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c and d are prime numbers. If c - d is an odd prime, then which of the

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Bunuel
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c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   29 Oct 2017, 05:22
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c and d are prime numbers. If c - d is an odd prime, then which of the following must be true?

(A) c is even

(B) d is odd

(C) c*d is odd

(D) d is even

(E) c*d - c is even
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D
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chetan2u
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   29 Oct 2017, 05:54
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Bunuel wrote:
c and d are prime numbers. If c - d is an odd prime, then which of the following must be true?

(A) c is even

(B) d is odd

(C) c*d is odd

(D) d is even

(E) c*d - c is even



Hi...

c-d can be odd when one of the two is even and one odd..
c-d as odd prime means d is even prime and c is odd prime..
Odd-even=odd

D
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   29 Oct 2017, 07:49
Bunuel wrote:
c and d are prime numbers. If c - d is an odd prime, then which of the following must be true?

(A) c is even

(B) d is odd

(C) c*d is odd

(D) d is even

(E) c*d - c is even


All prime numbers except 2 are odd, and we know ODD(Prime) - 2 = ODD(Prime)

So, correct answer will be (D) d is even
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   29 Oct 2017, 08:20
As c and d are primes, and c-d is also prime. So d is even.
Since 2 is the only even prime no. d = 2
So (D) is correct answer
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   30 Oct 2017, 21:40
Bunuel wrote:
c and d are prime numbers. If c - d is an odd prime, then which of the following must be true?

(A) c is even

(B) d is odd

(C) c*d is odd

(D) d is even

(E) c*d - c is even



If c-d is an odd prime then:
c>d
odd - odd = even
odd - even = odd
Since there is only 1 even prime number and it also happens to be the smallest prime, b MUST = 2 and thus D is the correct answer.
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   04 Nov 2017, 06:23
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We can solve this Sum by testing values.

c-d=Odd prime (given).
We can test this with the smallest prime nos. for simplicity: c=5,d=2 whose difference gives 3 another Odd prime.

Now as we found the values for c=5 and d=2,we can plug them in each ans.choice.

Only D is a Must Be True. Ans-D
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   04 Nov 2017, 10:13
Bunuel wrote:
c and d are prime numbers. If c - d is an odd prime, then which of the following must be true?

(A) c is even

(B) d is odd

(C) c*d is odd

(D) d is even

(E) c*d - c is even


Hi Bunuel,

Can you please help me to clarify my doubt for the above question. The question states that C & D are Prime Numbers and the option states that C & D are even/odd numbers. Is it right??

Also, odd prime numbers are all the prime numbers except 2 .. Am I right to think this??

Apologies if this is a stupid doubt :-)
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Bunuel
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   05 Nov 2017, 01:13
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rahul16singh28 wrote:
Bunuel wrote:
c and d are prime numbers. If c - d is an odd prime, then which of the following must be true?

(A) c is even

(B) d is odd

(C) c*d is odd

(D) d is even

(E) c*d - c is even


Hi Bunuel,

Can you please help me to clarify my doubt for the above question. The question states that C & D are Prime Numbers and the option states that C & D are even/odd numbers. Is it right??

Also, odd prime numbers are all the prime numbers except 2 .. Am I right to think this??

Apologies if this is a stupid doubt :-)


The only even prime is 2. All other primes are odd.

2. Properties of Integers



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink] New post   04 Jul 2020, 05:06
Bunuel wrote:
c and d are prime numbers. If c - d is an odd prime, then which of the following must be true?

(A) c is even

(B) d is odd

(C) c*d is odd

(D) d is even

(E) c*d - c is even


c(even)- d(even)= even (not require as question asked for odd prime no.)
c(even)-d(odd)=odd (require)
c(odd)-d(even)=odd(require)

for c(even)-d(odd)=odd
c=even (the only even prime no. =2)
no answer is possible as 2 itself is the lowest of all prime no. if you subtract it with any odd prime no. then answer would be -ve no.

for c(odd)-d(even)=odd

yes by subtraction you will get odd prime no.
5-2=3(odd)
7-3=5(odd)

so answer is D
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Re: c and d are prime numbers. If c - d is an odd prime, then which of the [#permalink]
04 Jul 2020, 05:06
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