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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 Attachment:
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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.



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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 equidistant 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 equidistances 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 midpoint 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. Hence, answer= C.




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