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05/02/2006 03:10:11 PM · #26 |
| I get 18 for the first one and 1/5 for the second one. |
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05/02/2006 03:10:39 PM · #27 |
I would guess the OP= Original Poster.
Here is my go at Problem #1
[9]x[6]=[m]
[9] is odd, therefore [9]= 3x m or dividing both sides by 3,
1/3 x 9= m which is 3 in this case.
[6] is even, therefore [6]= 1/2m or multiplying both sides by 2,
2x 6= m which is 12 in this case.
Now subsitituting into the original equation, but remember we are now in terms of m, not [m].
3x 12= m = 36.
So the next step is to convert m to [m].
If [m] is odd, [m]= 3x m or 3x 36 or 108 which is not odd.
If [m] is even, [m]= 1/2m or 1/2 x 36 or 18 which is even.
Thus, the answer should be [18].
Message edited by author 2006-05-02 15:12:10. |
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05/02/2006 03:12:52 PM · #28 |
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05/02/2006 03:19:04 PM · #29 |
Ok, so for the first one we have 18 and 81.... coincidence?? I think not.
However, I propose that the time has come to negotiate / settle this fairly. How about splitting the difference? (18+81)/2= 49.5 that way we can start bringing in standard deviations and probability of correctness..... and really confuse GMAT.
E
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05/02/2006 03:35:36 PM · #30 |
I think we are in agreement that the second is 1/5th.
However, I disagree on the first answer. I think it is 18 in a box. here is why:
for odd numbers boxM=3M
therefore the integer in box9 is 3
for even numbers boxM=M/2
therefore the integer in box6 is 12
therefore the integer resulting from (box9) x (box6) = 3 x 12 = 36
since 36 is even, the rule is box(1/2M)
Therefore the answer is box18
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05/02/2006 03:41:17 PM · #31 |
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05/02/2006 03:43:04 PM · #32 |
Originally posted by jemison:
I think we are in agreement that the second is 1/5th.
However, I disagree on the first answer. I think it is 18 in a box. here is why:
for odd numbers boxM=3M
therefore the integer in box9 is 3
for even numbers boxM=M/2
therefore the integer in box6 is 12
therefore the integer resulting from (box9) x (box6) = 3 x 12 = 36
since 36 is even, the rule is box(1/2M)
Therefore the answer is box18 |
I think that, perhaps, you are working backwards w.r.t. everyone else. The box notation would represent a function, so 9 in a box equates to 27 and 6 in a box equates to 3 etc.
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05/02/2006 03:53:20 PM · #33 |
| The answers are 27 and 1/5. Thanks everyone that took the time to post an explanation! Out of 300+ problems, these two were the nasty ones for me. |
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05/02/2006 03:57:29 PM · #34 |
Originally posted by General:
Answer to the second should be 1/5th,
Lets suppose she saved a $ every month, hence in a year she saved 12a$.
Lets suppose she spent b$ every month.
Lets suppose her salary was C$,C= a+b, (saving +expense)per month.
as per statement , she saves 12a$ in one year. This is equal to 3 times what she did not take home i.e. b.
12a$=3b$ or 4a$=b$
C= a+b or c= 4a +a = 5a
a=c/5 |
This is a really nice way to solve it. Thanks! |
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05/02/2006 03:57:43 PM · #35 |
BTW , where are you preparing from, for GMAT exam
Message edited by author 2006-05-02 15:58:33. |
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05/02/2006 04:10:49 PM · #36 |
Originally posted by General:
BTW , where are you preparing from, for GMAT exam |
I'm taking it in San Diego this coming Thursday. I live in Encinitas; though I'm moving to Italy on Saturday. :) |
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05/02/2006 04:15:10 PM · #37 |
Originally posted by Spazmo99:
Originally posted by posthumous:
Originally posted by Spazmo99:
Do you teach math?? |
ha! no, just trying to help the OP really understand the problem instead of just solving it. |
OK, well, I was pretty confused by all the added variables. My math teacher used to do that too. |
Sorry, I'm a conceptual thinker.
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05/03/2006 06:53:20 AM · #38 |
The correct answer for the first one is [27], not [18] or [81].
[9] = 3x9 = 27 (because 9 is odd)
[6] = 6/2 = 3 (because 6 is even)
Therefore [9] x [6] = 27 x 3 = 81 (NOT in a box)
For a small number of options, it's straightforward to evaluate each answer and see which of these equals 81.
[81] = 3 x 81 = 243
[54] = 54 / 2 = 27
[36] = 36 / 2 = 18
[27] = 3 x 27 = 81
[18] = 18 / 2 = 9
Showing that only the fourth of these options, [27], is equal to 81.
But if the number of options is larger and/or it's not feasible to evaluate them all, then we can work the problem the second half of the problem another way:
We want to find a number z such that [z] = 81. Based on the rules given, [z] = 81 if and only if one of the following statements is true:
(a) z is odd AND 3z = 81
OR
(b) z is even AND z/2 = 81
Looking at (a) 3z=81 is true when z=27, and 27 is odd, so this is a possible solution.
Looking at (b) z/2=81 is true when z = 162, and 162 is even, so this is also a possible solution.
Therefore [9] x [6] = [27] = [162] = 81
So it is a matter of seeing whether [27] or [162] is on the list (oh, and looking for an option like "both (b) and (d) above" :)
The answer for the second is 1/5 - no need for me to repeat the complete and accurate reasonings given earlier.
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05/03/2006 10:50:40 AM · #39 |
I get [18] for the first answer. Here is my rationale:
The rules say that [M] = 3m if m is odd and 1/2m if m is even.
So, m must be either 1/3[M] and odd, or 2[M] and even.
So for [9], m could be either 3 (which is 1/3[9] and odd) or 18 (which is 2[9] and even)
For [6], m can only be 12 (which is 2[6] and even). It cannot be 1/3[6] because 2 is not odd and therefore wouldn't satisfy the rule.
So, the result value of m for [9] X [6] is either 36 ( 3x12 ) or 216 ( 18x12 )
If m = 36 then [M] = [18] (1/2m because m is even); if m = 216, then [M] = [108] ( 1/2m because m is even ). So the answer [M] could be either [18] or [108].
Since [108] is not one of the answers listed but [18] is, then [18] is the only correct choice available. |
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05/03/2006 11:01:35 AM · #40 |
Originally posted by RonB:
I get [18] for the first answer. Here is my rationale:
The rules say that [M] = 3m if m is odd and 1/2m if m is even.
So, m must be either 1/3[M] and odd, or 2[M] and even.
So for [9], m could be either 3 (which is 1/3[9] and odd) or 18 (which is 2[9] and even)
For [6], m can only be 12 (which is 2[6] and even). It cannot be 1/3[6] because 2 is not odd and therefore wouldn't satisfy the rule.
So, the result value of m for [9] X [6] is either 36 ( 3x12 ) or 216 ( 18x12 )
If m = 36 then [M] = [18] (1/2m because m is even); if m = 216, then [M] = [108] ( 1/2m because m is even ). So the answer [M] could be either [18] or [108].
Since [108] is not one of the answers listed but [18] is, then [18] is the only correct choice available. |
I think you are working at it backwards - think of the box as a map f:Z->Z
so [m] = f(m) = {3m if m is odd; 1/2 m if m is even}
Your logic is dealing with the inverse of f (which isn't well defined), I don't think that is what the question asks.
[9][6] = f(9)*f(6) = (3*9) * (6/2) = 81. To write that in terms of f(x) for some x we see that f(27) = 3*27 = 81 or f(162) = 162/2 = 81, or in the strange stupid notation of the question [27] or [162]. |
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