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Given that a < 5, and b - a = 0, which of the following must

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Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 13 Aug 2014, 09:21
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Given that a < 5, and b - a = 0, which of the following must be true about b?

A. b = 5
B. b ≤ 5
C. b ≥ 5
D. b < 4
E. b > 5

OE
[Reveal] Spoiler:
a = b
If b ≤ 5, a has to be < 5, else (a - b) will not be = 0.


Similar to the previous post, I found this question hard. Please help.
[Reveal] Spoiler: OA

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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 13 Aug 2014, 09:35
goodyear2013 wrote:
Given that a < 5, and b - a = 0, which of the following must be true about b?

A. b = 5
B. b ≤ 5
C. b ≥ 5
D. b < 4
E. b > 5

OE
[Reveal] Spoiler:
a = b
If b ≤ 5, a has to be < 5, else (a - b) will not be = 0.


Similar to the previous post, I found this question hard. Please help.


b - a = 0 --> b = a. Thus since a < 5, then b < 5 too. For any number which is less than 5 would be true that it's less than or equal to 5.

Answer: B.
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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 14 Aug 2014, 08:53
If a=b and a<5, how can b be equal to 5? As defined, "a" can not be equal to 5, "a" must be less than five.

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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 28 Aug 2014, 07:14
Hi Bunuel,

Thank you for the explanation.
One thing I am not sure about the answer is why b can be 5 while a can not be.

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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 28 Aug 2014, 20:08
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goodyear2013 wrote:
Hi Bunuel,

Thank you for the explanation.
One thing I am not sure about the answer is why b can be 5 while a can not be.

Given that a < 5, and b - a = 0, which of the following must be true about b?

A. b = 5
B. b ≤ 5
C. b ≥ 5
D. b < 4
E. b > 5


We are given that b=a and we are given that \(a\neq{5}\) and a<5
A... Since a =b so Option A is out
C...if\(b\geq{5}\)...means b =5 or greater then 5...then\(b\neq{a}\)
Option D ....we can say b<5 but not b<4...what if a =4.1....
Option E.... b=a and a<5 so...b<5...

If you use of POE, You end up with B as answer...Also,look at the choices which satisfy our given condition the most...B still wins..
Hope it helps
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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 29 Aug 2014, 04:17
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goodyear2013 wrote:
Hi Bunuel,

Thank you for the explanation.
One thing I am not sure about the answer is why b can be 5 while a can not be.


b cannot be 5 either. The point is that if a number is less that 5 (x < 5), it would also be correct to say about it that it's less than or equal to 5 (x <= 5).
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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.


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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 28 Dec 2015, 21:25
Bunuel wrote:
goodyear2013 wrote:
Hi Bunuel,

Thank you for the explanation.
One thing I am not sure about the answer is why b can be 5 while a can not be.


b cannot be 5 either. The point is that if a number is less that 5 (x < 5), it would also be correct to say about it that it's less than or equal to 5 (x <= 5).


Hi Bunuel,
I do agree with you upto the point where b<5 is correct. However, if b<=5, then it could mean that b = 5. However, "a" can go upto 4.99999999....999 but never 5. In that case b is not equal to a. I picked option B for there is no other better choice.

Can you provide your views on my point above please?

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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 28 Dec 2015, 23:11
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Meetup wrote:
Bunuel wrote:
goodyear2013 wrote:
Hi Bunuel,

Thank you for the explanation.
One thing I am not sure about the answer is why b can be 5 while a can not be.


b cannot be 5 either. The point is that if a number is less that 5 (x < 5), it would also be correct to say about it that it's less than or equal to 5 (x <= 5).


Hi Bunuel,
I do agree with you upto the point where b<5 is correct. However, if b<=5, then it could mean that b = 5. However, "a" can go upto 4.99999999....999 but never 5. In that case b is not equal to a. I picked option B for there is no other better choice.

Can you provide your views on my point above please?


Hi Meetup,

The question asks "which of the following must be true about b"
We know that b < 5
Here b < 5 is a subset of b ≤ 5
Hence we can say for sure that the values of b that lie in b < 5 will lie in b ≤ 5

Does this help?

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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 10 Mar 2016, 10:01
Excellent Question...!!
If You examine 2 somehow is true for all values of B
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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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New post 18 Aug 2016, 03:24
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For such questions, representing the inequalities on the number line is a good and non-confusing way to solve the question.

From the question statement, we get that b = a and hence b < 5. Let’s represent this inequality along with all the options on a number line and try to find out the answer.


Image


So, now we need to find for b < 5, which of the inequality/equation always holds true. Therefore, in the number line representations of the options, we need to look for a representation that definitely covers all the values of b < 5 (probably, along with some other value(s)).

So, we will look for an inequality/equation in the options, which is always true for all the values of b < 5, i.e. an inequality/equation whose representation on the number line is a super set of the representation of b < 5.

It is important to note here that a representation that covers all the values of b < 5 and also covers some additional values will also be always true for any value that satisfies the inequality b < 5.



Now, looking at the number line representations of the options, we can see that among all the options it is only option B (b ≤5) that covers all the possible values of b < 5 (along with the additional point 5 on the number line).

So, option B is always true for any value satisfying b < 5.

Again, do not be confused by the fact that option B also includes 5 in its solution set, which is not true for b < 5. What is important to understand is that any value that satisfies b < 5 also satisfies b ≤5.


Hope this helps. :-D

Regards,
Harsh
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Re: Given that a < 5, and b - a = 0, which of the following must [#permalink]

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Re: Given that a < 5, and b - a = 0, which of the following must   [#permalink] 18 Dec 2017, 20:02
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