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25 Feb 2026, 09:24
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (02:08) correct
61%
(02:15)
wrong
based on 62
sessions
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Not Attempted Yet
If <x|y> is equal to the smallest integer greater than one third of the sum of x and 2y, what is the smallest integer b such that <4|b> is equal to b – 5 ?
A. 18
B. 19
C. 20
D. 21
E. 22
A. 18
B. 19
C. 20
D. 21
E. 22
28 Feb 2026, 01:25
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Given:
<x|y> is equal to the smallest integer greater than one third of the sum of x and 2y
<x|y> = smallest integer greater than 1/3 * (x+2y)
Now,
b-5 is just bigger than 1/3 * (4+2b) = (4+2b)/3
Basically, (4+2b)/3 is just a little less than b-5
This means: (4+2b)/3 ~ b-5
4+2b ~ 3b-15
b ~ 19
Now, because the question says strictly greater than, the fraction cannot be an integer.
So, if b = 19:
(4+38)/3 = 14, which is an integer => We need to go one number up.
Try b = 20:
(4+40)/3 = 14.67
Smallest integer greater than that = 15
And, 20-5 = 15
Hence, the correct answer is Option C - 20.
<x|y> is equal to the smallest integer greater than one third of the sum of x and 2y
<x|y> = smallest integer greater than 1/3 * (x+2y)
Now,
b-5 is just bigger than 1/3 * (4+2b) = (4+2b)/3
Basically, (4+2b)/3 is just a little less than b-5
This means: (4+2b)/3 ~ b-5
4+2b ~ 3b-15
b ~ 19
Now, because the question says strictly greater than, the fraction cannot be an integer.
So, if b = 19:
(4+38)/3 = 14, which is an integer => We need to go one number up.
Try b = 20:
(4+40)/3 = 14.67
Smallest integer greater than that = 15
And, 20-5 = 15
Hence, the correct answer is Option C - 20.
28 Feb 2026, 07:49
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Very well done : effective use of the notion of just bigger!
