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integers property

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Dec 05, 2014 5:52 pm
For all positive integers m, [m]=3m when m is odd and [m]=(1/2)m when m is even. What is [9] x [6] equivalent to?

A. [81]
B. [54]
C. [37]
D. [27]
E. [18]
[9] x [6] = ??

9 is ODD, so [9] = (3)(9) = 27
6 is EVEN, so [6] = 6/2 = 3
So, [9] x [6] = 27 x 3 = 81

However, the answer choices are as follows:

a) [81]
b) [54]
c) [37]
d) [27]
e) [18]

So, which of these equals 81?

27 is ODD, so [27] = (3)(27) = 81

So, the correct answer is D

Cheers,
Brent
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by [email protected] » Fri Dec 05, 2014 11:29 pm
Hi chacha0212,

This is an example of a symbolism question (you'll likely see 1 on Test Day, but you might see 2 depending on the Randomizer). Brent's solution is spot on, so I won't rehash that here. Symbolism questions are essentially a set of "instructions" telling you how a symbol "works"; you're then asked to perform some calculation using the symbol in question (the math involved is usually some type of basic algebra or arithmetic, so the work won't be hard).

In symbolism questions, you have to pay very careful attention to the details. I tend to sketch a quick example on my pad of what the symbol means before I tackle the specific question that's asked. Here, I would write:

[m] = 3m when m is ODD

[5] --> 15

[m] = m/2 when m is EVEN

[4] --> 2

From here, doing the work that's required to answer the given prompt isn't too tough.

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by jain2016 » Tue Jan 12, 2016 9:46 am
However, the answer choices are as follows:

a) [81]
b) [54]
c) [37]
d) [27]
e) [18]

So, which of these equals 81?

27 is ODD, so [27] = (3)(27) = 81

So, the correct answer is D

Hi Brent ,

Can you please explain the above part. I really don't understand.

Thanks in advance.

SJ
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by Brent@GMATPrepNow » Tue Jan 12, 2016 10:37 am
jain2016 wrote:
However, the answer choices are as follows:

a) [81]
b) [54]
c) [37]
d) [27]
e) [18]

So, which of these equals 81?

27 is ODD, so [27] = (3)(27) = 81

So, the correct answer is D

Hi Brent ,

Can you please explain the above part. I really don't understand.

Thanks in advance.

SJ
Many students correctly evaluate [9] x [6] to get:
[9] x [6] = 27 x 3 = 81
So, the correct answer is 81. But the answer choices are not listed as actual numbers.
That is, they are NOT given as A) 81, B) 54, C) 37, etc.
Instead they are listed as numbers WITHIN BRACKETS.
Since 81 is not the same as [81], we must find and answer choice that has the same value as 81.


Since 27 is ODD, we know that [27] = (3)(27) = 81
So, the correct answer is [27], which happens to equal 81

I hope that helps.

Cheers,
Brent
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