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

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Senior Manager
Joined: 21 Oct 2013
Posts: 414
Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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13 Aug 2014, 10:21
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55% (hard)

Question Stats:

54% (01:18) correct 46% (01:17) wrong based on 398 sessions

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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
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.
Math Expert
Joined: 02 Sep 2009
Posts: 55718
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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29 Aug 2014, 05:17
2
3
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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##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 55718
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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13 Aug 2014, 10:35
1
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
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.

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Intern
Joined: 30 Dec 2013
Posts: 4
Schools: AGSM '16
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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14 Aug 2014, 09:53
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.
Senior Manager
Joined: 21 Oct 2013
Posts: 414
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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28 Aug 2014, 08:14
1
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.
Director
Joined: 25 Apr 2012
Posts: 668
Location: India
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Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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28 Aug 2014, 21:08
3
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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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Intern
Joined: 23 Jul 2013
Posts: 14
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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28 Dec 2015, 22:25
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?
Senior Manager
Joined: 20 Aug 2015
Posts: 388
Location: India
GMAT 1: 760 Q50 V44
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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29 Dec 2015, 00:11
1
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?
Current Student
Joined: 12 Aug 2015
Posts: 2610
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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10 Mar 2016, 11:01
Excellent Question...!!
If You examine 2 somehow is true for all values of B
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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2892
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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18 Aug 2016, 04:24
3
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.

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.

Regards,
Harsh
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Joined: 09 Mar 2018
Posts: 1003
Location: India
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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27 Jan 2019, 20:21
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
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.

Never Assume anything

Said that a< 5, can mean a is any value from 4.9 to 4, from 3.23 to 3.17

b < = 5 covers all the values
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Re: Given that a < 5, and b - a = 0, which of the following must   [#permalink] 27 Jan 2019, 20:21
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# Given that a < 5, and b - a = 0, which of the following must

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