Spotting "Distance from 0" in the Statements immediately makes you think about Absolute Value:
Absolute Value of [R] = the Distance of the Number R from 0-Zero on the Number Line
[M] = the Distance of the Number M from 0-Zero on the Number Line
What is the Value of R?
S1: Distance b/w R and 0 = (3) * (Distance b/w M and 0)
[R] = 3 * [M]
if M = 1
R = +3 or R = -3 ------either Satisfy Statement 1. Not Sufficient.
S2: 12 is Halfway between M and R
shout out to
IanStewart for his Note Collections. One section covers this type of problem (and all of Coordinate Geometry) very thoroughly and in detail.
Rule: the Average of 2 Numbers will always be the Mid-Point ("halfway") between those 2 Numbers
So statement 2 is telling us that the Average of M and R = 12
(M + R)/2 = 12
M + R = 24
M could = 10 ---------> R could = 14
M could = 8 ---------> R could = 16
Not Sufficient
The hard part - Together:
S1: [R] = 3[M]
S2: R + M = 24
Thinking in terms of (+)positive and (-)negative numbers, for the first case we can try when M < 0:
[M] = (-)M
Let R = (+)Positive
R = 3 * (-M)
R = -3M
---Substitute into Statement 2----
-3M + M = 24
-2M = 24
M = -12 ----------> Since we assumed R is Positive, R would be = +36, which is 3 Times the Distance from 0 that -12 is.
Is 12 the Halfway Point between M = -12 and R = +36?
M = -12 ------> 24 Units away from 12
R = + 36 ------> 24 Units away from 12
Yes, 12 is the Halfway Point:
M = -12 and R = +36 are Valid. R can = 36.
Case 2: Let M >0 and R > 0 for this Case
R = 3M
R + M = 24
---substituting again----
3M + M = 24
4M = 24
M = +6 -------> Since we assumed R>0, Positive R would have to be 3 Times as far from 0. R would have to be = 18
12 is the Halfway Point between M = +6 and R = +18 (Statement 2 Satisfied also)
M can = +6
and
R can = +18
Since we have 2 Possible Values for R: (18 or 36) : even together the Statements are NOT Sufficient
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