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Math Expert V
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If a, b, c and d are positive integers, is d odd?  [#permalink]

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

(1) a/b=2c

(2) a/c=d+1

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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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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
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Retired Moderator G
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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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.
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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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.
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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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
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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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
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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I go with C

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

d = 2b-1 => definitely odd number
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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(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
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If a, b, c and d are positive integers, is d odd?  [#permalink]

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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.
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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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
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Re: If a, b, c and d are positive integers, is d odd?  [#permalink]

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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.

Please give kudos to the answer if I could help you understand Manager  G
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If a, b, c and d are positive integers, is d odd?  [#permalink]

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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.
Bunuel can you please help me know what am i missing? Regards
SandySilva If a, b, c and d are positive integers, is d odd?   [#permalink] 31 Aug 2018, 11:27
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