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If m and r are two numbers on a number line, what is the value of r?
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18 Dec 2009, 15:27
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If m and r are two numbers on a number line, what is the value of r? (1) The distance between r and 0 is 3 times the distance between m and 0. (2) 12 is halfway between m and r.
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Re: If m and r are two numbers on a number line, what is the value of r?
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18 Dec 2009, 17:49
TIP:On the GMAT we can often see such statement: \(k\) is halfway between \(m\) and \(n\) on the number line. Remember this statement can ALWAYS be expressed as: \(\frac{m+n}{2}=k\). Also on the GMAT when we see the distance between x and y, this can be expressed as \(xy\). BACK TO THE QUESTION.If m and r are two numbers on a number line, what is the value of r?(1) The distance between r and zero is 3 times the distance between m and zero > \(r0=3m0\) > \(r=3m\) > \(r=3m\) OR \(r=3m\). Clearly insufficient. (2) 12 is halfway between m and r > \(\frac{r+m}{2}=12\) > \(r+m=24\). Clearly insufficient. (1)+(2) \(r=3m\) OR \(r=3m\) and \(r+m=24\). \(r=3m\) > \(r+m=3m+m=24\) > \(m=6\) and \(r=18\) OR \(r=3m\) > \(r+m=3m+m=24\) > \(m=12\) and \(r=36\) Two different values for \(r\). Not sufficient. Answer: E.
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Re: If m and r are two numbers on a number line, what is the value of r?
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19 Dec 2009, 04:04
xcusemeplz2009 wrote: bth the statments are not suff...
s1) let m0=x, then r0=3x ( x can be 1,2,3,4,......anything)...not suff s2) m12=12r or r12=12m....(can have any value)...not suff
s1)+s2)if m12=1,2,3,4,5.... then 12r=3,6,9,12,15...any thing same for r12...hence from bth also we are not getting any particular value so E The answer is correct, but there is some problems in solution: (1) When you write: m=x and r=3x, it's not right: if m=x, then r=3x OR r=3x, as r=3m. (2) You wrote: m12=12r or r12=12m. If you look at it you'll see that these two equations are the same and derived from \(\frac{m+r}{2}=12\). Again: Statement: distance between r and x, is three times the distance between m and x can be expressed as \(rx=3mx\). Statement: \(k\) is halfway between \(m\) and \(r\) on the number line can be expressed as: \(\frac{m+r}{2}=k\).
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Re: If m and r are two numbers on a number line, what is the value of r?
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20 Dec 2009, 05:28
Bunuel wrote: xcusemeplz2009 wrote: bth the statments are not suff...
s1) let m0=x, then r0=3x ( x can be 1,2,3,4,......anything)...not suff s2) m12=12r or r12=12m....(can have any value)...not suff
s1)+s2)if m12=1,2,3,4,5.... then 12r=3,6,9,12,15...any thing same for r12...hence from bth also we are not getting any particular value so E The answer is correct, but there is some problems in solution: (1) When you write: m=x and r=3x, it's not right: if m=x, then r=3x OR r=3x, as r=3m. (2) You wrote: m12=12r or r12=12m. If you look at it you'll see that these two equations are the same and derived from \(\frac{m+r}{2}=12\). Again: Statement: distance between r and x, is three times the distance between m and x can be expressed as \(rx=3mx\). Statement: \(k\) is halfway between \(m\) and \(r\) on the number line can be expressed as: \(\frac{m+r}{2}=k\). thanks bunuel i cud not express it in a correct manner , but my intention was same since i tried on no. line and i got it in a easier way ,however cudn't express that in my post(appologies for that), on a no. line it was clear that the position of m and r is not fix with bth the given information hence insuff....
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Re: If m and r are two numbers on a number line, what is the value of r?
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07 Jan 2010, 12:49
IMO ... E.. Question: wat is r? ST1: The distance between r and 0 is 3 times the distance between m and 0 Since the statement has the term 'distance' in it, it signifies that we are not consider the ve or +ve possibility of the number position. Hence ST1 can be written algebrically as: r0 = 3m0 > r = 3m Clearly NOT SUFF as m could be anything and even if m is constant, r could be 3m or 3m ST2: 12 is halfway between m & r is clearly NOT SUFF as the same is true for (m=11,r = 13) , (m=10,r = 14).... Both ST1 and ST2 together would give us: m = 6 and r = 18, m=12 & r = 36 ...etc..Hence NOT SUFF.... OA as D.... ... Not sure..
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Re: If m and r are two numbers on a number line, what is the value of r?
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23 Mar 2011, 06:05
nikhilsrl wrote: If m and r are two numbers on a number line, what is the value of r? 1) The distance between r and 0 is 3 times the distance between m and 0. 2) 12 is halfway between m and r. OA is provided. I somehow remembered the answer for this question. Try m=6 and r=18. r=3m and 12 is midway OR m=12 and r=36; r=3*m and 12 is midway I don't remember any algebraic solution for this, but it would be great. Ans: "E"
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Re: If m and r are two numbers on a number line, what is the value of r?
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25 Mar 2011, 11:05
nikhilsrl wrote: If m and r are two numbers on a number line, what is the value of r? 1) The distance between r and 0 is 3 times the distance between m and 0. 2) 12 is halfway between m and r.
I used the number line and tested two cases. Case 1. Assume m is negative and r is positive, each dashed segments  is 1x m  0    r m = x r = 3x (3 times the distance between m and 0) If 12 is the midpoint, the graph becomes: m  0  12   r That means x = 12 and m = 12 and r = 36 Case 2. Assume both m and r are positive 0  m   r m = x r = 3x Add 12 as the mid point: 0  m  12  r Therefore m = 6 and r = 18 This shows that even if you combine the 2 statements, you still can't get a unique answer. Therefore the answer should be E.



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Re: If m and r are two numbers on a number line, what is the value of r?
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10 Nov 2011, 03:39
SwapnilRanadive wrote: Another DS good example
If m and r are two numbers on number line, what is the value of r? 1) The distance between r and 0 is 3 times the distance between m and 0 2) 12 is halfway between m and r *Edited the question. It should be r instead of n. Stmnt 1 alone: Too many values possible. Say r = 3, m = 1 OR r= 6, m = 2 etc Stmnt 2 alone: Again too many values possible. Think 12 is in the middle. m and r are equidistant from it so m = 11, r = 13 OR m = 10, r = 14 etc Both together: Focus on the logic behind it. You don't need to do any calculations. We are looking for two values equidistant from 12. Let's say both m and r are at 12 initially. Their distance from 0 is the same i.e. 12 at this point. As they both start moving away from 12 simultaneously, the distance of m from 0 is reducing and that of r from 0 is increasing. There will be point when the distance of m from 0 will be a third of the distance of r from 0. This will be our first pair (shown in blue). Let's say they keep moving. m will finally reach 0 when its distance from 0 is 0 while r will be at 24. Then m will move in the negative range and its distance from 0 will start increasing. Distance of r from 0 is continuing to increase. There will be a point again when distance of m from 0 is a third of the distance of r from 0 (shown in red). Attachment:
Ques4.jpg [ 7.07 KiB  Viewed 8174 times ]
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Re: If m and r are two numbers on a number line, what is the value of r?
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16 Nov 2011, 07:27
VeritasPrepKarishma wrote: SwapnilRanadive wrote: Another DS good example
If m and r are two numbers on number line, what is the value of r? 1) The distance between r and 0 is 3 times the distance between m and 0 2) 12 is halfway between m and r *Edited the question. It should be r instead of n. \(ab=c\) > Distance of \(a\) from \(b\) equals \(c\) Question: r=? Statement 1:\(r0=3*m0\) > \(r=3*m\) or \(r=3*m\), \(r\) depends on \(m\), and since we don't know \(m\), Insufficient.Statement 2:Number line is like a set with consecutive numbers. Since this set is an evenly spaced set we know that median=average. Because 12 is halfway of \(m\) and \(r\) : \(12=\frac{m+r}{2}\) > \(m+r=24\), Insufficient.Statement 1+2:\(r=3*m\) > \(r=3*(24r)\) > \(r=18\) \(r=3*m\) > \(r=3*(24r)\) > \(r=36\) Therefore Insufficient and the correct answer is E.



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Re: If m and r are two numbers on a number line, what is the value of r?
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04 Jan 2012, 06:33
Janealams wrote: Can somebody explain this to me please. stmnt1: let m = 4 then r = 12 let m = 6 then r = 18 Hence insuff stmnt2: We can have different combinations for this as well m= 10 and r = 14 m = 6 and r = 18 Hence insuff taking together when m = 6 then r = 18 and 12 is halfway between m and r also for m = 12 r = +36, 12 is halfway of m and r and r = 3 times the distance from 0 and m (distance is +ve value)



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Re: If m and r are two numbers on a number line, what is the value of r?
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29 Jan 2012, 11:00
Algebraically this can be solved as a system of two equations
r = 3m
\(\frac{m+r}{2}=12\)
1) m=6; r=18 2) m=12; r=36
Not sufficient, so the answer is E



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Re: If m and r are two numbers on a number line, what is the value of r?
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04 Mar 2013, 02:10
arjtryarjtry wrote: If m and r are two numbers on a number line, what is the value of r?
(1) The distance between r and 0 is 3 times the distance between m and 0. (2) 12 is halfway between m and r STAT1. Firstly, we dont know the value of m. So r being 3times m will not help.Also, r can be positive or negative so we are not sure about the value of r. So, INSUFFICIENT STAT2. 12 is halfway between m and r. Now. There are four cases. 1. Both m and r are positive. 2. Both m and r are negative 3. m is positive and r is negative 4. m is negative and r is positive So, NOT SUFFICIENT Taking both together: Still all the four cases mentioned in statement 2 are possible. So NOT SUFFICIENT. Answer will be E Hope it helps!
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Re: If m and r are two numbers on a number line, what is the value of r?
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16 Apr 2014, 07:45
TIP: On the GMAT we can often see such statement: k is halfway between m and n on the number line. Remember this statement can ALWAYS be expressed as: \frac{m+n}{2}=k. Also on the GMAT when we see the distance between x and y, this can be expressed as xy. Back to the question: If m and r are two numbers on a number line, what is the value of r? (1) The distance between r and zero is 3 times the distance between m and zero > r0=3m0 > r=3m > r=3m OR r=3m. Clearly insufficient. (2) 12 is halfway between m and r > \frac{r+m}{2}=12 > r+m=24. Clearly insufficient. (1)+(2) r=3m OR r=3m and r+m=24. r=3m > r+m=3m+m=24 > m=6 and r=18 OR r=3m > r+m=3m+m=24 > m=12 and r=36 Two different values for r. Not sufficient. Answer: E. tnx lot for this
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Re: If m and r are two numbers on a number line, what is the value of r?
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27 Apr 2014, 20:28
Bunuel wrote: TIP: On the GMAT we can often see such statement: \(k\) is halfway between \(m\) and \(n\) on the number line. Remember this statement can ALWAYS be expressed as:
\(\frac{m+n}{2}=k\).
Also on the GMAT when we see the distance between x and y, this can be expressed as \(xy\).
Back to the question: If m and r are two numbers on a number line, what is the value of r?
(1) The distance between r and zero is 3 times the distance between m and zero > \(r0=3m0\) > \(r=3m\) > \(r=3m\) OR \(r=3m\). Clearly insufficient.
(2) 12 is halfway between m and r > \(\frac{r+m}{2}=12\) > \(r+m=24\). Clearly insufficient.
(1)+(2) \(r=3m\) OR \(r=3m\) and \(r+m=24\).
\(r=3m\) > \(r+m=3m+m=24\) > \(m=6\) and \(r=18\) OR \(r=3m\) > \(r+m=3m+m=24\) > \(m=12\) and \(r=36\)
Two different values for \(r\). Not sufficient.
Answer: E. Bunuel, can you explain how \(r=3m\) > \(r=3m\) OR \(r=3m\)?



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Re: If m and r are two numbers on a number line, what is the value of r?
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28 Apr 2014, 03:24
TooLong150 wrote: Bunuel wrote: TIP: On the GMAT we can often see such statement: \(k\) is halfway between \(m\) and \(n\) on the number line. Remember this statement can ALWAYS be expressed as:
\(\frac{m+n}{2}=k\).
Also on the GMAT when we see the distance between x and y, this can be expressed as \(xy\).
Back to the question: If m and r are two numbers on a number line, what is the value of r?
(1) The distance between r and zero is 3 times the distance between m and zero > \(r0=3m0\) > \(r=3m\) > \(r=3m\) OR \(r=3m\). Clearly insufficient.
(2) 12 is halfway between m and r > \(\frac{r+m}{2}=12\) > \(r+m=24\). Clearly insufficient.
(1)+(2) \(r=3m\) OR \(r=3m\) and \(r+m=24\).
\(r=3m\) > \(r+m=3m+m=24\) > \(m=6\) and \(r=18\) OR \(r=3m\) > \(r+m=3m+m=24\) > \(m=12\) and \(r=36\)
Two different values for \(r\). Not sufficient.
Answer: E. Bunuel, can you explain how \(r=3m\) > \(r=3m\) OR \(r=3m\)? \(r=3m\) means that the distance from r to 0 is thrice the distance from m to 0: 0mr rm0 m0r r0m If r and m have the same sign (cases A and B), then r=3m but if r and m have different signs (cases C and D), then r=3m. Hope it's clear.
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Re: If m and r are two numbers on a number line, what is the value of r?
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07 Mar 2016, 12:21
1) m=6; r=18 2) m=12; r=36
Not sufficient,
E



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