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

 It is currently 18 Jan 2019, 22:21

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# A certain club has 20 members. What is the ratio of the

Author Message
Intern
Joined: 10 Aug 2007
Posts: 30

### Show Tags

20 Aug 2007, 22:32
Sergey_is_cool wrote:
9. 23. (0.8)^-5 / (0.4)^-4=

(A) 3/32
(B) 5/64
(C) 1/2
(D) 1
(E) 2

I got 5/64.... I found this one to be easier if I converted to fractions, so start with:

(4/5)^-5
----------
(2/5)^-4

apply properties of negative exponents:

(5/4)^5
----------
(5/2)^4

perform the division:

(5/4)^5 * (2/5)^4

bring out a 5/4 to get equal exponents:

(5/4) * (5/4)^4 * (2/5)^4

combine like-exponents:

(5/4) * (1/2)^4

and compute:

(5/4) * (1/16) = 5/64
Intern
Joined: 10 Aug 2007
Posts: 30

### Show Tags

20 Aug 2007, 22:38
[quote="Sergey_is_cool"]
10. There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
(A) 20
(B) 25
(C) 40
(D) 60
(E) 125
[/quote]

I got 20 for this:

5!/(3! * 1! * 1!) = (5 * 4 * 3 * 2)/(3 * 2) = 20
Manager
Joined: 03 Sep 2006
Posts: 232

### Show Tags

Updated on: 20 Aug 2007, 22:47
9. 23. (0.8)^-5 / (0.4)^-4=

I did it even easier:

(4/5)^-5 = (5/4)^5 = 5^5 / 4^5
(2/5)^-4 = (5/2)^4 = 5^4 / 2^4

5^5 * 2^4 ... 5 * 16
------------- = ----------------
4^5 * 5^4 ... 16 * 16 * 4

Ans. 5/64, hence B

What about 11? I'm stuck ...

Originally posted by Whatever on 20 Aug 2007, 22:46.
Last edited by Whatever on 20 Aug 2007, 22:47, edited 1 time in total.
Intern
Joined: 10 Aug 2007
Posts: 30

### Show Tags

20 Aug 2007, 22:46
Sergey_is_cool wrote:
11. A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

(A) 1: 2
(B) 4: 5
(C) 1: 1
(D) 3: 2
(E) 5: 3

Gonna guess A) 1:2 on this.

say x = car sales and y = truck sales:

.89x + 1.07y = 1.01 (x+y)
.89x + 1.07y = 1.01x + 1.01y
.06y = .12x
.06/.12 = x/y
1/2 = x/y
Manager
Joined: 03 Sep 2006
Posts: 232

### Show Tags

20 Aug 2007, 23:09
entranced wrote:
To this this, we need to examine the function. Since the tens digit is multiplied by three, if we play around with this digit, we should be able to modify the final result by 9.

Could you please explain more about "if we play around with this digit" and how you get numbers 113 and 193 - what was the logic?
Manager
Joined: 14 May 2006
Posts: 195

### Show Tags

20 Aug 2007, 23:15
entranced wrote:
Sergey_is_cool wrote:
6. The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80

I think the answer to this is 80. You want to f(m) to equal 9 * f(v). To this this, we need to examine the function. Since the tens digit is multiplied by three, if we play around with this digit, we should be able to modify the final result by 9.

let's say V = 113 --> f(v) = 2 * 1 * 3 * 1 * 5 * 3 = 90
let's say M = 193 --> f(m) = 2 * 1 * 3 * 9 * 5 * 3 = 810
810 = 90 * 9

so, 193 - 113 = 80

What if m=119 and v=111?

f(m) = 2 x 1 x 3 x 1 x 5 x 9 = 270
f(v) = 2 x 1 x 3 x 1 x 5 x 1 = 30

f(m)/9 = f(v)
30 = f(v)

m - v = 8 so isn't A also correct?
Manager
Joined: 14 May 2006
Posts: 195

### Show Tags

20 Aug 2007, 23:17

C, C, B, C, B, ?, E, D, ?, A, A

Can you please post the OAs?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4804
Location: Singapore

### Show Tags

20 Aug 2007, 23:58
entranced wrote:
Sergey_is_cool wrote:
6. The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80

I think the answer to this is 80. You want to f(m) to equal 9 * f(v). To this this, we need to examine the function. Since the tens digit is multiplied by three, if we play around with this digit, we should be able to modify the final result by 9.

let's say V = 113 --> f(v) = 2 * 1 * 3 * 1 * 5 * 3 = 90
let's say M = 193 --> f(m) = 2 * 1 * 3 * 9 * 5 * 3 = 810
810 = 90 * 9

so, 193 - 113 = 80

hmm... not so sure about this one. I did it the say way, but end up with 8 as the answer. I'm sure I can get 80 if i manipulate another way.

If f(m) = 810, then m = (2*1)(3*3)(5*9) --> m = 139
Then f(v) = 90, then m = (2*1)(3*3)(5*1) --> v = 131

THen m-v = 8
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4804
Location: Singapore

### Show Tags

21 Aug 2007, 00:03
At a certain food stand, the price of each apple is \$0.4 and the price of each orange is \$0.6. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is \$0.56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is \$0.52?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Total number of fruits brought = 10
Total number of apples brought = a
Total number of oranges brought = 10-a

Total price of the fruits = 5.6 = 0.4a + (10-a)0.6
5.6 = 0.4a + 6 - 0.6a
0.2a = 0.4
a = 2

We want average price to be 0.52. So assuming she returns x oranges.
# of apples = 2
# of oranges = 8-x

Average price = [2(0.4) + (8-x)(0.6)]/[2 + 8-x] = 0.52

x = 5
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4804
Location: Singapore

### Show Tags

21 Aug 2007, 00:11
Working alone at its constant rate, machine K took 3 hours to produce ¼ of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the unites produced last Friday. How many hours would it have taken machine
(A) 8
(B) 12
(C) 16
(D) 24
(E) 30

Let number of units be 24

K -> 6 units in 3 hours --> 2 units per hour
K+M -> 18 units in 6 hours --> 3 units per hour
M -> m units per hour

So K+M = 2 + m units per hour = 3; m = 1 unit per hour. To produce 24 units, machine M would need 24 hours.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4804
Location: Singapore

### Show Tags

21 Aug 2007, 00:13
(0.8)^-5 / (0.4)^-4=

(A) 3/32
(B) 5/64
(C) 1/2
(D) 1
(E) 2

(0.8)^-5 / (0.4)^-4
= 2^-5(0.4)^-5/(0.4)^-4
= 1/32(0.4)^-1
= 5/64
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4804
Location: Singapore

### Show Tags

21 Aug 2007, 00:13
There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
(A) 20
(B) 25
(C) 40
(D) 60
(E) 125

# of arrangements = 5!/3! = 20 ways
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4804
Location: Singapore

### Show Tags

21 Aug 2007, 00:22
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

(A) 1: 2
(B) 4: 5
(C) 1: 1
(D) 3: 2
(E) 5: 3

Total revenue in 1996 = x
Total revenue for cars in 1996 = c
Total revenue for trucks in 1996 = x-c

Total revenue in 1997 = 1.01x
Total revenue for cars in 1996 = 0.89c
Total revenue for trucks in 1997 = 1.07(x-x)

We want to find c/x-c

0.89c + 1.07x - 1.07c -c - x + c = 0.01x
-0.18c + 0.06x = 0
x = 3c

So total revenue for trucks in 1996 = x-c = 2c
and c/x-c = 1:2
Senior Manager
Joined: 03 May 2007
Posts: 257

### Show Tags

21 Aug 2007, 13:01
BCC145 wrote:

C, C, B, C, B, ?, E, D, ?, A, A

Can you please post the OAs?

OA are

C, C, B, C, B, D, E, D, A, B, A
Manager
Joined: 01 Oct 2007
Posts: 83

### Show Tags

01 Oct 2007, 13:06

The function f is defined for each positive three-digit integer n by f(n) = 2^x*3^y*5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?

Then it would have a unique solution m-v = 20, which is reported as the OA.
Non-Human User
Joined: 09 Sep 2013
Posts: 9433
Re: A certain club has 20 members. What is the ratio of the  [#permalink]

### Show Tags

30 Dec 2018, 12:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A certain club has 20 members. What is the ratio of the &nbs [#permalink] 30 Dec 2018, 12:10

Go to page   Previous    1   2   [ 36 posts ]

Display posts from previous: Sort by