel wrote:
If a, b, c and d are positive integers, is d odd?

(1) $$\frac{a}{b}=2c$$

(2) $$\frac{a}{c}=d+1$$

Official solution from The Economist.

Correct.

This is a DS Yes\No question asking whether d is odd. Answering a definite "Yes" or a definite "No", i.e., answering "d is odd" or "d is even" means Sufficient. If the answer is sometimes "Yes" and sometimes "No", i.e., "d can be either odd or even", it means Maybe which means Insufficient.

Stat.(1) tells you nothing about d and therefore cannot, on its own, be sufficient. d could be either odd or even. Hence, Stat.(1)->Maybe->IS->BCE.

Stat.(2): plug in $$a=2$$, $$c=1$$, so $$[m]2/1$$=d+1[/m], or $$d=1$$, which is odd. Plug in $$a=3$$, $$c=1$$, so $$\frac{3}{1}=d+1$$, or d=2, which is even. d could be either odd or even, so Stat.(2)->Maybe->IS->CE.

Stat.(1+2): manipulate the variables in both equations to get

$$a=2bc$$ and $$a=c(d+1)$$

--> $$2bc=c(d+1)$$.

Divide by c to get:

--> $$2b=d+1$$, which can also be represented as $$even=d+odd$$. d, therefore, must also be odd, so Stat.(1+2)->Yes->S->C.
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Intern
Joined: 17 Jan 2016
Posts: 39
Location: India
Concentration: General Management, General Management
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

07 Mar 2017, 00:46
S1: a/b=2c

No information is provided about d here. So this statement is not sufficient.

S2: a/c=d+1

Whether d is odd or even will depend on the values of a & c. But no information about values of a and c has been provided here.So this statement is not sufficient.

Combining both S1 & S2:

From S1 we have a=b*2c. Substituting this value in S2 we get

\frac{(b*2c)}{c=d+1}
On simplifying we have
2b=d+1 ie. d= 2b-1

now 2b is even so 2b-1 will be odd. Hence d is odd. So both S1 & S2 are sufficient together.

Ans - C
Intern
Joined: 03 Feb 2017
Posts: 5
Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

24 Aug 2017, 23:18
Statement 1 : (a/b) = 2c

c can be odd or even, but 2c will always be even. Hence (a/b) will be even.
So (a/b) can be (even/even) or (even/odd) -> Eg (6/3)
In both cases, a has to be even but b can be even or odd.

Statement 2 : (a/c) = d+1

From Statement 1 we know a is even for sure.
We also know that (even/even) or (even/odd) leads to even number.
So d+1 will be even. Hence d has to be odd number.

Manager
Joined: 30 Dec 2016
Posts: 231
GMAT 1: 650 Q42 V37
GPA: 4
If a, b, c and d are positive integers, is d odd?  [#permalink]

### Show Tags

31 Aug 2018, 11:27
thapliya wrote:
msk0657: Stat 1: a/b = 2c...here 2c will always be even...i.e. a and b have to be even...even / even will yield even

>> Not necessarily 12/3 = 4, we just know from this statement that a is even, but we dont know if b is even or not ...

Second statement does not give any new information as well ... a/c = d+1

IMHO, combining statement 1 and 2 also does not tell anything about d
from 1 we know that a is even, so combining 1& 2
if c is even then d is even
if c is odd then is odd ...can't conclude...Hence E for me.

I followed the somewhat same approach. from statement 1 we can conclude that a has to be even.
from statement(1+ 2)---> a= (d+1)*c
if c is even, then d can be either odd or even and a will be even.

Regards
SandySilva
If a, b, c and d are positive integers, is d odd?   [#permalink] 31 Aug 2018, 11:27
Display posts from previous: Sort by