## FDP p39; If x is a positive integer, what is the units..

If you're experiencing a roadblock with one of the Manhattan Prep GMAT math strategy guides, help is here!
KyleB713
Students

Posts: 2
Joined: Sun Mar 29, 2015 4:48 pm

### FDP p39; If x is a positive integer, what is the units..

I am having trouble understanding the problem on page 39 of the FDP guide. I see why statement 1 is insufficient but can't completely see why statement 2 is sufficient.

Based on the explanation provided, there are multiple numbers which satisfy statement 2: 45, 65, etc.

If this is the case, then how can it be sufficient with more than one possible answer for x? Or is the question simply, once statement 2 has been satisfied, that the units digit of the "test number(s)" be the same regardless of the number?
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: FDP p39; If x is a positive integer, what is the units..

Please note that the forum rules indicate you need to include the full text of the problem before we can discuss it, so that other students can benefit from the discussion as well.
Tim Sanders
Manhattan GMAT Instructor

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
KyleB713
Students

Posts: 2
Joined: Sun Mar 29, 2015 4:48 pm

### Re: FDP p39; If x is a positive integer, what is the units..

The full question:

If x is a positive integer, what is the units digit of x?

(1) The units digit of x/10 is 4.

(2) The tens digit of 10x is 5.
RonPurewal
Students

Posts: 19746
Joined: Tue Aug 14, 2007 8:23 am

### Re: FDP p39; If x is a positive integer, what is the units..

KyleB713 wrote:I am having trouble understanding the problem on page 39 of the FDP guide. I see why statement 1 is insufficient but can't completely see why statement 2 is sufficient.

Based on the explanation provided, there are multiple numbers which satisfy statement 2: 45, 65, etc.

If this is the case, then how can it be sufficient with more than one possible answer for x? Or is the question simply, once statement 2 has been satisfied, that the units digit of the "test number(s)" be the same regardless of the number?

the green thing is the point, because that's THE FOCUS OF THE QUESTION.
RonPurewal
Students

Posts: 19746
Joined: Tue Aug 14, 2007 8:23 am

### Re: FDP p39; If x is a positive integer, what is the units..

RonPurewal wrote:the green thing is the point, because that's THE FOCUS OF THE QUESTION.

that deserves to be in all capital letters, by the way, because this whole concept of FOCUS is the entire reason why DS exists in the first place.

note how this problem works:
• if you have THE PROPER FOCUS (= ONLY the units digit), you'll get the problem correct.
• if you try to find the actual value of x (= you're ignoring THE PROPER FOCUS), you'll get the problem incorrect.

in other words:
• if you have THE PROPER FOCUS, the problem will reward you.
• if you do not, the problem will punish you.

this is impossible to do with a multiple-choice problem. (if the problem contains enough information to find the value... well, you can find the value.)
but, with the format of DS—in which you may or may not have to combine the statements—it's possible to do this.
...and so that's how nearly ALL data sufficiency problems will work (unless you're scoring toward the bottom of the quant scale).

be aware!
MichaelM373
Course Students

Posts: 6
Joined: Tue Sep 22, 2015 4:33 pm

### Re: FDP p39; If x is a positive integer, what is the units..

After reading these replies, reading the text over and over, and sleeping on it I still do not understand why statement 2 is sufficient. I understand why any value for x ending in 5 would make it correct, but what about values that don't end in 5? Those values would make the statement false. Is it the fact that there are multiple values (45,65,15, etc.) that make the statement correct? I'm trying to look at this through the "business" mindset, but am missing it. Thanks in advance for your help.
-Mike
MichaelM373
Course Students

Posts: 6
Joined: Tue Sep 22, 2015 4:33 pm

### Re: FDP p39; If x is a positive integer, what is the units..

I guess the true question is why are some values ignored in statement 2, whereas statement 1 they aren't.
-Mike
RonPurewal
Students

Posts: 19746
Joined: Tue Aug 14, 2007 8:23 am

### Re: FDP p39; If x is a positive integer, what is the units..

the question is not "what is x?"
therefore, those are not multiple answers TO THE QUESTION.

take a look at the question again... the question is just "what is the units digit of x?"
if there's only one answer to this question, then that's "sufficient".

__

again, scroll up and read my post about "the entire reason why DS exists in the first place".
if you approach this question by trying to find the actual value of x -- rather than just that single digit that you actually WANT -- then, you have the wrong goal.
and, as i mentioned above, "right goal vs. wrong goal" is the whole reason why they invented this entire problem type.
Divs95
Students

Posts: 1
Joined: Wed Jul 06, 2016 2:36 pm

### Re: FDP p39; If x is a positive integer, what is the units..

If you assume x to be 34 or 44, then it would make statement 1 sufficient and then the answer will be A. However, if you assume x to be 45 or 65, then it would make statement 2 sufficient and the answer will be B.
How do you know which numbers to pick to test the situation? Do you always have to pick numbers that will satisfy statement 2 first?
RonPurewal
Students

Posts: 19746
Joined: Tue Aug 14, 2007 8:23 am

### Re: FDP p39; If x is a positive integer, what is the units..

statement 1 is not sufficient. it's impossible to "pick numbers that make it sufficient".

__

you wrote:
If you assume x to be 34 or 44, then it would make statement 1 sufficient

from this excerpt ^^ it's clear that, unfortunately, you don't understand the basics of data sufficiency.
in other words, it's clear that you still lack a basic understanding of what "sufficient" and "not sufficient" actually mean -- so, any attempts you're making to manipulate these concepts aren't going to work.

this forum isn't the place for basic explanations. but, if you are enrolled in one of our courses, just pay close attention to the early lessons, and you'll have the requisite basic understanding soon.
MichaelM373
Course Students

Posts: 6
Joined: Tue Sep 22, 2015 4:33 pm

### Re: FDP p39; If x is a positive integer, what is the units..

Thanks Ron. I think I understand now. When testing I need to test numbers that answer the question AND make the statement true, otherwise it is insufficient. So for this problem it doesn't matter what x is as long as it ends in 5, even if there are multiple possible values for x. Would you agree with that logic?
-Mike
RonPurewal
Students

Posts: 19746
Joined: Tue Aug 14, 2007 8:23 am

### Re: FDP p39; If x is a positive integer, what is the units..

MichaelM373 wrote: When testing I need to test numbers that answer the question AND make the statement true, otherwise it is insufficient

...still not really. if you don't make the statement(s) true, then that just doesn't count at all (it's neither "sufficient" nor "insufficient"). you ALWAYS have to make the statement(s) true.

again, you should really go through the intro DS part of one of the courses—there's really no substitute for that in a forum post, in terms of a thorough grounding in the DS format.