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If integers a and b are distinct factors of 30, which of the following

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If integers a and b are distinct factors of 30, which of the following  [#permalink]

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New post 13 Dec 2015, 04:43
1
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:57) correct 39% (01:54) wrong based on 163 sessions

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If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?

I. a^b + b^2
II. (a + b)^2
III. a + b

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

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If integers a and b are distinct factors of 30, which of the following  [#permalink]

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New post 13 Dec 2015, 10:35
Bunuel wrote:
If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?

I. a^b + b^2
II. (a + b)^2
III. a + b

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Factors of 30 are 1,2,3,6,5,10,15,30.

for options 1) & 3) consider a=2 and b=1 we find then 3 ,which is a factor

but for option 2) any values doesnt melts to any factor.
eg:-if we put a=3 and b=1 then (a+b)^2 =16 which is not a factor of 30

so Ans B.
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Re: If integers a and b are distinct factors of 30, which of the following  [#permalink]

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New post 13 Dec 2015, 12:06
1
following are the factors of 30
1*30
2*15
3*10 and
6*5

consider 1 and 2 for option a ,
we have 2^1+1^2=3 which is a factor of 30

consider 10 and 5 for option c as 10 +5 =15 which is also a factor of 30
Therefore its (b)
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Re: If integers a and b are distinct factors of 30, which of the following  [#permalink]

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New post 08 Apr 2017, 07:00
Let's first consider all factors of 30, and play around with them.

30 = 1 * 30, 2 * 15, 3 * 10, 5*6

Now, we got to find out if the options provided can represent any of the above factors.

I. a^b + b^2
consider, a= 1 and b= 3 => 1^3 + 3^2 = 10 (factor of 30) (possible)

II. (a + b)^2
this basically represents a perfect square that is below 30 and is a factor of 30.
perfect squares below 30 = 1, 4, 9, 16, 25 (except 1 none of these are factors of 30, and 1 cannot be considered here) (not possible)

III. a + b
this one should be easy to validate
consider (1+2), (2+3), and (1+5) (possible)

B is the answer.
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Re: If integers a and b are distinct factors of 30, which of the following  [#permalink]

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New post 09 Apr 2017, 21:22
the answer should be B
we can check for 1. a=1 and b=3 so result will be 10 this is factor of 30 so we can eliminate option A,D,andE as well
noe left whith B and C , for B take (1+2)^2=9 is not factor of 30 so B must be the answer
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Re: If integers a and b are distinct factors of 30, which of the following  [#permalink]

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New post 11 Apr 2017, 20:05
2
Hi All,

Roman Numeral questions are relatively rare on the GMAT - you will likely see just one in the Quant section. In addition, they are often built with a 'shortcut' so that you don't actually have to do all of the work to get the correct answer. To take advantage of that potential shortcut when it's available, you have to pay attention to how the answer choices are organized.

Here, we're told that A and B are INTEGERS and that they are DISTINCT (meaning different) factors of 30. We're asked which of the three Roman Numerals CANNOT be a factor of 30 (which really means 'cannot ever be a factor of 30 no matter how many different examples we can come up with..."). The word DISTINCT is important here - in Quant questions, that means the variables are DIFFERENT numbers. If we can prove - even if it's just with one example - that an option CAN be a factor of 30, then we can eliminate that option from the answers.

To start, let's list out the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

I. A^2 + B^2

Can you pick two DIFFERENT numbers from that list for A and B here that creates another value from that list?

IF....
A=1 and B= 2, then A^2 + B^2 = 5
Thus, Roman Numeral I COULD be a factor of 30.
Eliminate Answers A, D and E.

From the remaining answer choices, we know that one of the Roman Numerals CAN be a factor of 30 and the other CANNOT, so let's deal with the easier option first....

III. A + B

Can you pick two DIFFERENT numbers from that list for A and B here that creates another value from that list?

IF....
A=1 and B= 2, then A + B = 3
Thus, Roman Numeral III COULD be a factor of 30.
Eliminate Answer C

There's only one answer left...

Final Answer:

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Re: If integers a and b are distinct factors of 30, which of the following &nbs [#permalink] 11 Apr 2017, 20:05
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If integers a and b are distinct factors of 30, which of the following

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