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Conceptual->Rapid Fire GMAT-Quiz

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Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post Updated on: 24 Dec 2016, 01:45
6
6

Aloha..!!!



:eat :zoom :beatup



DAY-1


Topic -> Number Properties


RAPID FIRE QUIZ-1


Note ->Answering these Questions Shouldn't take us more than a minute/Question


Source -->Few are from E-gmat forum and the rest are Self made

Quote:



1)If p,q,r are positive integers such that p<q<r,then what is the maximum possible value of GCD of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r




2)If x and n are positive integers then the number of prime factors of nx will always be greater than or equal to the number of prime factors of x^n?
A)True
B)False
C)cannot be determined

True


3)If p,q,r are positive integers such that p<q<r,then what is the minimum possible value of LCM of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r



4)If P is cube of a prime number, then how many factors does P have?

Four


5)If P and Q are Prime numbers then Q^5+P*Q is always even?
A)True
B)False

False



6)Is 24175 a prime number ?
A)True
B)False

False


7)The sum of first 100 prime number is even?
A)True
B)False

False


8)If x is a positive integer such that x-29,x and x+6 are all prime numbers,what is the value of x?

31


9)If n and x are positive integers such that x^3-79 is divisible by 2 and n=x^3-x, then n is always divisible by 24?
A)True
B)False

True


10)If P is a perfect Square, then which of these may be the number of prime factors of P?
A)13
B)12
C)10
D)8
E)6



11)All the prime numbers greater than 3 can be written as either 6n+1 or 6n-1.
A)True
B)False

True


12)All the positive integers of the form 6n+1 or 6n-1 are prime numbers.
A)True
B)False

False


13)If a positive integer x has 11 factors,how many prime factors does it have?

One.Notice that 11 is a prime number


14)If x is a positive integer then what will be the remainder when 10^x is divided by 3?

One


15)If a and b are positive integers such that a>b and a*b is a prime number.If a is even then what is the value of a*b?
A)2
B)4
C)6
D)8
E)Cannot be determined



16)If the sum of N consecutive integers is an integer,then N must be even.
A)True
B)False

False


17)x^3+x^2+x^37+x^4 is never odd if x is an integer.?
A)True
B)False

18)If Prime factors of a positive integer x include 2,3,5,7 and 13,then what will the units digit of x?

Zero


19)The units digit of 3^49 +5^34 +8^5 is ?



20)For two positive integers p and q if LCM(p,q)=GCD(p,q),then which if the following must be true?
A)p>q
B)p≥q
C)p<q
D)p≤q
E)p=q




600-700 Questions




is-c-d-1-even-if-c-d-are-integers-230101.html#p1773389
if-x-is-a-positive-integer-what-is-the-value-of-x-230012.html
if-p-and-q-are-positive-integers-is-the-product-3p-q-divisible-by-230014.html
if-b-is-a-positive-integer-such-that-the-difference-between-its-only-230011.html
if-n-is-a-positive-integer-whose-factors-include-24-and-230013.html
if-x-and-y-are-positive-integers-is-4x-2-xy-y-230015.html
if-x-is-a-positive-integer-less-than-99-and-also-a-multiple-of-the-230016.html
if-x-373p-423-q-where-p-and-q-are-positive-integers-230017.html
if-x-and-y-are-positive-integers-is-x-2-x-y-230019.html
find-the-lowest-number-which-has-both-x-and-y-as-factors-where-x-230020.html
how-many-even-different-factors-does-the-integer-p-have-132835.html
how-many-different-prime-factors-does-positive-integer-n-have-198238.html?fl=similar
how-many-positive-factors-does-the-positive-integer-x-have-210889.html?fl=similar
if-x-is-a-positive-integer-then-find-x-227377.html?fl=similar
how-many-distinct-factors-does-positive-integer-k-have-189049.html?fl=similar
how-many-factors-does-x-have-if-x-is-a-positive-integer-188673.html?fl=similar
how-many-prime-factors-does-positive-integer-n-have-111673.html#p1773258
how-many-prime-factors-does-n-have-140159.html#p1766418
how-many-factors-does-36-2-have-126422.html?fl=similar
how-many-positive-distinct-prime-factors-does-5-20-5-17-have-189492.html?fl=similar
if-x-and-y-are-integers-is-the-unit-digit-of-x-2-y-2-zero-229222.html
if-a-and-b-are-integers-is-a2-b2-even-206203.html#p1773359
if-k-is-a-positive-3-digit-number-is-k-prime-230103.html#p1773361
topic230115.html#p1773365
is-p-a-prime-number-230018.html


"Hardcore" 700+ Level Questions



x-2-p-q-n-1-find-x-if-p-q-and-n-are-positive-integers-194323.html
topic230034.html
if-an-0-and-n-is-a-positive-integer-is-n-odd-186684.html#p1780703
the-sum-of-n-consecutive-positive-integers-is-45-what-is-126861.html
if-x-p-nk-12-where-n-and-k-are-positive-integers-is-x-divisible-230029.html
if-x-p-n-k-p-where-n-and-k-are-positive-integers-is-x-divisible-b-209265.html
q-and-x-are-positive-integers-greater-than-1-is-it-possible-to-expres-230118.html#p1773307
topic230030.html#p1773312
topic230026.html#p1773332
ramen-lives-with-her-family-she-decided-to-host-a-dinner-at-her-230031.html
a-function-is-defined-as-f-n-the-number-of-factors-of-n-if-f-p-q-r-194467.html?fl=similar
functions-f-n-and-g-n-are-defined-for-a-positive-integer-n-as-230112.html#p1773335
is-3a-2b-5c-even-if-0-a-b-c-and-a-b-and-c-are-integers-209268.html
how-many-prime-numbers-exist-between-200-and-185996.html
if-n-is-a-positive-integer-less-than-100-what-is-the-value-of-n-230105.html#p1773364
topic230120.html#p1773371
topic230028.html
topic230113.html#p1773378
find-the-remainder-when-x2-is-divided-by-230027.html
topic230033.html

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Originally posted by stonecold on 10 Dec 2016, 07:13.
Last edited by stonecold on 24 Dec 2016, 01:45, edited 2 times in total.
Updated.
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 10 Dec 2016, 08:12
8)If x is a positive integer such that x-29,x and x+6 are all prime numbers,what is the value of x?

bit confused on the answer as 5.

5-29 is -24.

I was thinking 31 as the answer?

am I missing some concept ?
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 10 Dec 2016, 08:17
Dev1212 wrote:
8)If x is a positive integer such that x-29,x and x+6 are all prime numbers,what is the value of x?

bit confused on the answer as 5.

5-29 is -24.

I was thinking 31 as the answer?

am I missing some concept ?




No Dev.
You are Absolutely Right.
I made a typing error.


And thank you for attempting the Quiz.
I Hope it helped. :shock: :shock:


Regards
Stone Cold
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 10 Dec 2016, 08:21
Thank You StoneCold.

It is indeed helpful mate. Hell Yeahhh !!! That's the bottom line 'coz Stone Cold said so !

+1 mate

stonecold wrote:
Dev1212 wrote:
8)If x is a positive integer such that x-29,x and x+6 are all prime numbers,what is the value of x?

bit confused on the answer as 5.

5-29 is -24.

I was thinking 31 as the answer?

am I missing some concept ?




No Dev.
You are Absolutely Right.
I made a typing error.


And thank you for attempting the Quiz.
I Hope it helped. :shock: :shock:


Regards
Stone Cold
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 15 Dec 2016, 23:34
Quote:
3)If p,q,r are positive integers such that p<q<r,then what is the minimum possible value of LCM of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r

[Obscure] Spoiler:
r

Hi stonecold,
I don't know how to approach this one could you clarify.
In such questions i generally choose numbers so i took p=1,q=2,r=3; L.C.M=6(or in this case p*q*r)
This is maximum possible value of LCM
Now,how do you find the minimum??
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 16 Dec 2016, 02:05
1)If p,q,r are positive integers such that p<q<r,then what is the maximum possible value of GCD of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r
I love this sum. It is pure concept. We will go by one by one options
1 can be GCD if P Q R is Co – prime to each other.
P*Q*R – can be LCM, but never a GCD.
Within P,Q,R – only the smallest number can be GCD – to understand this you may chose 3 numbers. Write them in their canonical form. From that to find GCD we will take common factors with their lowest power, so the small number P only can be GCD.

2)If x and n are positive integers then the number of prime factors of nx will always be greater than or equal to the number of prime factors of x^n?
A)True
B)False
C)cannot be determined
I am not sure how to explain this, but I choose few numbers and tested. It is always true.
3)If p,q,r are positive integers such that p<q<r,then what is the minimum possible value of LCM of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r
Same as first qs.
P*q*r is maximum LCM possible
R is the minimum LCM possible.
As I told early you can try it by the way I mentioned in first qs.

4. If P is cube of a prime number, then how many factors does P have?
The number of factors can be found by adding one to the power. So four in this case.
Another example how to find factors: 23 * 32 = (3+1) * (2+1) = 4*3 =12 factors


5)If P and Q are Prime numbers then Q^5+P*Q is always even?
Interesting one, the problem in the sum is with prime number 2. If they say p and Q are >2 then it would be different.
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 16 Dec 2016, 08:24
1
karanchamp1 wrote:
Quote:
3)If p,q,r are positive integers such that p<q<r,then what is the minimum possible value of LCM of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r

[Obscure] Spoiler:
r

Hi stonecold,
I don't know how to approach this one could you clarify.
In such questions i generally choose numbers so i took p=1,q=2,r=3; L.C.M=6(or in this case p*q*r)
This is maximum possible value of LCM
Now,how do you find the minimum??


Hi karanchamp1

When two or more numbers are involved => LCM can never be less than any of the numbers(Since all the numbers are factors to the LCM and A factor of any number can never be greater than the number itself )
Hence --> Least value of LCM possible = Highest of all the numbers involved.In this case r will the least LCM.

The same rule can be Applied for GCD as => GCD can never be greater than any of the involver numbers(As GCD is a factor to each number and A factor of any number can never be greater than the number itself)
Hence --> Highest value of GCD = Smallest of all the numbers involved,which would be p in this case.



Thank you for attempting the Quiz.
I hope it was helpful .


Regards
Stone Cold

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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 16 Dec 2016, 10:11
stonecold wrote:
karanchamp1 wrote:
Quote:
3)If p,q,r are positive integers such that p<q<r,then what is the minimum possible value of LCM of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r

[Obscure] Spoiler:
r

Hi stonecold,
I don't know how to approach this one could you clarify.
In such questions i generally choose numbers so i took p=1,q=2,r=3; L.C.M=6(or in this case p*q*r)
This is maximum possible value of LCM
Now,how do you find the minimum??


Hi karanchamp1

When two or more numbers are involved => LCM can never be less than any of the numbers(Since all the numbers are factors to the LCM and A factor of any number can never be greater than the number itself )
Hence --> Least value of LCM possible = Highest of all the numbers involved.In this case r will the least LCM.

The same rule can be Applied for GCD as => GCD can never be greater than any of the involver numbers(As GCD is a factor to each number and A factor of any number can never be greater than the number itself)
Hence --> Highest value of GCD = Smallest of all the numbers involved,which would be p in this case.




Thank you for attempting the Quiz.
I hope it was helpful .


Regards
Stone Cold

Hi stonecold
Thanks for the prompt explanation man, and your quiz is is really intriguing and fun to solve :-D
Also,
You've got any similar thread of hard questions on inequalities,I find them really confusing sometimes (there are so many cases and I always miss that one exceptional case).It would really be helpful.
I feel like a parasite sucking all the resources in :),D-day is coming next month ,hope you understand :)
Thanks again and KUDOS!!
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 16 Dec 2016, 10:34
1
karanchamp1 wrote:
stonecold wrote:

Hi karanchamp1

When two or more numbers are involved => LCM can never be less than any of the numbers(Since all the numbers are factors to the LCM and A factor of any number can never be greater than the number itself )
Hence --> Least value of LCM possible = Highest of all the numbers involved.In this case r will the least LCM.

The same rule can be Applied for GCD as => GCD can never be greater than any of the involver numbers(As GCD is a factor to each number and A factor of any number can never be greater than the number itself)
Hence --> Highest value of GCD = Smallest of all the numbers involved,which would be p in this case.




Thank you for attempting the Quiz.
I hope it was helpful .


Regards
Stone Cold

Hi stonecold
Thanks for the prompt explanation man, and your quiz is is really intriguing and fun to solve :-D
Also,
You've got any similar thread of hard questions on inequalities,I find them really confusing sometimes (there are so many cases and I always miss that one exceptional case).It would really be helpful.
I feel like a parasite sucking all the resources in :),D-day is coming next month ,hope you understand :)
Thanks again and KUDOS!!


I am Glad you liked the Quiz.

I am working on a similar Quiz on Statistics.
On the GMAT Statistics is very Crucial.(or so i have heard)
It will be up in a day or two.
And it will have everything you need for Statistics.


Now,Coming to your Doubt on inequality here is my suggestion =>

If you are looking for conceptual understanding,then go through this Post by Bunuel -> inequalities-made-easy-206653.html

Next Download this PDF Here => 50-gmat-data-sufficiency-questions-on-inequalities-167841.html

It has 50 Great Hand Picked Inequality Questions.

After solving each of these 50 Questions -> I think you will ready to fight inequalities. :)


Regards
Stone Cold

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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 16 Dec 2016, 10:45
stonecold wrote:
karanchamp1 wrote:
stonecold wrote:

Hi karanchamp1

When two or more numbers are involved => LCM can never be less than any of the numbers(Since all the numbers are factors to the LCM and A factor of any number can never be greater than the number itself )
Hence --> Least value of LCM possible = Highest of all the numbers involved.In this case r will the least LCM.

The same rule can be Applied for GCD as => GCD can never be greater than any of the involver numbers(As GCD is a factor to each number and A factor of any number can never be greater than the number itself)
Hence --> Highest value of GCD = Smallest of all the numbers involved,which would be p in this case.




Thank you for attempting the Quiz.
I hope it was helpful .


Regards
Stone Cold

Hi stonecold
Thanks for the prompt explanation man, and your quiz is is really intriguing and fun to solve :-D
Also,
You've got any similar thread of hard questions on inequalities,I find them really confusing sometimes (there are so many cases and I always miss that one exceptional case).It would really be helpful.
I feel like a parasite sucking all the resources in :),D-day is coming next month ,hope you understand :)
Thanks again and KUDOS!!


I am Glad you liked the Quiz.

I am working on a similar Quiz on Statistics.
On the GMAT Statistics is very Crucial.(or so i have heard)
It will be up in a day or two.
And it will have everything you need for Statistics.


Now,Coming to your Doubt on inequality here is my suggestion =>

If you are looking for conceptual understanding,then go through this Post by Bunuel -> inequalities-made-easy-206653.html

Next Download this PDF Here => 50-gmat-data-sufficiency-questions-on-inequalities-167841.html

It has 50 Great Hand Picked Inequality Questions.

After solving each of these 50 Questions -> I think you will ready to fight inequalities. :)


Regards
Stone Cold

Thanks man,these threads will suffice for now :-D
You are the best :-D
KUDOS!!!!!!!!!!!!!!!!!
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 07 Jan 2017, 00:28
StoneCold this was massively helpful. It tested my concepts and in fact pushed me to think a bit further. Thank you for this!
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New post 15 Jan 2017, 14:34
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New post 15 Jan 2017, 14:39
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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 25 Jan 2018, 19:21
10)If P is a perfect Square, then which of these may be the number of prime factors of P?
A)13
B)12
C)10
D)8
E)6

can you explain this question, I agree that total no of factors shall be odd, but the number of prime factors can be any numbers.
For example take 13 prime numbers say (p1, p2, p3....p13)
Now the number P = (p1*p2*p3*...p13)^2 is a perfect square having 13 prime factors.

Please correct me, if I miss anything.

stonecold wrote:

Aloha..!!!



:eat :zoom :beatup



DAY-1


Topic -> Number Properties


RAPID FIRE QUIZ-1


Note ->Answering these Questions Shouldn't take us more than a minute/Question


Source -->Few are from E-gmat forum and the rest are Self made

Quote:



1)If p,q,r are positive integers such that p<q<r,then what is the maximum possible value of GCD of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r




2)If x and n are positive integers then the number of prime factors of nx will always be greater than or equal to the number of prime factors of x^n?
A)True
B)False
C)cannot be determined

True


3)If p,q,r are positive integers such that p<q<r,then what is the minimum possible value of LCM of p,q,r.?
A)p
B)q
C)r
D)1
E)p*q*r



4)If P is cube of a prime number, then how many factors does P have?

Four


5)If P and Q are Prime numbers then Q^5+P*Q is always even?
A)True
B)False

False



6)Is 24175 a prime number ?
A)True
B)False

False


7)The sum of first 100 prime number is even?
A)True
B)False

False


8)If x is a positive integer such that x-29,x and x+6 are all prime numbers,what is the value of x?

31


9)If n and x are positive integers such that x^3-79 is divisible by 2 and n=x^3-x, then n is always divisible by 24?
A)True
B)False

True


10)If P is a perfect Square, then which of these may be the number of prime factors of P?
A)13
B)12
C)10
D)8
E)6



11)All the prime numbers greater than 3 can be written as either 6n+1 or 6n-1.
A)True
B)False

True


12)All the positive integers of the form 6n+1 or 6n-1 are prime numbers.
A)True
B)False

False


13)If a positive integer x has 11 factors,how many prime factors does it have?

One.Notice that 11 is a prime number


14)If x is a positive integer then what will be the remainder when 10^x is divided by 3?

One


15)If a and b are positive integers such that a>b and a*b is a prime number.If a is even then what is the value of a*b?
A)2
B)4
C)6
D)8
E)Cannot be determined



16)If the sum of N consecutive integers is an integer,then N must be even.
A)True
B)False

False


17)x^3+x^2+x^37+x^4 is never odd if x is an integer.?
A)True
B)False

18)If Prime factors of a positive integer x include 2,3,5,7 and 13,then what will the units digit of x?

Zero


19)The units digit of 3^49 +5^34 +8^5 is ?



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A)p>q
B)p≥q
C)p<q
D)p≤q
E)p=q




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Re: Conceptual->Rapid Fire GMAT-Quiz  [#permalink]

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New post 25 Jan 2018, 20:13
gmatbusters wrote:
10)If P is a perfect Square, then which of these may be the number of prime factors of P?
A)13
B)12
C)10
D)8
E)6

can you explain this question, I agree that total no of factors shall be odd, but the number of prime factors can be any numbers.
For example take 13 prime numbers say (p1, p2, p3....p13)
Now the number P = (p1*p2*p3*...p13)^2 is a perfect square having 13 prime factors.

Please correct me, if I miss anything.



You are right. The number of factors of a perfect square must be odd but the number of prime factors can be any.
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Re: Conceptual->Rapid Fire GMAT-Quiz &nbs [#permalink] 25 Jan 2018, 20:13
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