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

It is currently 20 Jul 2018, 15:24

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

A collection of U.S. coins consists of pennies, nickels, dimes, and qu

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 28 Mar 2018, 02:50
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

77% (01:54) correct 23% (01:29) wrong based on 39 sessions

HideShow timer Statistics

A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1831
Premium Member CAT Tests
A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 29 Mar 2018, 19:53
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

You can't just add ratio parts and look for the answer that is NOT a multiple of 16. The answers are all multiples of 16.

Respectively, each answer, divided by 16, has a quotient of 5, 6, 7, 10, and 15

One way to find which answer is impossible:

Call the multiplier x
Find x if 6x=30
If 5x = 30
If 3x = 30
If 2x = 30
The arithmetic is not complicated. Multiply and sum.

If there are 30 of the 6x coin:
6x = 60, and x = 5
5x = 25, 3x = 15, 2x = 10
30 + 25 + 15 + 10 = 80. That's answer A

If there are 30 of the 5x coin:
5x = 30 and x = 6
6x = 36, 3x = 18, 2x = 22
30 + 36 + 18 + 12 = 96. That's answer B

If there are 30 of the 3x coin:
3x = 30 and x = 10
6x = 60, 5x = 50, 2x = 20
30 + 60 + 50 + 20 = 160 That's Answer D

If there are 30 of the 2x coin:
2x = 30 and x = 15
6x = 90, 5x = 75, 3x = 45
30 + 90 + 75 + 45 = 240. That's Answer E

112 does not work

Answer C
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 623
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post Updated on: 29 Mar 2018, 23:40
The ratio is 2:3:5:6
Let the coins are 2x,3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C
_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS


Originally posted by gmatbusters on 29 Mar 2018, 20:00.
Last edited by gmatbusters on 29 Mar 2018, 23:40, edited 1 time in total.
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2948
Location: India
GPA: 3.12
Premium Member
A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 29 Mar 2018, 22:58
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?
6
(A) 80
(B) 96
(C) 112
(D) 160
(E) 240



Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

Since the number of coins of one of the denominators is 30, either 2x,3x,5x, or 6x must be 30.

If 2x = 30 -> x = 15. 16x = 240
If 3x = 30 -> x = 10. 16x = 160
If 5x = 30 -> x = 6. 16x = 96
If 6x = 30 -> x = 5. 16x = 80

Only Option C(112) CANNOT be the total number of coins in the collection.
_________________

You've got what it takes, but it will take everything you've got

SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1831
Premium Member CAT Tests
A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 29 Mar 2018, 23:02
pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240



Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

Evaluating answer options,
(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.

pushpitkc and maybe gmatbusters . . .

16*7 = 112

:?
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1831
Premium Member CAT Tests
A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 29 Mar 2018, 23:07
gmatbusters wrote:
The ratio is 2:3:5:6
Let the coins are 2x,2x 3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C

gmatbusters , I don't follow your steps.

What are your steps, please?

And is
Quote:
Let the coins are 2x,2x 3x, 5x, 6x


that part a typo?
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 623
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 29 Mar 2018, 23:39
Since the ratio is given we can suppose the no of coins as 2x,3x,5x,6x.total =16x

If 2x =30
We get x = 15

Total = 15*16 = 240. Hence 240 is possible.

Similarly for other cases.


We find that x is not equal to 7. Hence 112 is not possible.

Hope it is clear now.

generis wrote:
gmatbusters wrote:
The ratio is 2:3:5:6
Let the coins are 2x,3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C

gmatbusters , I don't follow your steps.

What are your steps, please?

And is
Quote:
Let the coins are 2x,2x 3x, 5x, 6x


that part a typo?


Posted from my mobile device
_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 623
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 29 Mar 2018, 23:42
Yes you are right.2x has been written twice inadvertently. it is a typo. Tganks for pointing out.

I revised it.

generis wrote:
gmatbusters wrote:
The ratio is 2:3:5:6
Let the coins are 2x,2x 3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C

gmatbusters , I don't follow your steps.

What are your steps, please?

And is
Quote:
Let the coins are 2x,2x 3x, 5x, 6x


that part a typo?


Posted from my mobile device
_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 623
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 29 Mar 2018, 23:48
We find that if total is 112,which is 16*7 doesnt gives any number of coin as 30.

If we take 112 as total, and ratio as 2:3:5:6.
Then the coins will be
2*112/(2+3+5+6) =14,
3*112/(2+3+5+6) =21,
5*112/(2+3+5+6) =35,
6*112/(2+3+5+6) =42.

No denomination is present as 30 numbers. which is against the question.

Hence 112 is not the total number of coins.


generis wrote:
pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240



Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

Evaluating answer options,
(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.

pushpitkc and maybe gmatbusters . . .

16*7 = 112

:?


Posted from my mobile device
_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 623
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 30 Mar 2018, 00:01
This approach is not applicable to this question, as all the options are multiple od 16.

pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240



Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

Evaluating answer options,
(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.


Posted from my mobile device
_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2948
Location: India
GPA: 3.12
Premium Member
A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 30 Mar 2018, 05:41
generis wrote:
pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240



Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

Evaluating answer options,
(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.

pushpitkc and maybe gmatbusters . . .

16*7 = 112

:?


Thanks for informing generis - Corrected my solution!
_________________

You've got what it takes, but it will take everything you've got

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679
Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

Show Tags

New post 09 Apr 2018, 16:32
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240


We can create the ratio of pennies : nickels : dimes : quarters = 2x : 3x : 5x : 6x

So the total number of coins is 16x.

If there are 30 pennies, then x = 15 and 16x = 240.

If there are 30 nickels, then x = 10 and 16x = 160.

If there are 30 dimes, then x = 6 and 16x = 96.

If there are 30 quarters, then x = 5 and 16x = 80.

Thus, 112 cannot be the total number of coins.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu &nbs [#permalink] 09 Apr 2018, 16:32
Display posts from previous: Sort by

A collection of U.S. coins consists of pennies, nickels, dimes, and qu

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

Events & Promotions

PREV
NEXT


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®.