The sum of the four integers a, b, c, and d is 24. How many of these

Question

The sum of the four integers a, b, c, and d is 24. How many of these integers are even?

(1) a + b = 11

(2) b + c = 12

zhanbo · Answer

(1) Only
a + b = 11
One must be even, and the other must be odd.
=> c + d = 13
One must be even, and the other must be odd.
So, two of these integers are even. 
Sufficient

(2) Only
b + c = 12
b and c can be two odd integers, or two even integers. 
Not sufficient.

The answer is thus  (A) .

Zazen89 · Answer

Q) a+b+c+d=24

1.a+b=11----> either a or b is even
c+d=13 ----> either c or d is even
 thus 2 integers are even...... Sufficient

2. b+c=12 -----> b and c both can be either odd or even
 a+d= 12------> a and d both can be either odd or even
Thus insufficient

Answer: A

eeshajain · Answer

Please explain why aren't we considering the possiblity of zero being one of the integers?

considering zero as a possible integer
1) a+b=11
a=0, b=1
c+d = 13
c = 1, d=23

in this scenario we have only 1 even integer.

Bunuel · Answer

Your example has arithmetic mistakes. Also, note that 0 IS an even integer, so zero can be one of the integers.

If a + b = 11 and you set a = 0, then b must be 11, not 1.

Then c + d = 13 must be odd, so c and d must be one odd and one even. For example, c = 1 and d = 12.

So even with zero allowed, you still get exactly two even integers: a = 0 and d = 12.

ZERO:

1. Zero is an  INTEGER .

2. Zero is an  EVEN  integer.

3. Zero is  neither positive nor negative  (the only one of this kind)

4. Zero is  divisible by EVERY integer except 0 itself  ( \frac{0}{x} = 0 , so 0 is a divisible by every number, x).

5. Zero is a  multiple of EVERY integer  ( x*0 = 0 , so 0 is a multiple of any number, x)

6. Zero is  NOT a prime number  (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed:  anything/0 is undefined .

8. Any non-zero number  to the power of 0 equals 1  ( x^0 = 1 )

9.  0^0  case is  NOT tested on the GMAT .

10. If the exponent n is positive (n > 0),  0^n = 0 .

11. If the exponent n is negative (n < 0),  0^n  is undefined, because  0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0} , which is undefined.  You CANNOT take 0 to the negative power .

12.  0! = 1! = 1 .

Hope it helps.

The sum of the four integers a, b, c, and d is 24. How many of these

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The sum of the four integers a, b, c, and d is 24. How many of these

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