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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  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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Difficulty:   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.

Math Expert V
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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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 V
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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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.

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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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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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
GPA: 3.21
Re: Given that a < 5, and b - a = 0, which of the following must  [#permalink]

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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  B
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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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.

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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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.

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 D
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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Excellent Question...!!
If You examine 2 somehow is true for all values of B
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e-GMAT Representative D
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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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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VP  G
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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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.

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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