If x is an integer, is x even?

Question

Competition Mode Question

(1) x is equal to the difference between two consecutive prime numbers
(2) x is greater than 1

yashikaaggarwal · Answer

If x is an integer, is x even?

Solution: 
Note: difference between any two consecutive prime numbers is even except 2&3

(1) x is equal to the difference between two consecutive prime numbers
Case 1: consecutive prime = 2&3
Difference = 1 (odd)

Case 2: consecutive prime = 3&5
Difference = 2(even)
(Insufficient)

(2) x is greater than 1
X can be odd as well as even 
(Insufficient)

Combining both.
Since the difference between the two consecutive prime numbers is always an even other than 3&2 pair giving 1, and X is greater than 1.
So X is definitely even

Answer is c

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CrackverbalGMAT · Answer

Constraint given here is that x is an integer.

Statement (1)  : x is the difference between 2 consecutive prime numbers

Let these 2 prime numbers be a and b

If a = 2 and b = 3, then difference is b - a = 1, which is an odd number

All other differences between 2 consecutive prime numbers would be even, as difference of 2 odd numbers would be even.

Statement (1) is insufficient. Our answer choices could be B, C or E

Statement (2)   : x > 1.

From this statement x could be any value from 2 to infinity.

Statement (2) is insufficient. Our answer choices could be C or E.

Combining Statements (1) and (2)  :

x is the difference between any 2 consecutive prime numbers and x is greater than 1

In such a case the 2 consecutive prime numbers cannot be 2 and 3 as their difference is equal to 1.

Difference between any other 2 consecutive prime numbers would be even, as it would be the difference between 2 odd numbers.

Both statements together are sufficient.

Option C

Arun Kumar

v12345 · Answer

Statement 1: Insufficient 
x can be 3-2 = 1 or 5-3 = 2, that is even or odd.
 Statement 2: Insufficient 
x can be 2,3,4 etc.
 Combining, Sufficient 
x will be always even.
Hence, OA is (C).

pankulbansal · Answer

Answer: C

Statement 1 
 x  can be odd or even
 Case 1: Consecutive Prime Numbers 3 and 2 
Difference: 1 (Odd)
 Case 2: Any other pair of consecutive prime numbers 
Difference will be even, because all prime numbers are odd, except 2, and difference between two odd numbers will be even
 Hence, Statement 1 not sufficient

Statement 2 
 x>1 
 x  can be anything, odd or even
 Hence, Statement 2 not sufficient

Both Statements Together 
Since  x>1 , the two consecutive prime numbers cannot be 3 and 2, because their difference will be 1
Hence x will be even, since the consecutive prime numbers will be odd
 Hence both statements together are sufficient

Hence answer is C

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • x is an integer.
• We need to find if x is an even number.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  x is equal to the difference between two consecutive prime numbers.
 • We know that  except 2 all other prime numbers are odd. 
• So, there can be two cases:
 o Case 1: If x is equal to the difference between 3 and 2,
  Then, x = 3-2 = 1, here x is an odd number. 
o Case 2: If x is the difference between any two consecutive prime numbers which are greater than 2.
  Then, x = odd – odd = even.  
• We are getting two contradictory results. 
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  x is greater than 1
 • According to this statement, x can be 2, 3, 4, 5….etc.
 o So, x may be even or may be odd.  
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining. 
 • From statement 1: 
 o x is either 1 or an even number. 
• From statement 2:
 o x > 1 
• On Combining both statements, we get,
 o x is an even number.  
Thus, the correct answer is  Option C.

GMATinsight · Answer

QUestion: Is x EVEN?

STatement 1 : x is equal to the difference between two consecutive prime numbers

Prime numbers are {2, 3, 5, 7, 11...}

i.e x = 3-2 = 1 ODD or
i.e x = 5-3 = 2 EVEN

NOT SUFFICIENT

Statement 2 : x is greater than 1

x can be any integer greater than 1 hence

NOT SUFFICIENT

COmbining the statements

x is a difference of two  consecutive  prime numbers and x > 1

Since all prime numbers other than 2 are ODD

and Difference of two consecutive prime numbers other than 2 = ODD - ODD = EVEN

hence since x = 1 only if consecutive primes are 3 and 2 so we can NOT take this case and for all other cases of two consecutive prime numbers, the difference ODD - ODD = EVEN hence

SUFFICIENT

Answer: Option C

HoneyLemon · Answer

imo ,  C  
If x is an integer, is x even?

(1) x is equal to the difference between two consecutive prime numbers
 -- x can be 1 , if two primes are 3 and 2 .. or any other even number , if two primes are 11 and 7 . Not sufficient .. 
(2) x is greater than 1
 -- x can be odd or even .Not sufficient ..

Combining 1 and 2 .. x can only be an even .. since both the prime number greater than 2 is only odd .

QuantMadeEasy · Answer

Step 1: Understanding statement 1 alone 
First few prime numbers numbers are 2, 3, 5, 7, 11 and so on
x = 3 - 2 = 1 is odd
x = 5 - 3 = 2 is even
Insufficient

Step 2: Understanding statement 2 alone 
x = 2, 3,4 ...
Insufficient

Step 3: Clubbing statement 1 and 2 
x is greater than 1 and is equal to the difference between two consecutive prime numbers
x = 5 - 3 = 2 is even or in other words x = odd - odd = even 
Sufficient

IMO C

Saasingh · Answer

OA D?

Is x even ?

(1) 2 3 5 7 11 ...

As one can see, the only even prime = 2. 
(3-2) NOT EVEN....................... whereas, (5-3) = 2, EVEN

Not sufficient.

(2) x greater than 1. ---> could be anything 2,3,4,5,6. (not sufficient)

combine both ---> x cannot be 1. Therefore, sufficient (because diff of primes must be even as primes will be odd numbers only now , because prime = 2 possibility is eliminated).

NiftyNiffler · Answer

If x is an integer, is x even?

(1) x is equal to the difference between two consecutive prime numbers
(2) x is greater than 1

st1) Only two consecutive prime numbers are 2 and 3. So SUFFICIENT

st2) x can take any value. INSUFFICIENT

So, the answer should be  A

exc4libur · Answer

(1) insufic
3-2=1 odd
5-3=2 even

(2) insufic

(1/2) sufic
prime > 2 is an odd
odd-odd=even

Ans (C)

bidskamikaze · Answer

If x is an integer, is x even?

(1) x is equal to the difference between two consecutive prime numbers 
Case 1: prime numbers 2 & 3 ----- Answer  NO 
Case 2: prime numbers 3 & 5 ----- Answer  YES 
Insufficient.

(2) x is greater than 1 
Insufficient by itself.

Combine:
Case 1 above is eliminated. Also, all prime numbers except 2 are odd. So in any case, Odd - Odd = Even.
Sufficient.

Answer C.

Jawad001 · Answer

If x is an integer, is x even?

(1) x is equal to the difference between two consecutive prime numbers
(2) x is greater than 1

Solution: 
Prime numbers = 2, 3, 5, 7, 11, 13 …

From statement (1): Difference between two prime number 
(a) 3-2 = 1(Odd)
(b) 5-3 = 2(Even)
Hence, statement (1) Not sufficient.

From statement (2), x could be = 2, 3, 4, 5, 6, 7……….
Not Sufficient.

Combining statements (1) and (2), x must be 2, which is even.
Hence sufficient.
Answer: C

singhamit06 · Answer

Difference between 2 prime numbers can be either 2 or 4 hence A is the right answer.
1 is not as prime number.

sood1596 · Answer

Question:  x even i.e is x is divisible by 2.

Statement 1-
x - difference between 2 consecutive prime numbers
Lets put some value 
case 1 : x = 3-2 = 1 (Not even)
Case 2: 7-5 = 2 (Even)
Case 3 : 23-19 = 4 (Even)
Since we cant answer the question with certainty. Not sufficient

Statement 2: 
x>1
x can be any value 2,3,4 ,5,6 
Since we cant answer the question with certainty. Not sufficient

Statement 1 & 2 together
Since x>1 and x according to statement 1 will be even except in one case which gets eliminated due to the 2nd statement.

We can answer the question with certainty
Sufficient

Answer - C

suchita2409 · Answer

(1) x is equal to the difference between two consecutive prime numbers.

3-2 =1 odd
5-3 =2 even.
Insufficient.

(2) x is greater than 1.
Clearly Insufficient.

Combining them we get.
(x is greater than 1) .
The diiference between any two consecutive primes is always even.

C.

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chaitralirr · Answer

If x is an integer, is x even?

(1) x is equal to the difference between two consecutive prime numbers
(2) x is greater than 1

X is even

Statement 1: X= Z-y

The two consecutive prime numbers are 2, 3 so the difference is 1

Hence x is not a prime number sufficient.

Statement 2: 
X<1

X can be 2 or 3 can be even or odd

IMO A

ndawar · Answer

If x is an integer, is x even?

(1) x is equal to the difference between two consecutive prime numbers
(2) x is greater than 1
 1. the consecutive prime number pairs are 1,2 difference =1 ,
5,7 difference 2 so both even and odd value of x is possible
2. x greater then 1 but obvious many values of x even and odd both

taking both statements together we van eliminate the case of 1,2 difference =1 but 
2,3 difference again 1 
5,7 difference 2 
again we got two values 
so E is correct answer

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If x is an integer, is x even?

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If x is an integer, is x even?

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