If a, b, c, and d are consecutive integers, and a

Question

If  a, b, c,  and  d  are consecutive integers, and  a<b<c<d,  which of the following must be even?

A.  a⋅c

B.  a−2c

C.  a−d

D.  b+d

E.  a+d

KabxW · Answer

This is a very simple question if we know about the rules of Odd-Even. However, if one does not know we can even plug in numbers:

I am using both the approaches for everyone's clarity:

Approach 1: O-E Rules 
A lot of GMAT Students remember these:
O +/-O = E ||| O x O = O
E +/- E = E ||| E x E = E
O +/- E = O ||| O x E = E
It really helps if you know these. Now since they are consecutive numbers, there are only 2 choices available:

1. Either a,b,c,d = O,E,O,E
2. Or a,b,c,d = E,O,E,O

Take note that the 1st and 3rd & 2nd and 4th numbers will be the same i.e. Either both Odd or both Even. 
Let's test options:
(A) OxO or ExE: Not always even
(B) O - OxE or E - ExE: In 1 case it's Odd and in other E. Therefore, not always even
(C)O - E or E - O: Always Odd
(D)  E + E or O + O: Always even 
(E) Same as Option (C): Always Odd

So Ans is (D)

Approach 2: This is a much quick approach and can be done mentally too.
Put a,b,c,d as 1,2,3,4 and 2,3,4,5

Test out the options for both. 
(A) 1 x3 gives Odd while 2x4 gives Even: Not always even
(B)1 - 2(3) gives Odd while 2-2(4) gives even: Not always even
(C) 1-4 gives Odd while 2-5 also gives Odd. Always Odd
 (D) 2+4 gives Even as well as 3+5 gives Even. Therefore, our answer: Always Even 
(E) Similar to Option C

ANSWER: (D)

Thus, both approaches are simple but if you don't remember the rules plugging in approach seems useful and quick.
Cheers!

unraveled · Answer

a<b<c<d  has two possibilities:
1. e < o < e < o 
2. o < e < o < e

A.  a⋅c 
e.e = e YES
o.o = o NO

Not MUST but CAN be true.

B.  a−2c 
e - 2.e = e YES
o - 2.o = o NO

Not MUST but CAN be true.

C.  a−d 
e - o = o
o - e = o

Never a MUST, nor CAN.

D.  b+d 
e + e = e
o + o = e

MUST as its always true.

E.  a+d 
e + o = o
o + e = o

Never a MUST, nor CAN.

Answer D.

MathRevolution · Answer

a < b < c < d (consecutive)

Case I: odd < even < odd < even

Case II: even < odd < even < odd

Even = even + even = even and odd + odd = even.

Must be: only when b + d in both cases

Answer D

If a, b, c, and d are consecutive integers, and a<b<c<d, which of the

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