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If a, b, c, and d are numbers on the number line shown and if

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Intern
Joined: 10 Aug 2015
Posts: 19
If a, b, c, and d are numbers on the number line shown and if [#permalink]

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11 Jun 2016, 11:39
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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

Source: GMAT OG 2016 Quant Review

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Manager
Joined: 19 Dec 2015
Posts: 112
Location: United States
GMAT 1: 720 Q50 V38
GPA: 3.8
WE: Information Technology (Computer Software)
Re: If a, b, c, and d are numbers on the number line shown and if [#permalink]

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11 Jun 2016, 12:14
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Imagine these points represent elements on an arithmetic progression, and the equal spacing between them is k. Then, b = a+k, c = a+2k and d = a+3k. We need to calculate a+c = a+a+2k = 2a + 2k. So we need to know the values of a and k.
S1 : a+b = a+ a+k => 2a+k = -8. Not sufficient.
S2 : a+d = a + a + 3k => 2a +3k = 0. Not sufficient.

Combining both statements, we have 2 equations and 2 variables. Thus we can solve for the values of a and k. Thus C.
Intern
Joined: 02 Jun 2016
Posts: 31
Location: India
GMAT 1: 660 Q44 V36
GMAT 2: 680 Q46 V38
GPA: 3.77
WE: General Management (Computer Software)
Re: If a, b, c, and d are numbers on the number line shown and if [#permalink]

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10 Dec 2017, 06:40
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I approached by testing values-

Question- a+c=? This means, we need to know the value of a and the value of the equi-distant space between each of the points, or we need to know the value of a and c separately.

S1: It is only given that the sum of the values of a and b result to -8. So,
Case1:$$a$$ -ve and $$b$$ -ve
If a=-7 and b=-1, then a+b = -8 , distance= 6 and c= 5

Case2:$$a$$ -ve and $$b$$ +ve
If a=-10 and b=2, then a+b = -8 , distance= 12 and c= 14

Two different values for c (and hence a+c) , thus Statement 1 INSUFFICIENT.

S2: a+d = 0,
Just tells us that d=-a, or that 0 is midpoint between b and c because of the equi-distances between each pair of points.
[ ie. $$|a+b+ b/2| = |c/2 + c+d|$$ ]
So a and b are negative, while c and d are positive.
However, this doesn't provide any information about actual value of c or the value of equal distance. Hence, INSUFFICIENT.

Combining (1) and (2),
From statement 2, we know that a and b MUST be to the left of zero (negative) and 0 should be midpoint between b and c. From Statement 1, the sum of a and b should be -8.
Only a=-6 and b=-2 ( distance= 4, c=2) satisfy these conditions. (ie. if a=-7 and b=-1 then c=5, but we know from S2, that 0 has to be mid-point of b and c, so these are not correct values of a and b).
Since the values of a and b are locked, so is the value of c locked.

Hence, we can answer the question with certainty, and the statements together are SUFFICIENT.
Re: If a, b, c, and d are numbers on the number line shown and if   [#permalink] 10 Dec 2017, 06:40
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