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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: 18
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
7
31
00:00

Difficulty:

65% (hard)

Question Stats:

65% (01:37) correct 35% (01:50) wrong based on 579 sessions

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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:

teste.jpg [ 19.96 KiB | Viewed 6514 times ]
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
22
8
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: 36
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
2
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.
Manager
Joined: 10 Sep 2014
Posts: 70
Re: If a, b, c, and d are numbers on the number line shown and if [#permalink]

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01 Jun 2018, 09:58
Bunuel, VeritasPrepKarishma, ScottTargetTestPrep could you share your approach for this problem please? Thanks.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
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Posts: 2738
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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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05 Jun 2018, 10:28
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

Attachment:
teste.jpg

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

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Manager
Joined: 08 Apr 2017
Posts: 82
If a, b, c, and d are numbers on the number line shown and if [#permalink]

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10 Jun 2018, 18:11
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

Source: GMAT OG 2016 Quant Review

Attachment:
teste.jpg

This is how it's spaced

a b c d

Let a = x and the spacing between a & b = y. Since, they are equally spaced, the spacing between b & c and c & d is also y.

So lets convert this in terms of x & y

a = x

b = x + y

c = x + 2y

d = x + 3y

We want a + c => x + (x + 2y) = 2x + 2y {we basically need the values for x & y}

Now, lets looks at each statement:

A -> a + b = -8
By using the above expression we get
x + (x + y) = -8 ........... (1)

This is clearly insufficient as we have both x & y in the expression

b -> a + d = 0
By using the above expression we get
x + (x + 3y) = 0 ............ (2)

This is clearly insufficient as we have x in terms of y.

On combining (1) & (2)
we get the values of x & y.

If a, b, c, and d are numbers on the number line shown and if   [#permalink] 10 Jun 2018, 18:11
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