GmaT Practice Exam 6 - Primefactors

Question

Hello BTG

Got the following question yesterday in the Practice exam 6.
It seem to me, that it is asking for all primefactors less than 100.
But is there a way to quickly calculate this, as I image listing them up and counting is not the best approach.

Thanks in advance

GMATGuruNY · Answer

How many positive integers less than 100 are neither multiples of 2 nor multiples of 3?

a)30
b)31
c)32
d)33
e)34

WRITE IT OUT and LOOK FOR A PATTERN.

1, 2, 3
4, 5, 6
7, 8, 9
10, 11, 12

As illustrated by the values in red, 1 of every 3 positive integers is neither even nor a multiple of 3.
Thus, of the 99 positive integers less than 100, exactly 1/3 will be neither even nor a multiple of 3:
(1/3)(99) = 33.

The correct answer is D.

Brent@GMATPrepNow · Answer

How many positive integers less than 100 are neither multiples of 2 nor multiples of 3?

a)30
b)31
c)32
d)33
e)34

WRITE IT OUT and LOOK FOR A PATTERN.

1, 2, 3
4, 5, 6
7, 8, 9
10, 11, 12

As illustrated by the values in red, 1 of every 3 positive integers is neither even nor a multiple of 3.
Thus, of the 99 positive integers less than 100, exactly 1/3 will be neither even nor a multiple of 3:
(1/3)(99) = 33.

The correct answer is D.

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OptimusPrep · Answer

lucas211 wrote:Hello BTG

Got the following question yesterday in the Practice exam 6.
It seem to me, that it is asking for all primefactors less than 100.
But is there a way to quickly calculate this, as I image listing them up and counting is not the best approach.

How many positive integers less than 100 are neither multiples of 2 nor multiples of 3?

a)30
b)31
c)32
d)33
e)34

Thanks in advance

I am not sure what you meant by saying "it is asking for all prime factors less than 100"
Are you saying that the question is asking about prime factors of 100??

As for the question, the best way would be to write the numbers down and find a pattern.
Numbers less than 100 that are neither multiples of 2 or 3.

Multiples of 2 = 2, 4, ... 98 - 49 numbers
Multiples of 3 = 3, 6, 9, ... 99 = 33
Multiples of 6 - 6, 12, ... 96 - 16numbers

Hence total numbers that are either multiples of 2 or 3 = 49 + 33 - 16 = 66
Hence numbers that are not multiples of 2 or 3 = 99 - 66 = 33

Correct Option: D

lucas211 · Answer

OptimusPrep wrote:lucas211 wrote:Hello BTG Got the following question yesterday in the Practice exam 6. It seem to me, that it is asking for all primefactors less than 100. But is there a way to quickly calculate this, as I image listing them up and counting is not the best approach. How many positive integers less than 100 are neither multiples of 2 nor multiples of 3? a)30 b)31 c)32 d)33 e)34 Thanks in advance I am not sure what you meant by saying "it is asking for all prime factors less than 100" Are you saying that the question is asking about prime factors of 100?? As for the question, the best way would be to write the numbers down and find a pattern. Numbers less than 100 that are neither multiples of 2 or 3. Multiples of 2 = 2, 4, ... 98 - 49 numbers Multiples of 3 = 3, 6, 9, ... 99 = 33 Multiples of 6 - 6, 12, ... 96 - 16numbers Hence total numbers that are either multiples of 2 or 3 = 49 + 33 - 16 = 66 Hence numbers that are not multiples of 2 or 3 = 99 - 66 = 33 Correct Option: D Hello Optimusprep Thanks for your reply. I had misunderstood the question, as I thought it was asking for the prime factors less than the number 100. Thanks again

Krabhay · Answer

To find the positive integers less than 100 that are not divisible by 2 or 3, we need to find the number of integers that are divisible by 2, 3 and 6 individually.
No of integers divisible by 2 =N2 = 50
No of integers divisible by 3 = N3 = 33
No of integers divisible by 6 = N6 = 16
So, no of integers not divisible by 2 or 3 = 100 – (N2 + N3 – N6) = 100 – (67) = 33.

meenakshimiyer · Answer

To find the positive integers less than 100 that are not divisible by 2 or 3, we need to find the number of integers that are divisible by 2, 3 and 6 individually.
No of integers divisible by 2 =N2 = 50
No of integers divisible by 3 = N3 = 33
No of integers divisible by 6 = N6 = 16
So, no of integers not divisible by 2 or 3 = 100 – (N2 + N3 – N6) = 100 – (67) = 33.

Scott@TargetTestPrep · Answer

How many positive integers less than 100 are neither multiples of 2 nor multiples of 3?

a)30
b)31
c)32
d)33
e)34

We can use the following equation:

Number of integers from 1 to 99, inclusive = (number of integers that are multiples of 2 or 3) + (number of integers that are neither multiples of 2 nor 3)

Furthermore:

Number of integers that are multiples of 2 or 3 = number of multiples of 2 + number of multiples of 3 - number of multiples of both 2 and 3

Notice that the number of multiples of both 2 and 3 is also the number of multiples of 6.

Let’s determine the number of multiples of 2 from 1 to 99 inclusive using the following equation:

(largest multiple of 2 in the set - smallest multiple of 2 in the set)/2 + 1

(98 - 2)/2 + 1 = 49

Now we can determine the number of multiples of 3 from 1 to 99 inclusive using the same concept:

(99 - 3)/3 + 1 = 33

Finally, let’s determine the number of multiples of 6, since some multiples of 2 are also multiples of 3; we must subtract those out so they are not double-counted.

(96 - 6)/6 + 1 = 16

Thus, there are 49 + 33 - 16 = 66 multiples of 2 or 3 from 1 to 99, inclusive. Therefore, there are 99 - 66 = 33 numbers from 1 to 99 inclusive that are not multiples of 2 or 3.

Answer: D

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