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stonecold

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[12]

Updated on: 24 Dec 2016, 01:45

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.

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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

Show Spoiler

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

Show Spoiler

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

Show Spoiler

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

Show Spoiler

Four

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

Show Spoiler

False

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

Show Spoiler

False

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

Show Spoiler

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?

Show Spoiler

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

Show Spoiler

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

Show Spoiler

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

Show Spoiler

True

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

Show Spoiler

False

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

Show Spoiler

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?

Show Spoiler

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

Show Spoiler

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

Show Spoiler

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?

Show Spoiler

Zero

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

Show Spoiler

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

Show Spoiler

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

Dev1212

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10 Dec 2016, 08:12

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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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10 Dec 2016, 08:17

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Dev1212

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

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

Regards
Stone Cold

Dev1212

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10 Dec 2016, 08:21

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Thank You StoneCold.

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

+1 mate

stonecold

Dev1212

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

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

Regards
Stone Cold

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15 Dec 2016, 23:34

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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??

vivekkumar987

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16 Dec 2016, 02:05

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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.

stonecold

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[1]

16 Dec 2016, 08:24

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karanchamp1

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 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

karanchamp1

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16 Dec 2016, 10:11

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stonecold

karanchamp1

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
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!!

stonecold

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[1]

16 Dec 2016, 10:34

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karanchamp1

stonecold

Hi stonecold
Thanks for the prompt explanation man, and your quiz is is really intriguing and fun to solve :-D

,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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16 Dec 2016, 10:45

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stonecold

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stonecold

Hi stonecold
Thanks for the prompt explanation man, and your quiz is is really intriguing and fun to solve :-D

,D-day is coming next month ,hope you understand

Thanks again and KUDOS!!

Regards
Stone Cold

Thanks man,these threads will suffice for now :-D

You are the best :-D

KUDOS!!!!!!!!!!!!!!!!!

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StoneCold this was massively helpful. It tested my concepts and in fact pushed me to think a bit further. Thank you for this!

stonecold

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deeksha6

StoneCold this was massively helpful. It tested my concepts and in fact pushed me to think a bit further. Thank you for this!

Thank you for the Feedback.
Appreciate it.
Here is another mock test for you to solve -> https://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

stonecold

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15 Jan 2017, 14:39

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A New Mock test has been Updated

https://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Number of Questions -> 100.

Topics Covered -> Basic Concepts of Divisibility,factors and Primes

stonecold

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17 Jan 2017, 06:49

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A New Mock test has been Updated

https://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Number of Questions-> 100.

Topics Covered -> Advanced Concepts of ->Divisibility,factors and Primes
Difficulty Level-> 700+

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24 Jan 2017, 21:57

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Three More Mock Tests have been updated.

Mock Test -2 --->https://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Mock Test -3 --->https://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023

Mock Test -4 --->https://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768052

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25 Jan 2018, 19:21

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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

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

Show Spoiler

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

Show Spoiler

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

Show Spoiler

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

Show Spoiler

Four

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

Show Spoiler

False

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

Show Spoiler

False

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

Show Spoiler

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?

Show Spoiler

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

Show Spoiler

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

Show Spoiler

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

Show Spoiler

True

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

Show Spoiler

False

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

Show Spoiler

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?

Show Spoiler

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

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

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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?

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Zero

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

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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

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600-700 Questions