Rounding to the Nearest tenth

[andre.jacobovitz]

I have a question on the following problem in the CAT exam:

If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth?

(1) x = 5

(2) y = 9


The solution for (1) says:
(1) SUFFICIENT: When x = 5, then 8.35y rounded to the nearest tenth equals 8.4. Therefore, we have answered the question with a definite "No," so statement (1) is sufficient.

I don't get it. What if y > 5? Couldn't it be that 8.35y rounded to the nearest tenth is 8.6? Isn't only if y < 5 that 8.35y is 8.4?

Thanks!

[RonPurewal]

I don't get it. What if y > 5? Couldn't it be that 8.35y rounded to the nearest tenth is 8.6?

no. you're trying to round the wrong digit: you're not supposed to be rounding the "5" up or down.
since you're rounding to the NEAREST TENTH, you need to be rounding the TENTHS DIGIT, which is currently "3", either up (to 4) or down (to 3).
this rounding will of course be based on the digit that follows the "3", but you can only round a "3" down to a 3 or up to a 4. it's impossible to round 8.3.... to 8.6, no matter what may come after the 3.

if x = 5, then you have a tenths digit of "3" followed by a "5". therefore, you round that tenths digit up to a "4", no matter what, hence, sufficient.

here's a good takeaway here:
if you don't see what's up when there's a variable in place, then you should PLUG IN ACTUAL NUMBERS AND SEE WHAT HAPPENS.
in this problem, when you plug in x = 5, you get 8.35Y. if you don't see what's going on there, then try plugging in actual numbers 0 through 9 for Y:
8.350, 8.351, 8.352, 8.353, 8.354, ..., 8.359
as you can see, all of these round up to 8.4, and there is no possible way you're going to get 8.6 out of any of them.

--

analogy:
if i tell you to round 35x to the nearest hundred, you can't get 600.
you're trying to do that here, although the fact that you're dealing with decimals here probably makes it somewhat less obvious what's wrong in this case.

--

[kunal.gore]

I don't get it. What if y > 5? Couldn't it be that 8.35y rounded to the nearest tenth is 8.6?

no. you're trying to round the wrong digit: you're not supposed to be rounding the "5" up or down.
since you're rounding to the NEAREST TENTH, you need to be rounding the TENTHS DIGIT, which is currently "3", either up (to 4) or down (to 3).
this rounding will of course be based on the digit that follows the "3", but you can only round a "3" down to a 3 or up to a 4. it's impossible to round 8.3.... to 8.6, no matter what may come after the 3.

if x = 5, then you have a tenths digit of "3" followed by a "5". therefore, you round that tenths digit up to a "4", no matter what, hence, sufficient.

here's a good takeaway here:
if you don't see what's up when there's a variable in place, then you should PLUG IN ACTUAL NUMBERS AND SEE WHAT HAPPENS.
in this problem, when you plug in x = 5, you get 8.35Y. if you don't see what's going on there, then try plugging in actual numbers 0 through 9 for Y:
8.350, 8.351, 8.352, 8.353, 8.354, ..., 8.359
as you can see, all of these round up to 8.4, and there is no possible way you're going to get 8.6 out of any of them.

--

analogy:
if i tell you to round 35x to the nearest hundred, you can't get 600.
you're trying to do that here, although the fact that you're dealing with decimals here probably makes it somewhat less obvious what's wrong in this case.

--

how come 8.35 rounds to 8.4? why not 8.3... it is equally close to both if y were 0.

[Ben Ku]

The rounding rule states this:
If the next digit is LESS than 5, then round DOWN.
If the next digit is GREATER THAN or EQUAL to 5, then round UP.

So 5.34 would be rounded to 5.3, while 5.35 would be rounded to 5.4.

Hope that helps.