ramonguib wrote:
If a, b, c, and d are numbers on the number line shown and if the tick marks are equally spaced, what is the value of a +c ?
(1) a + b = -8
(2) a + d = 0
We need to determine the value of a + c. Notice that b is the midpoint of a and c, thus b =
(a + c)/2. So if we know the value of b, then we can determine a + c.
Statement One Alone:
a + b = -8
We see that we don’t have sufficient information to answer the question. For example, if a = -5 and b = -3, then c = -1 and a + c = -6. However, if a = -6 and b = -2, then c = 2 and a + c = -4. Statement one alone is not sufficient.
Statement Two Alone:
a + d = 0
Since the numbers are evenly spaced, we see that if a + d = 0, then b + c = 0. However, we still can’t determine the value of a + c. For example, if a = -3 and d = 3, then b = -1 and c = 1 and a + c = -2. However, if a = -6 and d = 6, then b = -2 and c = 2 and a + c = -4. Statement two alone is not sufficient.
Statements One and Two Together:
Recall that b = (a + c)/2. Therefore, from statement one, if a + b = -8, then
a + (a + c)/2 = -8
a + a/2 + c/2 = -8
2a + a + c = -16
3a + c = -16
Similarly, from statement two, if b + c = 0, then
(a + c)/2 + c = 0
a/2 + c/2 + c = 0
a + c + 2c = 0
a + 3c = 0
Adding 3a + c = -16 and a + 3c = 0, we have
4a + 4c = -16
a + c = -4
Answer: C
_________________
★
★
★
★
★
250 REVIEWS
5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews