Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Sep 2014, 16:25

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Baker's Dozen

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
22 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3538

Kudos [?]: 27237 [22] , given: 2725

Baker's Dozen [#permalink] New post 08 Mar 2012, 12:27
22
This post received
KUDOS
Expert's post
30
This post was
BOOKMARKED
I'm posting the next set of medium/hard PS questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers. Good luck!

1. A password on Mr. Wallace's briefcase consists of 5 digits. What is the probability that the password contains exactly three digit 6?

A. 860/90,000
B. 810/100,000
C. 858/100,000
D. 860/100,000
E. 1530/100,000

Solution: baker-s-dozen-128782-20.html#p1057502

2. If y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2}}, then y is NOT divisible by which of the following?
A. 6^4
B. 62^2
C. 65^2
D. 15^4
E. 52^4

Solution: baker-s-dozen-128782-20.html#p1057503

3. For the past k days the average (arithmetic mean) cupcakes per day that Liv baked was 55. Today Bibi joined and together with Liv they baked 100 cupcakes, which raises the average to 60 cupcakes per day. What is the value of k?
A. 6
B. 8
C. 9
D. 10
E. 12

Solution: baker-s-dozen-128782-20.html#p1057504

4. What is the smallest positive integer k such that 126*\sqrt{k} is the square of a positive integer?
A. 14
B. 36
C. 144
D. 196
E. 441

Solution: baker-s-dozen-128782-20.html#p1057505

5. There are 7 red and 5 blue marbles in a jar. In how many ways 8 marbles can be selected from the jar so that at least one red marble and at least one blue marble to remain in the jar?
A. 460
B. 490
C. 493
D. 455
E. 445

Solution: baker-s-dozen-128782-20.html#p1057507

6. A pool has two water pumps A and B and one drain C. Pump A alone can fill the whole pool in x hours, and pump B alone can fill the whole pool in y hours. The drain can empty the whole pool in z hours, where z>x. With pumps A and B both running and the drain C unstopped till the pool is filled, which of the following represents the amount of water in terms of the fraction of the pool which pump A pumped into the pool?
A. \frac{yz}{x+y+z}

B. \frac{yz}{yz+xz-xy}

C. \frac{yz}{yz+xz+xy}

D. \frac{xyz}{yz+xz-xy}

E. \frac{yz+xz-xy}{yz}

Solution: baker-s-dozen-128782-20.html#p1057508

7. Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number of shares that Fritz owns is 2/3 rd of number of the shares of the other three shareholders, number of the shares that Luis owns is 3/7 th of number of the shares of the other three shareholders and number of the shares that Alfred owns is 4/11 th of number of the shares of the other three shareholders. If dividends of $3,600,000 were distributed among the 4 shareholders, how much of this amount did Werner receive?
A. $60,000
B. $90,000
C. $100,000
D. $120,000
E. $180,000

Solution: baker-s-dozen-128782-20.html#p1057509

8. A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185 what is the sum of the 5 smallest integers of set A?
A. -165
B. -175
C. -195
D. -205
E. -215

Solution: baker-s-dozen-128782-20.html#p1057512

9. If x and y are negative numbers, what is the value of \frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}?
A. 1+y
B. 1-y
C. -1-y
D. y-1
E. x-y

Solution: baker-s-dozen-128782-20.html#p1057514

10. If x^2<81 and y^2<25, what is the largest prime number that can be equal to x-2y?
A. 7
B. 11
C. 13
D. 17
E. 19

Solution: baker-s-dozen-128782-20.html#p1057515

11. In an infinite sequence 1, 3, 9, 27, ... each term after the first is three times the previous term. What is the difference between the sum of 13th and 15th terms and the sum of 12th and 14th terms of the sequence?
A. 10*3^11
B. 20*3^11
C. 10*3^12
D. 40*3^11
E. 20*3^12

Solution: baker-s-dozen-128782-40.html#p1057517

12. x, y and z are positive integers such that when x is divided by y the remainder is 3 and when y is divided by z the remainder is 8. What is the smallest possible value of x+y+z?
A. 12
B. 20
C. 24
D. 29
E. 33

Solution: baker-s-dozen-128782-40.html#p1057519

13. If x=\frac{(8!)^{10}-(8!)^6}{(8!)^{5}-(8!)^3}, what is the product of the tens and the units digits of \frac{x}{(8!)^3}-39?
A. 0
B. 6
C. 7
D. 12
E. 14

Solution: baker-s-dozen-128782-40.html#p1057520
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesManhattan GMAT Discount Codes
3 KUDOS received
Intern
Intern
avatar
Joined: 28 Feb 2011
Posts: 35
Followers: 0

Kudos [?]: 6 [3] , given: 1

Re: Baker's Dozen [#permalink] New post 08 Mar 2012, 17:01
3
This post received
KUDOS
1) Ans B

The 3 digits that will be '6' can be selected in 5c3 = 10 ways

The remaining two digits can be any digit from 0 to 9 other than 6 i.e 9 digits.

so favorable outcomes = 5c3 *9*9*1*1*1 = 810
total outcome = 10*10*10*10 *10 = 10^5

P(exactly three 6) = 810/10^5


2) Ans E

y = (3^5-3^2)^2/ (5^7 -5^4)^-2

Numerator (3^2(3^3-1))^2 = (3^2(26) )^2 = 3^4*13^2*2^2

Denominator (5^4(5^3-1))^-2 = 1/(5^4(124))^2 = 1/5^8*4^2*31^2 = 1/5^8*2^4*31^2

Numerator/denominator = 3^4 *13^2 *2^2 *5^8 *2^4*31^2 = 3^4*13^2*31^2*2^6

From answer choices we see that 52^4 is not divisble by y


3) Ans B

Old sum/k = 55
old sum = 55 k

old sum +100 /k+1 = 60
old sum+100 = 60k+60

55k+100 = 60k+60

5k = 40 k= 8


4) Ans D

126 * sqrt k = a^2 where a is a +ve integer

7*2*3^2 *sqrt k = a^2

So we need one two and one 7 to make 'a' a perfect square
if k = 196 , 7*2*3^2*sqrt 196 = 2^2*7^2*3^2

5) For selecting 8 marbles from 12 marbles, a maximim of 4 marble can remain in
the jar . The scenarios for atleast 1 red marble and 1 blue marble to remain are:

1r1b 7c1*5c1 = 35
1r2b 7c1*5c2 = 70
2r1b 7c2*5c1 = 105
2r2b 7c2*5c2 = 210
3r1b 7c3*5c1 = 175
1r3b 7c1*5c3 = 70

Total 665 . Not sure if the logic is right..

6) Ans E

Work done by pump a,b,c in 1 hr = 1/x , 1/y, 1/z respectively

Working simultaneously, work done by them in 1 hr is:

1/x+1/y-1/z

yz +xz -xy/xyz job done in 1 hr

So whole job will be completed in xyz/yz+xz-xy hrs

Since pump A work for x hrs, fraction of job completed by pump A is :

x/(xyz/yz+xz-xy) = yz+xz-xy/yz


8) Ans) D

let the 7 consecutive odd integers be:

x, x+2, x+4, x+6, x+8, x+10, x+12 (in ascending order)

Sum of the 5 largest integers is x+12 +x+10 +x+8 +x+6 +x+4 = 5x+40

So 5x +40 = -185
5x = -225
x = -45

Sum of the 5 smallest integers = x+x+2+x+4+x+6+x+8 = 5x+20

5x+20 = (5*-45) +20 = -225+20 = -205


9) Ans c

sqrt x^2 = |x| = -x (since X<0)

sqrt (-y*|y|) = sqrt(-y*-y) sqrt y^2 = y

sqrt x^2/x - sqrt(-y*|y|) = -x/x - y = -1-y


10) Ans c

x^2<81 -9<x<9 y^2<25 -5<y<5

For x -2y to be a maximim prime number, x should be maximim prime number
and y minimum prime number

So x-2y = 7 - (2*-3) =13


11) Ans B

nth term of GP sereis is an = a1*r^n-1 where r =3 common ratio , a1 -=1

a13 = 1*3^12

a15 = 1^3^14

a13+a15 = 3^12 +3^14 = 3^12(1+3^2) = 3^12*10

Similarly a12 = 3^11 a14 = 3^13

a12+14 = 3^11+3^13 = 3^11*10

(a13+a15) - (a12+a14) = 3^12*10 - 3^11*10

3^11*10(3-1) = 3^11 *20


12)Ans B

x = yq1+3 y>3 since divisor should be greater than remainder

y = zq1+8 z>8 since divisor should be greater than remainder

so least value of z is 9 and least value of y 8 since for 8/9 remainder is 8

least value of x is 3 since for 3/8 remainder is 3

Least value of x+y+z = 3+8+9 = 20


13) Ans D

x = (8!)^10 - (8!)^6 / (8!)^5 -(8!)^3

Numerator, taking 8!^6 common ,(8!)^6 ((8!)^4-1) = (8!)^6 [(8!)^2+1)(8!)^2-1)]

Denominator, taking 8!^3 common (8!)^3 [(8!)^2-1]

x = (8!)^6 [(8!)^2+1)(8!)^2-1)] / (8!)^3 [(8!)^2-1]

x = (8!)^3[(8!)^2+1)

x = (8!)^5 +(8!)^3


x/(8!)^3 -39 = [(8!)^5 +(8!)^3/(8!)^3] -39

= [(8!)^2 +1]-39

=(8!)^2-38

8!^2 is a big number and will have 2 trailing zeros..

So some big number ending in 00 - 38 will have
digits 2,6 in units and tens palce respectively

So product is 2*6 =12
1 KUDOS received
Manager
Manager
avatar
Joined: 12 Oct 2011
Posts: 133
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Followers: 3

Kudos [?]: 65 [1] , given: 23

Re: Baker's Dozen [#permalink] New post 09 Mar 2012, 11:28
1
This post received
KUDOS
In regards to question 13, how do you know that (8!)^2 will have two 0's at the end?
1 KUDOS received
Intern
Intern
User avatar
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 8 [1] , given: 14

Re: Baker's Dozen [#permalink] New post 09 Mar 2012, 22:41
1
This post received
KUDOS
BN1989 wrote:
In regards to question 13, how do you know that (8!)^2 will have two 0's at the end?



You figure it out by knowing that there is a 5 as a factor in the final number.

example 8! = 8*7*6*5...*1

Now if u know how many fives are there you will have that number of zeros in the end because at least that many number of 2 will there for sure ...

Now IF u want to figure out how may fives are there in (which is equivalent to finding how many zeros in the end of the number )
then simply keep dividing the factorial by 5 and adding it to the result until 5^x exceeds the factorial, i know i have used very confusing language but a example will simplify things for sure

how many zeros at the end of 312!
answer :- 312!/5 + 312!/5^2 + 312!/5^3 = 62 + 12 + 2 (now note i stopped at 5^3, because 5^4 =25*25=625 which is more that 312 ) hence :- 62 + 12 + 2 =76 number of 5s in the factorial and same number of zeros in the end because these many number of 2s will obviously be there in factorial and will form 10s .

IF you are still confused I would suggest you to download Bunuel's math's notes and even if you are not confused i would still suggest you to do the same , :wave
1 KUDOS received
Intern
Intern
User avatar
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 8 [1] , given: 14

Re: Baker's Dozen [#permalink] New post 09 Mar 2012, 23:01
1
This post received
KUDOS
2)e
3)b
4)d
6)e
7)d
8)b
9)c
10)c
11)b
12) b
13)d

Bunuel could you please provide us/me with the answer keys so that I can cross check
thanks once again for the questions and a amazing post .
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3538

Kudos [?]: 27237 [1] , given: 2725

Re: Baker's Dozen [#permalink] New post 09 Mar 2012, 23:22
1
This post received
KUDOS
Expert's post
utkarshlavania wrote:
2)e
3)b
4)d
6)e
7)d
8)b
9)c
10)c
11)b
12) b
13)d

Bunuel could you please provide us/me with the answer keys so that I can cross check
thanks once again for the questions and a amazing post .


I'll provide OA's with detailed solutions after some discussion in a couple of days. If you need OA's asap pm me and I'll send you them.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Intern
Intern
User avatar
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 8 [1] , given: 14

Re: Baker's Dozen [#permalink] New post 09 Mar 2012, 23:38
1
This post received
KUDOS
Bunuel wrote:
utkarshlavania wrote:
2)e
3)b
4)d
6)e
7)d
8)b
9)c
10)c
11)b
12) b
13)d

Bunuel could you please provide us/me with the answer keys so that I can cross check
thanks once again for the questions and a amazing post .


I'll provide OA's with detailed solutions after some discussion in a couple of days. If you need OA's asap pm me and I'll send you them.


Bunuel i have messaged you, looking forward
thanks once again ...
1 KUDOS received
Intern
Intern
User avatar
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 8 [1] , given: 14

Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 00:24
1
This post received
KUDOS
[quote2]9. If x and y are negative numbers, what is the value of \frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}?
A. 1+y
B. 1-y
C. -1-y
D. y-1
E. x-y

Correction/suggestion/advice/confirmation --- needed
Answer to 9th question If x and y are negative numbers, what is the value of \frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}?[/b]
Sqrtx^2/x-sqrt(-y*|y|) = |x|/x-|y|= -1-y
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3538

Kudos [?]: 27237 [0], given: 2725

Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 00:41
Expert's post
utkarshlavania wrote:
[quote2]9. If x and y are negative numbers, what is the value of \frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}?
A. 1+y
B. 1-y
C. -1-y
D. y-1
E. x-y

Correction/suggestion/advice/confirmation --- needed
Answer to 9th question If x and y are negative numbers, what is the value of \frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}?[/b]
Sqrtx^2/x-sqrt(-y*|y|) = |x|/x-|y|= -1-y


Hint: what is |y| if y<0? and what is -1-|y| then?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Intern
Intern
User avatar
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 8 [1] , given: 14

Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 01:38
1
This post received
KUDOS
-y = +y and |y| no matter what, comes out as positive hence Sqrt (-y*|y| ) comes out as possitive y and sqrtx^2 =|x|= positive x , of course from your tone i get that i'm going wrong some where but
2 KUDOS received
Director
Director
User avatar
Status: Enjoying the GMAT journey....
Joined: 26 Aug 2011
Posts: 735
Location: India
GMAT 1: 620 Q49 V24
Followers: 60

Kudos [?]: 289 [2] , given: 264

GMAT ToolKit User Premium Member
Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 04:20
2
This post received
KUDOS
Ans 1
Total number of ways = 10 x 10 x 10 x 10 x 10 = 100,000
total number ways with exactly three six = 5C3 * 9*9 = 810
correct Answer B
p.s IMO one more zero is required in the denominator.

Ans 2
resolving the numerator/denominator, we get
3^4 * 5^8 * 2^2 *13^2 * 2^2 *62^2
so A to D is divisible by the above
Correct Answer E
Ans 3
This one is little simple
the equation is 55*k +100 = 60(k + 1)
thus 5k = 40
k = 8
Correct Answer B
Ans 4
3*3*7*2*\sqrt{k} is the square of a positive integer( suppose X^2)
so we need 7 and 2 and put them in square root as 14 * 14= 196
Correct Answer D
_________________

Fire the final bullet only when you are constantly hitting the Bull's eye, till then KEEP PRACTICING.

A WAY TO INCREASE FROM QUANT 35-40 TO 47 : a-way-to-increase-from-q35-40-to-q-138750.html

Q 47/48 To Q 50 + the-final-climb-quest-for-q-50-from-q47-129441.html#p1064367

Three good RC strategies three-different-strategies-for-attacking-rc-127287.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23064
Followers: 3538

Kudos [?]: 27237 [0], given: 2725

Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 05:13
Expert's post
utkarshlavania wrote:
-y = +y and |y| no matter what, comes out as positive hence Sqrt (-y*|y| ) comes out as possitive y and sqrtx^2 =|x|= positive x , of course from your tone i get that i'm going wrong some where but


What I meant is that if y<0 then |y|=-y and -1-|y|=-1-(-y)=-1+y.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 139 [1] , given: 73

GMAT ToolKit User
Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 06:42
1
This post received
KUDOS
Quote:
8. A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185 what is the sum of the 5 smallest integers of set A?
A. -165
B. -175
C. -195
D. -205
E. -215


x ;x+2;x+2*2;x+2*3....x+2*6

since the set has consecutive odd integers, then mean =median

mean of 5 largest integers=-185/5= -37
median of 5 largest integers is the 3d of the largest or the 5th of the whole set A= x+2*4
x+8=-37 ;x=-45

median of the first 5 small integers =-45+2*2=-41


the sum of the first small odd integers=number of integers*mean (or median)=5*median=5*(-41)=-205
answ is
[Reveal] Spoiler:
D

_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

1 KUDOS received
Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 139 [1] , given: 73

GMAT ToolKit User
Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 06:54
1
This post received
KUDOS
Quote:
13. If x=\frac{(8!)^{10}-(8!)^6}{(8!)^{5}-(8!)^3}, what is the product of the tens and the units digits of \frac{x}{(8!)^3}-39?
A. 0
B. 6
C. 7
D. 12
E. 14


x=((8!)^6*((8!)^4-1))/((8!)^3*((8!)^2-1))=(8!)^3*((8!)^2+1)


((8!)^3*((8!)^2+1) /(8!)^3)) -39=(8!)^2+1)-39
note, that 8! has 5 and 2. so 8! ends with 0. then (8!)^2 will end by two 0s.
***00-38=62
6*2=12
answ is
[Reveal] Spoiler:
D




4. What is the smallest positive integer k such that 126*\sqrt{k} is the square of a positive integer?

A. 14
B. 36
C. 144
D. 196
E. 441

126*\sqrt{k}=3*7*3*2*sqrt{k}=3^2*7*2
so we need one more 7*2 (14)
sqrootk=14
k=196
answ is
[Reveal] Spoiler:
D


what an irony. all the 3 questions are
[Reveal] Spoiler:
D
heh


9. If x and y are negative numbers, what is the value of \frac{\sqrt{x^2}}{x}-\sqrt{-y*|y|}?

A. 1+y
B. 1-y
C. -1-y
D. y-1
E. x-y
-x/x-|y|=-1-(-y)=y-1 since y<0 ; x<0
[Reveal] Spoiler:
D
is the answ
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true


Last edited by LalaB on 10 Mar 2012, 08:08, edited 1 time in total.
1 KUDOS received
Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 139 [1] , given: 73

GMAT ToolKit User
Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 07:03
1
This post received
KUDOS
12. x, y and z are positive integers such that when x is divided by y the remainder is 3 and when y is divided by z the remainder is 8. What is the smallest possible value of x+y+z?
A. 12
B. 20
C. 24
D. 29
E. 33

x/y the remainder is 3 . then the smallest x is 3

y/z the remainder is 8. then the smallest y is 8 and z is 9

3+8+9=20

answ is B
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

1 KUDOS received
Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 139 [1] , given: 73

GMAT ToolKit User
Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 07:17
1
This post received
KUDOS
10. If x^2<81 and y^2<25, what is the largest prime number that can be equal to x-2y?
A. 7
B. 11
C. 13
D. 17
E. 19

-9<x<9
-5<y<5

-9<x<9
-10<2y<10
x-2y<9-(-10)
x-2y<19

the answer is 17. D again :) the mystical letter for today heh


11. In an infinite sequence 1, 3, 9, 27, ... each term after the first is three times the previous term. What is the difference between the sum of 13th and 15th terms and the sum of 12th and 14th terms of the sequence?
A. 10*3^11
B. 20*3^11
C. 10*3^12
D. 40*3^11
E. 20*3^12

1, 3, 9, 27 ok please pay attention to the fact that the term of sequence has 3 one less than the number of the term,i.e.
the 3d term is 9, but the number has two 3s (one less than the term). the 4th term is 3*3*3 ,which has three 3s.

ok, then we have the following-
the q. asks us to find out -
(13th term+15th term) -(12th term +14th term)

(3^12+3^14)-(3^11-3^13)=
3^11(3-1)+3^13(3-1)=
2*3^11(1+3^2)=
20*3^11
the answer is B

p.s. also note, that answer choices B and D are leaders of the day heh
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Intern
Intern
User avatar
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 8 [0], given: 14

Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 08:03
Bunuel wrote:
utkarshlavania wrote:
-y = +y and |y| no matter what, comes out as positive hence Sqrt (-y*|y| ) comes out as possitive y and sqrtx^2 =|x|= positive x , of course from your tone i get that i'm going wrong some where but


What I meant is that if y<0 then |y|=-y and -1-|y|=-1-(-y)=-1+y.



isn't -1 -|y|=-1-y for the same reason |x|/x became -1 because numerator x was positive and denominator x was negative .
sqrt(negative -y *|y|) so negative -y =postive y and |y| = positive hence when y comes out it comes as positive y and because of the negative sign
-1 - y=-1-y :| :( :crying
please help bunuel :(
Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 139 [0], given: 73

GMAT ToolKit User
Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 08:12
utkarshlavania wrote:
Bunuel wrote:
utkarshlavania wrote:
-y = +y and |y| no matter what, comes out as positive hence Sqrt (-y*|y| ) comes out as possitive y and sqrtx^2 =|x|= positive x , of course from your tone i get that i'm going wrong some where but


What I meant is that if y<0 then |y|=-y and -1-|y|=-1-(-y)=-1+y.



isn't -1 -|y|=-1-y for the same reason |x|/x became -1 because numerator x was positive and denominator x was negative .
sqrt(negative -y *|y|) so negative -y =postive y and |y| = positive hence when y comes out it comes as positive y and because of the negative sign
-1 - y=-1-y :| :( :crying
please help bunuel :(


sqroot of (negative number ^2) = (negative number ^2)^1/2=negative number

for example sqroot (-5*|5|)=sqroot (-5^2)=((-5)^2)^1/2=-5
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Intern
Intern
User avatar
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 8 [0], given: 14

Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 10:55
LalaB wrote:
(


sqroot of (negative number ^2) = (negative number ^2)^1/2=negative number

for example sqroot (-5*|5|)=sqroot (-5^2)=((-5)^2)^1/2=-5[/quote]

agreed but here isn't the concept little different, as it is already mentioned that y is negative hence -y= positive y
1 KUDOS received
Intern
Intern
avatar
Joined: 02 Jan 2011
Posts: 9
Followers: 0

Kudos [?]: 2 [1] , given: 0

Re: Baker's Dozen [#permalink] New post 10 Mar 2012, 23:34
1
This post received
KUDOS
I am not so certain whether I am right but I would go with D in #9.

IF x<0 and y<0 then sqrt(x^2)/x=|x|/x, then -x/x=-1; because there is a minus in front of x, than -(-x) should be positive.

sqrt two negative y gives square root of y^2, than because y<1, y is negative as well. -y.

From the expression we've got -1+y, thus D should be a correct answer.
Re: Baker's Dozen   [#permalink] 10 Mar 2012, 23:34
    Similar topics Author Replies Last post
Similar
Topics:
201 Experts publish their posts in the topic Devil's Dozen!!! Bunuel 123 19 Mar 2012, 05:54
Turtles and Bakers beach icandy 27 03 Feb 2009, 11:16
To Joshephine baker humtum0 4 13 Sep 2007, 18:41
Baker was perhaps not the most gifted soloist in the ecotopia 14 29 May 2006, 07:41
Baker was perhaps not the most gifted soloist in the qhoc0010 9 15 Jan 2005, 13:27
Display posts from previous: Sort by

Baker's Dozen

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2   3   4   5   6   7    Next  [ 127 posts ] 



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

Powered by phpBB © phpBB Group and phpBB SEO

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®.