It is currently 21 Oct 2017, 02:05

### 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 June
Open Detailed Calendar

# 2 PS Questions, bugging me

Author Message
Intern
Joined: 08 Jun 2010
Posts: 4

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

2 PS Questions, bugging me [#permalink]

### Show Tags

14 Aug 2010, 12:47
00:00

Difficulty:

(N/A)

Question Stats:

50% (01:25) correct 50% (00:50) wrong based on 7 sessions

### HideShow timer Statistics

All,

I came upon this sample question online and I'm trying to figure out how they came up with their solution because of their solution makes no sense to me. Can anyone help?

QUESTION #1 (Fractions):
After installing a powerful pump onto a large gasoline tank, John pumped gasoline out of the tank. Each time John ran the pump, it removed 1/3 of the gas remaining in the tank. Assuming the gas tank was full when John began, what fraction of the total gas in the tank at the beginning was removed if John ran the pump three times?

Choices:
A) 8/27
B) 1/27
C) 2/3
D) 19/27 ---> was the chosen answer
E) 27/28

QUESTION #2 (Expression Simplification):
What is the units digit of 6^15 - 7^4 - 9^3?

A) 8
B) 7
C) 6 ---> they those this answer, WHY?
D) 5
E) 4

**For question #2, I guess I see why it will be 6 since the unit digit of 6^15 is far greater than 7^4 and 9^3 but I'm hoping to see how you arrive at that solution

Thanks!!

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

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 404

Kudos [?]: 249 [1], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: 2 PS Questions, bugging me [#permalink]

### Show Tags

14 Aug 2010, 13:12
1
KUDOS
broker wrote:
All,

I came upon this sample question online and I'm trying to figure out how they came up with their solution because of their solution makes no sense to me. Can anyone help?

QUESTION #1 (Fractions):
After installing a powerful pump onto a large gasoline tank, John pumped gasoline out of the tank. Each time John ran the pump, it removed 1/3 of the gas remaining in the tank. Assuming the gas tank was full when John began, what fraction of the total gas in the tank at the beginning was removed if John ran the pump three times?

Choices:
A) 8/27
B) 1/27
C) 2/3
D) 19/27 ---> was the chosen answer
E) 27/28

QUESTION #2 (Expression Simplification):
What is the units digit of 6^15 - 7^4 - 9^3?
/
A) 8
B) 7
C) 6 ---> they those this answer, WHY?
D) 5
E) 4

**For question #2, I guess I see why it will be 6 since the unit digit of 6^15 is far greater than 7^4 and 9^3 but I'm hoping to see how you arrive at that solution

Thanks!!

1. 19/27.

Total gasoline -- 1 unit.

First time the pump is run:
Amount of gasoline removed -- (1/3), amount remaining - 1 - (1/3) = (2/3)

Second time the pump is run:
Amount of gasoline removed -- (1/3) * (2/3), amount remaining - (2/3) - (1/3) * (2/3) -- 4/9

Third time the pump is run:
Amount of gasoline removed -- (1/3) * (4/9).

Hence total gasoline removed -- (1/3) + (2/9) + (4/27).

= (19/27) units.

2. 6
Explanation:
6^15 - 7^4 - 9^3

6^15 -- unit digit would be 6. (Unit digit repeats for all positive power of 6 i.e., 6^1, 6^2 .... is always 6.)

7^4 -- 1.

9^3 -- 9.

Hence 6^15 - (7^4 + 9^3)

= 6 - (1 + 9) == 6 - 10

6^15 --- would be something like XXX..X6
(7^4 + 9^3) -- would be something like XXX..10

And hence when you subtract the 6 with 0, the unit digit would remain in the answer.
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Last edited by ezhilkumarank on 14 Aug 2010, 13:24, edited 3 times in total.

Kudos [?]: 249 [1], given: 50

Intern
Joined: 08 Jun 2010
Posts: 4

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

Re: 2 PS Questions, bugging me [#permalink]

### Show Tags

14 Aug 2010, 13:15
ezhilkumarank,

can you pls take me through your thought process? i already know the answer, as indicated in my post, but want to know how's solved.

thx

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

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 404

Kudos [?]: 249 [1], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: 2 PS Questions, bugging me [#permalink]

### Show Tags

14 Aug 2010, 13:23
1
KUDOS
broker wrote:
ezhilkumarank,

can you pls take me through your thought process? i already know the answer, as indicated in my post, but want to know how's solved.

thx

Edited my post to include the explanation.
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Kudos [?]: 249 [1], given: 50

Intern
Joined: 08 Jun 2010
Posts: 4

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

Re: 2 PS Questions, bugging me [#permalink]

### Show Tags

14 Aug 2010, 13:31
wow, what a difference a straight forward explanation can do! you did in few lines what they did in almost a full page of explanations. thanks a bunch!!

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16611

Kudos [?]: 273 [0], given: 0

Re: 2 PS Questions, bugging me [#permalink]

### Show Tags

23 Jun 2017, 11:58
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: 2 PS Questions, bugging me   [#permalink] 23 Jun 2017, 11:58
Display posts from previous: Sort by