Greatest possible integer value of x+y?

Question

I found a interesting question in one exam.

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

(A) 18
(B) 20
(C) 23
(D) 24
(E) 25

MySol: For max value of x+y , x should be 9. So x+y = 9+14 = 23

But this is not correct. Can someone explain.

score 11 · Accepted Answer · answered Sep 06 '13 at 18:43

11

Note that $x+y=2x+5$. The greatest possible integer value of $2x$ occurs at $x=9.5$.

Remark: Unfortunately, a bit of a trick question. Not nice! One of my many objections to multiple choice questions is that they are too often designed to fool people into giving the "wrong" answer.

answered Sep 06 '13 at 18:43

André Nicolas

507,029

What do you mean by not nice? – vikiiii Sep 06 '13 at 18:47
6

I mean it is not a nice qustion to ask, since the main intent seems to be to get people to choose $23$. – André Nicolas Sep 06 '13 at 18:48
5

There's ambiguity on what number system to use for x and y. If x and y are integers then 23 is correct, however if rationals are allowed then 24 is the answer. – JB King Sep 06 '13 at 19:45
I did the problem in my head and came up with 24 by mistake. – Michael Sep 06 '13 at 21:05
All standardized tests that I know of state in the introduction of every math section that all variables represent Real numbers unless otherwise stated, so there is no actual ambiguity if you understand the rules. Also, standardized tests are not subject tests, they are reasoning tests; this is a very good reasoning question: "Do you actually think about all of the facets or jump to easy conclusions?" – John Sep 06 '13 at 23:42

score 4 · Answer 2 · answered Sep 06 '13 at 18:41

4

$x<10\implies y=x+5<15\implies x+y<10+15=25$

If $x+y$ has to be integer, $ x+y\le24$

Observe that the equality occurs if $x+y=24 \iff x+(x+5)=24\iff x=\frac{24-5}2=9.5$

i.e., $x,y$ are individually non-integer unlike your assumption

answered Sep 06 '13 at 18:41

lab bhattacharjee

274,582

In particular, consider $x = 9.5$, $y = 14.5$. – qaphla Sep 06 '13 at 18:42
But why my solution is wrong? – vikiiii Sep 06 '13 at 18:42
@vikiiii, as you have assumed $x,y$ individually to be integer – lab bhattacharjee Sep 06 '13 at 18:43
Okay..x+y should be integer .But x and y need not be integers. – vikiiii Sep 06 '13 at 18:45
@vikiiii, please find the edited answer – lab bhattacharjee Sep 06 '13 at 18:46
3

@vikiiii the question doesn't actually say that but if it were already supposed that $x$ and $y$ are integers then it would be redundant to ask for the greatest possible integer value of $x+y$. But your interpretation giving $23$ as the answer isn't really wrong. – Dan Brumleve Sep 06 '13 at 18:47

score 0 · Answer 3 · answered Sep 06 '13 at 18:44

0

$x+y = x+x+5 = 2x + 5$ and since $5<x<10$, we have $15<2x+5<25$.

answered Sep 06 '13 at 18:44

Alraxite

5,647

Greatest possible integer value of x+y?

3 Answers3