If a and b are even integers, which of the following is an odd integer

Question

Tough and Tricky questions: Number Properties.

If a and b are even integers, which of the following is an odd integer?

A. ab + 2
B. a(b − 1)
C. a(a + 5)
D. 3a + 4b
E. (a + 3)(b − 1)

Kudos for a correct  solution .

Source: Chili Hot GMAT

hopeful101candidate · Answer

If a and b are even integers, then:

A. ab + 2: even + even = even
B. a(b − 1): even(odd) = even
C. a(a + 5): even(odd) = even
D. 3a + 4b: even + even = even
E. (a + 3)(b − 1): (odd)(odd) = odd.

Answer is E.

AliciaSierra · Answer

Key :
 Even + Even = Even 
 Even + Odd = Odd 
 Odd + Odd = Even 
 Even*Even = Even 
 Even*Odd = Even 
 Odd*Odd = Odd

As per question stem,  a  and  b  are even integers. Let us see each option.

A. ab + 2 --> even*even+ even = even+even = even
B. a(b − 1) --> even(even-1) = even*odd = even
C. a(a + 5) --> even(even+odd)= even
D. 3a + 4b --> odd*even+even*even = even
 E. (a + 3)(b − 1) --> odd*odd= odd

Answer : E

PareshGmat · Answer

Answer = E. (a + 3)(b − 1)

Say a = 2, b = 2

A >> 2*2 + 2 = 6 >> Even

B & C >> No need to check; it getting multiplied directly by 2, so would always be even

D >> 3*2 + 4*2 = 6+8 = 14 >> Even

E >> (2+3)(2-1) = 5 * 1 = 5 >> ODD

akumar5 · Answer

Testing all the option individually :
Given both a & b are even
Let a=2 & b=4

A. ab + 2
 EVEN 
B. a(b − 1)
 Product of even and odd is EVEN.
C. a(a + 5)
 Product of even and odd is EVEN
D. 3a + 4b
 EVEN
E. (a + 3)(b − 1)
 Product of odd and odd is ODD.

Answer is E

devmillenium2k · Answer

a and b are even integers.

A) ab + 2 => even*even+ even => even+even => even
B) a(b − 1) => even(even-1) => even*odd => even
C) a(a + 5) => even(even+odd) => even
D) 3a + 4b => odd*even+even*even => even
E) (a + 3)(b − 1) => odd*odd => odd

Answer E

Bunuel · Answer

Official Solution:

If a and b are even integers, which of the following is an odd integer?

A) ab + 2
B) a(b − 1)
C) a(a + 5)
D) 3a + 4b
E) (a + 3)(b − 1)

Picking Numbers

This key strategy involves first picking numbers and then substituting them into the answer choices. Whenever a problem involves variables, we may consider using this strategy. For this particular problem, pick the numbers a = 2 and b = 4 because both are even integers, yet both are still small and manageable numbers. Now substitute. Answer choice E is correct. You can be confident that if it works for your chosen set of numbers, it will also work for all other numbers as well. There is no need to try other numbers.

ab + 2 (2 × 4) + 2 = 10 even
a(b − 1) 2(4 − 1) = 6 even
a(a + 5) 2(2 + 5) = 14 even
3a + 4b (3 × 2) + (4 × 4) = 22 even
(a + 3)(b − 1) (2 + 3)(4 − 1) = 15 odd

Answer: E.

RR88 · Answer

Option E

a,b are Even integers. Odd: O, Even: E & Fraction: F

A. ab + 2 = E*E + 2 = E + 2 = E
B. a(b − 1) = E*(E - 1) = E
C. a(a + 5) = E*(E + 5) = E
D. 3a + 4b = 3*E + 4*E = E
E. (a + 3)(b − 1) = (E +3)*(E - 1) = O*O = O

jhavyom · Answer

If a and b are even integers, which of the following is an odd integer?

E. (a + 3)(b − 1)
(even + 3)(even - 1)
odd *odd = odd

MathRevolution · Answer

EVEN * EVEN = EVEN
EVEN * ODD = EVEN
EVEN + EVEN = EVEN
EVEN + ODD = ODD
ODD * ODD = ODD

'a' and 'b' are even:

Option A: Even * Even + Even = Even

Option B: Even ( Even -1): Even * Odd = Even

Option C: Even( Even + Odd): Even * Odd = Even

Option D: 3*Even + 4 Even: Even + Even = Even

Option E: (Even + Odd)(Even - Odd): Odd * Odd = ODD

Answer E

ScottTargetTestPrep · Answer

Solution:
 
We recall 5 arithmetic facts: (1) even +/- even = even (2) even +/- odd = odd (3) even x even = even (4) even x odd = even (5) odd x odd = odd

Let’s evaluate each answer choice, using these arithmetic facts.

Choice A: ab + 2 . Using (3) and (1), we see that this answer is even.

Choice B: a(b - 1). Using (2) and (4), we see that this answer is even.

Choice C: a(a + 5) . Using (2) and (4), we see that this answer is even.

Choice D: 3a + 4b . Using (4), (3), and (1), we see that this answer is even.

Choice E: (a + 3)(b - 1). Using (2), (2), and (5), we see that this answer is odd.

Answer: E

If a and b are even integers, which of the following is an odd integer

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a and b are even integers, which of the following is an odd integer

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards