Hi,
I got this question on a MGMAT CAT exam. I don't really understand the explanation they provided to the problem...Can anyone help shed some light on this? Or perhaps an alternate method to solve?
Thanks
Joan, Kylie, Lillian, and Miriam all celebrate their birthdays today. Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women today?
A)51
B)52
C)53
D)54
E)55
Anwser:
D
t may be easiest to represent the ages of Joan, Kylie, Lillian and Miriam (J, K, L and M) on a number line. If we do so, we will see that the ages represent consecutive integers as shown in the diagram.
Since the ages are consecutive integers, they can all be expressed in terms of L: L, L + 1,
L + 2, L + 3. The sum of the four ages then would be 4L + 6. Since L must be an integer (it’s Lillian’s age), the expression 4L + 6 describes a number that is two more than a multiple of 4:
4L + 6 = (4L + 4) + 2
[4L + 4 describes a multiple of 4, since it can be factored into 4(L + 1) or 4 * an integer.]
54 is the only number in the answer choices that is two more than a multiple of 4 (namely, 52).
The correct answer is D.
I got this question on a MGMAT CAT exam. I don't really understand the explanation they provided to the problem...Can anyone help shed some light on this? Or perhaps an alternate method to solve?
Thanks
Joan, Kylie, Lillian, and Miriam all celebrate their birthdays today. Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women today?
A)51
B)52
C)53
D)54
E)55
Anwser:
D
t may be easiest to represent the ages of Joan, Kylie, Lillian and Miriam (J, K, L and M) on a number line. If we do so, we will see that the ages represent consecutive integers as shown in the diagram.
Since the ages are consecutive integers, they can all be expressed in terms of L: L, L + 1,
L + 2, L + 3. The sum of the four ages then would be 4L + 6. Since L must be an integer (it’s Lillian’s age), the expression 4L + 6 describes a number that is two more than a multiple of 4:
4L + 6 = (4L + 4) + 2
[4L + 4 describes a multiple of 4, since it can be factored into 4(L + 1) or 4 * an integer.]
54 is the only number in the answer choices that is two more than a multiple of 4 (namely, 52).
The correct answer is D.
