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Compare the fraction
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26 Dec 2016, 16:32
26 Dec 2016, 16:32
3
Expert Reply
3
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Question Stats:
82% (01:09) correct
17% (01:02) wrong based on 146 sessions
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Quantity A |
Quantity B |
15/16 + 1/256 |
1 - 1/64 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Drill 1
Question: 3
Page: 310
Question: 3
Page: 310
Re: Compare the fraction
[#permalink]
26 Dec 2016, 16:48
26 Dec 2016, 16:48
5
Expert Reply
Explanation
In Quantity A, \(\frac{15}{16}+\frac{1}{256}=\frac{241}{256}\),
and in Quantity B, \(1-\frac{1}{64}=\frac{63}{64}\). If you multiply the numerator and denominator of \(\frac{63}{64}\) by 4, you obtain a common denominator: \(\frac{63}{64}=\frac{252}{256}\).
Clearly \(\frac{252}{256} > \frac{241}{256}\), so Quantity B is greater.
In Quantity A, \(\frac{15}{16}+\frac{1}{256}=\frac{241}{256}\),
and in Quantity B, \(1-\frac{1}{64}=\frac{63}{64}\). If you multiply the numerator and denominator of \(\frac{63}{64}\) by 4, you obtain a common denominator: \(\frac{63}{64}=\frac{252}{256}\).
Clearly \(\frac{252}{256} > \frac{241}{256}\), so Quantity B is greater.
General Discussion
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Compare the fraction
[#permalink]
27 Jan 2017, 13:56
27 Jan 2017, 13:56
2
sandy wrote:
Quantity A |
Quantity B |
15/16 + 1/256 |
1 - 1/64 |
Quantity A: 15/16 + 1/256
Quantity B: 1 - 1/64
I want to add 1/64 to both quantities (you'll see why shortly). So, let's first rewrite 15/16 as 60/64 to get:
Quantity A: 60/64 + 1/256
Quantity B: 1 - 1/64
Add 1/64 to both quantities to get:
Quantity A: 61/64 + 1/256
Quantity B: 1
Let's apply some number sense
If we were to add 1/64 to 61/64, we'd get 62/64, which is less than 1.
Since 1/256 is LESS THAN 1/64, we can conclude that 61/64 + 1/256 = some number that's less than 1
So, we have:
Quantity A: some number that's less than 1
Quantity B: 1
Answer: B
