Given that a

Question

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

Bunuel · Accepted Answer

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.

Nidzo · Answer

b - a = 0
becomes b = a
Let a be 4 or -4, as it is the largest integer that a can be given a < 5, which means in this case b must be 4 or -4.

A. b = 5  cannot be as a cannot be 5 
B. b ≤ 5  covers both instances 
C. b ≥ 5  cannot be as a must be under 5 
D. b < 4  if a is 4 then this will not allow b to be 4 
E. b > 5  cannot be as a must be under 5

Answer B

nsdl1985 · Answer

but how come less than and equal to 5?
I mean in case of b<=5, we cover both possibilities. Less than criteria is fulfilled but b also equal to 5, how this criteria can be satisfied?
For b=5, a is not equal to 5.. So how come answer B is right?

Bunuel · Answer

b ≤ 5 means that b is less than OR equal to 5. We know that b < 5, so saying b ≤ 5 would be correct.

To understand the underline concept better practice other  Trickiest Inequality Questions Type: Confusing Ranges .

stne · Answer

Brian123 ,

Yes, I would like to agree with you on his one, though I haven't gone through the link posted by Bunuel ,   maybe there is something there which corrects our understanding. Please go through the link as posted by Moderator and see if it helps

Anyway, According to me too correct answer should have been  b <5  rather than  b \leq 5

From the stem we know  b = a

we also know  a < 5

Hence  b < 5

b= 5   cannot be true as  a < 5 .

sujoykrdatta , can you help us understand, thank you.

sujoykrdatta · Answer

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 Think of what values of a are possible: a = 4.99..., 4.1, 4, 3.8, 3, 2 ... Since b - a = 0, we have: b = a Thus, the values of b are: b = 4.99..., 4.1, 4, 3.8, 3, 2 ... Clearly, values of b are less than 5. Now, the choices don't include that as an answer So we need to find the NEXT BEST OPTION A. b = 5 - clearly wrong C. b ≥ 5 - clearly wrong D. b < 4 - not completely wrong, but we have missed out the values like 4.1, 4.8, etc. Hence, it is INCOMPLETE E. b > 5 - clearly wrong B. b ≤ 5 - all values of b are included, and we also have an extra value b = 5. We haven't missed any value. Hence, this is the most complete solution. Note: When we say b ≤ 5, it is read as b is LESS THAN OR EQUAL TO 5. Hence, it isn't wrong. Hope this helps! Posted from my mobile device

stne · Answer

Right Sir, Thank you.

Brian123 , Hope this helps. Remember  b < 5  ,  OR   b= 5

OR = Does not compulsorily have to be true.

Hence  b=5   need not be true.

I stand corrected.

bumpbot · Answer

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

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