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Sue has only pennies, dimes, and nickels in a jar. The jar has at leas

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Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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New post 16 Feb 2016, 00:04
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Sue has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar? (penny = 1 cent, nickel = 5 cents, dime = 10 cents)

A. 51 cents
B. 53 cents
C. 55 cents
D. 57 cents
E. 59 cents
[Reveal] Spoiler: OA

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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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New post 24 Feb 2016, 23:29
Bunuel wrote:
Sue has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?

A. 51 cents
B. 53 cents
C. 55 cents
D. 57 cents
E. 59 cents


First of all, we need to understand the conversion between pennies, dimes and nickels.
This might be obvious for the US citizens, but here is the conversion for the others.

1 dime = 10 cents
1 nickel = 5 cents
1 penny = 1cent


Do not worry, you are not expected to know this conversion on the GMAT.

Given: The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime
Required: Total amount in the jar.

Considering the options:

Option A. 51 cents - 4 dime, 2 nickel, 1 penny
Option B. 53 cents - 4 dime, 2 nickel, 3 penny
Option C. 55 cents - This is not possible
Option D. 57 cents - 5 dime, 1 nickel, 2 penny
Option E. 59 cents - 5 dimes, 1 nickel, 4 penny

Correct Option: C

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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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New post 24 Feb 2016, 23:55
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Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5.

so answer is C

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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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New post 22 Aug 2017, 23:05
Bunuel wrote:
Sue has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?

A. 51 cents
B. 53 cents
C. 55 cents
D. 57 cents
E. 59 cents


For a Non US citizen like me i dunno how to approach this question . No idea whats a Nickle ,dime or a penny. Do we need to remember this conversion?

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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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New post 22 Aug 2017, 23:21
goforgmat wrote:
Bunuel wrote:
Sue has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?

A. 51 cents
B. 53 cents
C. 55 cents
D. 57 cents
E. 59 cents


For a Non US citizen like me i dunno how to approach this question . No idea whats a Nickle ,dime or a penny. Do we need to remember this conversion?


Penny = 1 cent, nickel = 5 cents, dime = 10 cents.

The question itself will supply the relative conversions such as this one. Though you should have a few basic ones memorized: 1 hour = 60 minutes, ...

Check other Conversion problems to practice in Special Questions Directory.
_________________

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

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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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New post 23 Aug 2017, 07:07
My approach:

Total money value = (1 x P) + (5 x N) + (10 x D) = P + 5(N+2D) so Total - P = 5(N+2D)
where P, N, D are numbers of penny, nickel, and dimes respectively.

Form the question, P =1,2,3, or 4

So Total - P must be divisible by 5
Check if the answer can minus any of the values of P mentioned above to have a multiple of 5:

A. 51 -1 = 50.
B. 53 - 3 = 50.
C. 55 can't make any multiple of 3 with P. Stop here, this is the answer.

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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas [#permalink]

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New post 23 Aug 2017, 07:41
NamVu1990 wrote:
My approach:

Total money value = (1 x P) + (5 x N) + (10 x D) = P + 5(N+2D) so Total - P = 5(N+2D)
where P, N, D are numbers of penny, nickel, and dimes respectively.

Form the question, P =1,2,3, or 4

So Total - P must be divisible by 5
Check if the answer can minus any of the values of P mentioned above to have a multiple of 5:

A. 51 -1 = 50.
B. 53 - 3 = 50.
C. 55 can't make any multiple of 3 with P. Stop here, this is the answer.


Thanks! This is a great way to solve this problem.



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Re: Sue has only pennies, dimes, and nickels in a jar. The jar has at leas   [#permalink] 23 Aug 2017, 07:41
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