FOR ALL POSITIVE INTEGERS m/gmat prep

[Guest]

FOR ALL POSITIVE INTEGERS m, m(there is a box around m)= 3m(no box here m) when m is odd and m(there is a box around m)=1/2m(no box around m here) when m is even. Which of the following is equivalent to 9 times 6(there is a box around each 9 and 6).

The answer is 27.

What's the best way to solve this problem

[Guest]

Please disregard. Thanks...

[guest]

actually. i need an explanation for this.

[RonPurewal]

FOR ALL POSITIVE INTEGERS m, m(there is a box around m)= 3m(no box here m) when m is odd and m(there is a box around m)=1/2m(no box around m here) when m is even. Which of the following is equivalent to 9 times 6(there is a box around each 9 and 6).

The answer is 27.

What's the best way to solve this problem

the way you've transcribed the problem, the answer should be 81, not 27, unless the answer 27 is also in a box (which is probably the case - i bet you just forgot to mention this)
if there's a box around a 9, then, according to the rule promulgated above, that means 3 x 9, or 27.
if there's a box around a 6, then, according to that same rule, that means (1/2)(6), or 3.
27 x 3 = 81.

if the 27 you've cited as the answer is also in a box, then, since 27 is odd, that's actually 3 x 27, or 81.
if the 27 is not in a box, then it's the wrong answer.

[zdob]

What does box around M mean?

[RonPurewal]

already two extensive threads for this one

1)
different-values-of-m-t6057.html

2)
for-all-positive-integers-m-t7834.html

[shobhit.dixit]

wow. what a question. Thanks Ron for that explanation. i would have never seen it.

GMAT folks are evil....

[RonPurewal]

wow. what a question. Thanks Ron for that explanation. i would have never seen it.

GMAT folks are evil....

interestingly, the gmat doesn't really feature questions that could be honestly classified as "trick questions".
there are certainly questions that require the reader to read the problem carefully, noting any instances of notation or any specific wordings -- such as this one -- but one thing that the gmat writers DO NOT do, in general, is write problems that play on words in unusual ways, or demand that you understand unusual definitions.

for instance, in technical mathematical speak, it's perfectly okay to speak of "the sum of all numbers in a set" even if there is only one number in the set. for instance, if set T contains only the number 16, then "the sum of all numbers in set T" is 16.
the gmat will not do this to you.
also, such numbers as 0, -5, etc. are technically multiples of 5, but the gmat will also stay away from testing you on that sort of thing, too.

so the problem writers aren't really as evil as you might think -- you just have to be really careful when you go over the problems.

[salman30]

wow. what a question. Thanks Ron for that explanation. i would have never seen it.

GMAT folks are evil....

interestingly, the gmat doesn't really feature questions that could be honestly classified as "trick questions".
there are certainly questions that require the reader to read the problem carefully, noting any instances of notation or any specific wordings -- such as this one -- but one thing that the gmat writers DO NOT do, in general, is write problems that play on words in unusual ways, or demand that you understand unusual definitions.

Very tricky - thanks Ron!

for instance, in technical mathematical speak, it's perfectly okay to speak of "the sum of all numbers in a set" even if there is only one number in the set. for instance, if set T contains only the number 16, then "the sum of all numbers in set T" is 16.
the gmat will not do this to you.
also, such numbers as 0, -5, etc. are technically multiples of 5, but the gmat will also stay away from testing you on that sort of thing, too.

so the problem writers aren't really as evil as you might think -- you just have to be really careful when you go over the problems.

[RonPurewal]

salman30, did you actually type a response to that post?

nothing was in your most recent post, other than an exact quote of my post from upthread; there were no words/questions/comments of your own.