GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 May 2019, 15:46

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Fresh Meat!!!

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55188
Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:11
24
94
The next set of PS questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers.

1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

I. 63
II. 126
III. 252


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

Solution: fresh-meat-151046-80.html#p1215318


2. Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. 29
B. 56
C. 57
D. 63
E. 64

Solution: fresh-meat-151046-100.html#p1215323

3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Solution: fresh-meat-151046-100.html#p1215329


4. The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of positive perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38

Solution: fresh-meat-151046-100.html#p1215335


5. Which of the following is a factor of 18!+1?

A. 15
B. 17
C. 19
D. 33
E. 39

Solution: fresh-meat-151046-100.html#p1215338


6. If the least common multiple of a positive integer x, 4^3 and 6^5 is 6^6. Then x can take how many values?

A. 1
B. 6
C. 7
D. 30
E. 36

Solution: fresh-meat-151046-100.html#p1215345


7. The greatest common divisor of two positive integers is 25. If the sum of the integers is 350, then how many such pairs are possible?

A. 1
B. 2
C. 3
D. 4
E. 5

Solution: fresh-meat-151046-100.html#p1215349


8. The product of a positive integer x and 377,910 is divisible by 3,300, then the least value of x is:

A. 10
B. 11
C. 55
D. 110
E. 330

Solution: fresh-meat-151046-100.html#p1215359


9. What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?

A. 0
B. 1
C. 5
D. 7
E. 8

Solution: fresh-meat-151046-100.html#p1215367


10. If x is not equal to 0 and x^y=1, then which of the following must be true?

I. x=1
II. x=1 and y=0
III. x=1 or y=0


A. I only
B. II only
C. III only
D. I and III only
E. None

Solution: fresh-meat-151046-100.html#p1215370


Kudos points for each correct solution!!!
_________________
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55188
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 21 Apr 2013, 23:04
6
25
7. The greatest common divisor of two positive integers is 25. If the sum of the integers is 350, then how many such pairs are possible?

A. 1
B. 2
C. 3
D. 4
E. 5

We are told that the greatest common factor of two integers is 25. So, these integers are \(25x\) and \(25y\), for some positive integers \(x\) and \(y\). Notice that \(x\) and \(y\) must not share any common factor but 1, because if they do, then GCF of \(25x\) and \(25y\) will be more that 25.

Next, we know that \(25x+25y=350\) --> \(x+y=14\) --> since \(x\) and \(y\) don't share any common factor but 1 then (x, y) can be only (1, 13), (3, 11) or (5, 9) (all other pairs (2, 12), (4, 10), (6, 8) and (7, 7) do share common factor greater than 1).

So, there are only three pairs of such numbers possible:
25*1=25 and 25*13=325;
25*3=75 and 25*11=275;
25*5=125 and 25*9=225.

Answer: C.
_________________
Most Helpful Community Reply
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:28
3
4
1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

I. 63
II. 126
III. 252


Side square = 15x \(AreaS = \frac{15^2}{2}x^2\)
Diagonals= 9x, 11x\(AreaR = \frac{11*9*x^2}{2}\)
Difference = \(\frac{15^2x^2-11*9x^2}{2}= \frac{126x^2}{2}= 63x^2\)
\(63=3*3*7\)
if x=1 diff = 63 possible and easy to see
\(126=2*3*3*7\) x sould be \(\sqrt{2}\) => no integer
\(252=2*2*3*3*7\) x=2 possible

IMO D. I and III only
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
General Discussion
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:31
1
1
2. Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

At most 3 letters = 0 letters or 1 letter or 2 letters or 3 letters
0=1
1=7C1=7
2=7C2=21
3=7C3=35
\(1+7+21+35=64\)

IMO E. 64
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:34
2
2
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

It's like asking how many subsets has {1,2,3,4,5}
\(2^5=32\)

IMO D. 32
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 611
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:35
2
1
5. Which of the following is a factor of 18!+1?

A. 15
B. 17
C. 19
D. 33
E. 39

18! and 18!+1 are consecutive integers, thus co-prime. All options apart from C are present in 18!. Thus 19 is the only factor present in 18!+1.

C.
_________________
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 611
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:47
1
1
4. The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38

The no of primes less than 30 = 10 primes. Also,the number of perfect squares less than 30 = 1,4,9,16,25 = 5. Thus, for 31<x<37, the total sum is 16.

C.
_________________
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:49
1
4. The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

perfect squares = 1 4 9 16 25 36
prime numbers = 2 3 5 7 11 13 17 19 23 19 31 37

The first number that makes f(x) + g(x) = 16 is 32 and the last is 36

IMO C. 31 < x < 37
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 611
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post Updated on: 18 Apr 2013, 02:11
2
1
7. The greatest common divisor of two positive integers is 25. If the sum of the integers is 350, then how many such pairs are possible?

A. 1
B. 2
C. 3
D. 4
E. 5

The two numbers can be represented as 25a and 25b, where a and b are co-prime.Also, 25(a+b) = 350 --> (a+b) = 14
Thus, a=1,b=13 or a=3,b=11 or a=9,b=5.

C.
_________________

Originally posted by mau5 on 17 Apr 2013, 06:55.
Last edited by mau5 on 18 Apr 2013, 02:11, edited 2 times in total.
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 06:58
1
1
6. If the least common multiple of a positive integer x, 4^3 and 6^5 is 6^6. Then x can take how many values?

\(2^6, 2^5*3^5,2^6*3^6\) and \(x\)
\(x\) MUST have a \(3^6\) and can have any \(2^n\) with \(0\leq{n}\leq{6}\). So x can have \(7\) values

IMO C. 7
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 611
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 07:01
1
1
8. The product of a positive integer x and 377,910 is divisible by 3,300, then the least value of x is:

A. 10
B. 11
C. 55
D. 110
E. 330

We know that 377910 is not divisible by 11. Also, 3300 = 3*11*5^2*2^2. Now, as 377910 is divisible by 30, we are left with 11,5,2.Thus, the least value of x = 11*5*2 = 110.

D.
_________________
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 07:04
1
2
7. The greatest common divisor of two positive integers is 25. If the sum of the integers is 350, then how many such pairs are possible?

\(GMD = 5^2\) the numbers are \(5^2k\) and \(5^2q\) where q and k do not share any factor
\(25k+25q=350\) \(25(k+q)=350\) \(k+q=14\)
The possible numbers that summed give us 14 are: 1+13, 2+12,... those however must have no factor in common
and those pairs are:1+13,3+11,5+9

IMO C.3
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 07:11
1
8. The product of a positive integer x and 377,910 is divisible by 3,300, then the least value of x is:

\(3,300=3*11*2*5*2*5\)
\(377,910=37791*2*5\)
\(377,910*x/3300=\frac{37791*2*5*x}{3*11*2*5*2*5}\) Now x must contain 2*5, because 37791 is divisible by 3 x must not contain a 3, because 37791 is not divisible by 11 x must have it.
\(x=2*5*11=110\)

IMO D. 110
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 611
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 07:15
10. If x is not equal to 0 and x^y=1, then which of the following must be true?

I. x=1
II. x=1 and y=0
III. x=1 or y=0

A. I only
B. II only
C. III only
D. I and III only
E. None

From the given inequality, for any y and x=1, we would have x^y = 1. Also, for any x(and not equal to 0) and y = 0, we would again have the same inequality.
_________________
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 07:20
1
10. If x is not equal to 0 and x^y=1, then which of the following must be true?

I. x=1 False \(100^0=1\)
II. x=1 and y=0 False \(2^0=1\)
III. x=1 or y=0 True
Infact there are two cases: every number with a 0 exponent equals 1, and 1 raised to any exp equals 1.

IMO C. III only
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 07:23
1
2
5. Which of the following is a factor of 18!+1?

\(18!\) and \(18!+1\) are consecutives so they do not share any factor (except 1).
A,B,D and E are factors of \(18!\) (ie:\(33=3*11\) both contained in \(18!\))

IMO C.19
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 07:38
2
2
9. What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?

1/3=0.333
1/9=0.333/3=0.111
1/27=0.037 and then repeats
1/37=0.027 and then repeats
We can work on the first 3 digits: 0.111+0.333+0.027+0.037=0.508
After the 0 we have at first place a 5, second a 0, third an 8; and so on 4th=5, 5th=0, 6th=8. Every 10th position we have a "change" 10th=5 20th=0 30th=8 and so on
100th=5 and finally 101st=0

IMO A.0

Thanks for the set Bunuel!
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 611
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 09:28
1
2
9. What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?

A. 0
B. 1
C. 5
D. 7
E. 8

1/37 = 27/999= 0.027(recurring)
1/27 = 37/999 = 0.037(recurring)
1/9 = 0.111(recurring)
1/3 = 0.333(recurring)

The total = 0.508(recurring) Thus the next 2 digits after the 99th digit = 5 then 0.

A.
_________________
Manager
Manager
avatar
Joined: 11 Jun 2010
Posts: 73
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 10:15
1
Q2.

# Empty Set = 1
# Sets with 1 element = 7C1 = 7
# Sets with 2 elements = 7C2 = 21
# Sets with 3 elements = 7C3 = 35

# Subsets containing at most 3 letters = 1 + 7 + 21 + 35 = 64
Ans E
Manager
Manager
avatar
Joined: 11 Jun 2010
Posts: 73
Re: Fresh Meat!!!  [#permalink]

Show Tags

New post 17 Apr 2013, 10:20
1
1
Q3:

With 6 different elements in a set, total number of subsets = 2^6 = 64
With 5 different elements in a set, total number of subsets = 2^5 = 32
Hence from set of 6, if we do not include 0 in any set, that would be equivalent to considering just 5 elements out of 6 sets and how many subsets can be obtained from 5 elements. that should be 2^5 = 32 sub sets.
And D
GMAT Club Bot
Re: Fresh Meat!!!   [#permalink] 17 Apr 2013, 10:20

Go to page    1   2   3   4   5   6   7   8   9    Next  [ 173 posts ] 

Display posts from previous: Sort by

Fresh Meat!!!

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.