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

Question

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

chetan2u · Answer

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

Abhishek009 · Answer

All prime numbers except 2 are odd, and we know ODD(Prime) - 2 = ODD(Prime)
 
 So, correct answer will be (D) d is even

frndrobinster · Answer

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

SiddharthaGAMT · Answer

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.

Sangeeta2018 · Answer

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

rahul16singh28 · Answer

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

Bunuel · Answer

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

2. Properties of Integers  
     Theory   
 Math: Number Theory 
 Number Properties: Tips and hints 
 Advanced Number Properties on GMAT (All 5 parts) 
 Do you make these 3 mistakes in GMAT Even-Odd Questions?  
 Everything about Factorials on the GMAT 
 Solving Complex Problems Using Number Line 
     Questions   
 Tough New Set: Number Properties Set 
 Power of a Number in a Factorial Problems 
 Number Properties Ability Quiz 
 Special Numbers and Sequences Problems 
 The E-GMAT Number Properties Knockout: 10 Great 700+ Ques for you! 
 Trailing Zeros Problems 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

HouseStark · Answer

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

bumpbot · Answer

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

Prep Toolkit

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