If M and R are two numbers on a numberline,what is the value of R ?
a) The distance between R and 0 is three times the distance between M and 0
b) 12 is halfway between M and R
GMAT Prep DS Numberline
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M and R might lie anywhere on the number line.
From [1]
M = 1, R =3
M -1, R = -3
M = 2, R = 6
So we have multiple answers and hence [1] is not sufficient
From [2]
M = 5, R =17
M = 6, R = 18
M = 7, R = 19
So again we have multiple answers and [2] is not sufficient.
Combining [1] and [2],
M = 6 and R = 18 is the only answer
So [1] and [2] together are sufficient.
Whats the OA?
Thanks
From [1]
M = 1, R =3
M -1, R = -3
M = 2, R = 6
So we have multiple answers and hence [1] is not sufficient
From [2]
M = 5, R =17
M = 6, R = 18
M = 7, R = 19
So again we have multiple answers and [2] is not sufficient.
Combining [1] and [2],
M = 6 and R = 18 is the only answer
So [1] and [2] together are sufficient.
Whats the OA?
Thanks
-
- Junior | Next Rank: 30 Posts
- Posts: 22
- Joined: Tue Mar 27, 2007 6:30 am
-
- Junior | Next Rank: 30 Posts
- Posts: 22
- Joined: Tue Mar 27, 2007 6:30 am
Hi erdnah,
Is there a algebraic eqn /method for solving this . I also chose C as the answer assuming the values to be 6 and 18.
Is there a algebraic eqn /method for solving this . I also chose C as the answer assuming the values to be 6 and 18.
Of course there'll be a method to solve this, but I don't know it; if got a meeting in a min, perhaps I'll find some seconds to think about it
The important thing is, that it is asked for the distance, which can never be negative (move 0 to 12 and you should still get two - complete positive - solutions).
The important thing is, that it is asked for the distance, which can never be negative (move 0 to 12 and you should still get two - complete positive - solutions).
Statement 1 is obviously not sufficient and so is Statement# 2
Combining Statement1 and Statement2:
R HAS to lie on the positive side of zero, because 12 is in the middle of M & R.
Scenario A:
========
M lies on the positive size of 0(zero). Point P represents number 12. The points are in the following order: O M P R.
OM = x,
MP = PR = y, say. (from statement# 2)
OR = x+2y = 3(OM) (from statement #1)
x+2y = 3x, therefore x = y
Also, x+y = 12(from statement# 1). therefore x = 6 and R=18
Scenario B:
=======
M lies on the negative side of 0(zero). Point P represents number 12. The points are in the following order: M O P R
MO = x,
MP = PR = y, say (from statement# 2)
OR = 2y-x = 3OM
2y-x = 3x => y = 2x.
Also MP - OM = OP = 12
y - x = 12 => x = 12.
Therefore y = 24. Hence R is 36.
Hence the answer is E.
Combining Statement1 and Statement2:
R HAS to lie on the positive side of zero, because 12 is in the middle of M & R.
Scenario A:
========
M lies on the positive size of 0(zero). Point P represents number 12. The points are in the following order: O M P R.
OM = x,
MP = PR = y, say. (from statement# 2)
OR = x+2y = 3(OM) (from statement #1)
x+2y = 3x, therefore x = y
Also, x+y = 12(from statement# 1). therefore x = 6 and R=18
Scenario B:
=======
M lies on the negative side of 0(zero). Point P represents number 12. The points are in the following order: M O P R
MO = x,
MP = PR = y, say (from statement# 2)
OR = 2y-x = 3OM
2y-x = 3x => y = 2x.
Also MP - OM = OP = 12
y - x = 12 => x = 12.
Therefore y = 24. Hence R is 36.
Hence the answer is E.