If x is an integer, then x(x + 2)(x + 3) is

Question

A. odd whenever x is odd
B. even only when x is even
C. even only when x is odd
D. divisible by 3 when x is odd
E. divisible by 2

Kinshook · Answer

If x is an integer, then x(x + 2)(x + 3) is

A. odd whenever x is odd
x ->odd
x+2 - > odd
x + 3 - > even
x(x + 2)(x + 3) - >odd * odd * even = even
FALSE
B. even only when x is even
x->odd
x+2 - > odd
x + 3 - > even
x(x + 2)(x + 3) - >odd * odd * even = even
FALSE
C. even only when x is odd
x->even
x(x + 2)(x + 3) - > even
FALSE
D. divisible by 3 when x is odd
x->odd
x +1 -> even and may be divisible by 3
(x+1)(x+2)(x+3) is divisible by 3
FALSE
E. divisible by 2
(x+2)(x+3) is divisible by 2
TRUE

IMO E

Archit3110 · Answer

for given series x(x + 2)(x + 3)
x=1 ; 1*3*4
x=2 ; 2*4*5
using given options we can say
 A. odd whenever x is odd ; NO
B. even only when x is even ; NO
C. even only when x is odd; NO
D. divisible by 3 when x is odd; NO
E. divisible by 2: YES always

OPTION E

GMATinsight · Answer

Substituting x = 1, x(x + 2)(x + 3) = 1*3*4
Substituting x = 2, x(x + 2)(x + 3) = 2*4*5

Result is always even i.e. Options A, B and C are out

FOr Option D, Substituting x = 5, x(x + 2)(x + 3) = 5*7*8 so OptionD is OUT

The result is always even hence

Answer: Option E

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • The number x is an integer

To find  
We need to determine
 • Depending on x, what should be true about the given expression x (x + 2) (x + 3)

Approach and Working  
We know that x is an integer and we have no other information available about x
 • Hence, we can   infer   that x being an integer, can be either even or odd only

Let us   consider all the possible cases  :
 Case 1 : x is even
 • If x is even, then x (x + 2) (x + 3) = even x even x odd = even

Case 2 : x is odd
 • If x is odd, then x (x + 2) (x + 3) = odd x odd x even = even

We can see that, for any value of x, the expression x (x + 2) (x + 3) is always even

• Hence, we can also   infer   that the given expression is always divisible by 2

Thus, option E is the correct answer.

Correct Answer: Option E

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bumpbot · Answer

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If x is an integer, then x(x + 2)(x + 3) is

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If x is an integer, then x(x + 2)(x + 3) is

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