X is the product of five integers a, b, c, d, e. Is X odd?

Question

(1) Integers a, b, c, d, e are evenly spaced from each other such that a < b < c < d < e.

(2) Sum of a, b, c, d, e is odd.

HYCC7WP04 · Answer

a , b , c ,d, e evenly spaced so they can be ODD, ODD, ODD, ODD, ODD,ODD or EVEN ODD EVEN ODD EVEN or ODD EVEN ODD EVEN ODD 
a+b+c+d+e = odd given so, it can be O+O+O+O+O whose product i.e. X will be odd but other case ie O+E+O+E+O is also odd but product will not be odd
SO, the answer should be E

superbenson · Answer

I saw evenly places as EVEN ODD EVEN ODD EVEN or ODD EVEN ODD EVEN ODD only. am I wrong?

lovenish · Answer

Statement (1) Integers a, b, c, d, e are evenly spaced from each other such that a < b < c < d < e.

Case 1: a = odd Integer

1.a= odd integer and the spacing between number is even = 2.
3 , 5, 7, 9, 11 ----> Product of odd will odd

2. .a= odd integer and the spacing between number is odd = 3.
3, 6, 9, 12, 15 ----> Product of Odd and Even will be even

Case2 :a = even Integer

Product will always be even

so first statement is insufficient as we get 2 answer odd and even in different cases

Statement (2) Sum of a, b, c, d, e is odd.

1. all odd ( Spacing between does not matter)
3 +7+ 9+ 13+ 15= odd . ----> product of all 5 digits will be odd

2. combination of even odd( Spacing between does not matter)
3 +4+ 9+ 14+ 15 = odd ----> product of all 5 digits will be even

so Second statement is also insufficient as we get 2 answer odd and even in different cases

combining two statements.
1. all odd
3 +5+ 7+ 9+ 11= odd . ----> product of all 5 digits will be odd

2. combination of even & odd
3 +6+ 9+ 12+ 15 = odd ----> product of all 5 digits will be even

if we combine two statements still we get we odd and even so insufficient.

Answer Is E.

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HYCC7WP04 · Answer

i think we have to analyse all possible scenarios ... OA is not provided ..

aserghe1 · Answer

These 2 examples satisfy both statements:

(1,3,5,7,9) --> X is odd
(1,2,3,4,5) --> X is even

Answer: E

alldaytestprep · Answer

X is the product of five integers a, b, c, d, e. Is X odd?

(1) Integers a, b, c, d, e are evenly spaced from each other such that a < b < c < d < e.

(2) Sum of a, b, c, d, e is odd.

For a product to be odd, ALL of it's terms must be odd --> Rephrase question: Are a, b, c, d, & e all odd??

1)

2 * 4 * 6 * 8 * 10 ---> not all odd
1 * 3 * 5 * 7 * 9 ---> all odd
-------------------------------------> INSUFFICIENT

2)

1 * 3 * 5 * 7 * 9 ---> all odd
2 * 3 * 4 * 5 * 7 ----> not all odd
--------------------------------------> INSUFFICIENT

1 & 2)
1 * 3 * 5 * 7 * 9 ------> all odd
3 * 8 * 13 * 18 * 23 ----> not all odd
------------------------------------------> INSUFFICIENT

Answer: E

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X is the product of five integers a, b, c, d, e. Is X odd?

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X is the product of five integers a, b, c, d, e. Is X odd?

Prep Toolkit

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My Rewards