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

Question

(1) The units digit of x/10 = 4
(2) The tens digit of 10x = 5

I'm having a hard time understanding how the book tries to describe the logic of this question.

Using the example from the MGMAT, Fractions decimals and percents book #1, pg39.

for #1They test a few cases such as 45, and 46 where the units digit=4 (4.5 &4.6) but then they say if we had chosen 54, the units digit=5 so the stmt is not SUFF because it can give a diff answer if we pick a diff number for x.

2) They test two number 45 and 65 where the tens digit =5 (450, 650) but then they say if we had chosen 46 the tens digit = 6 so stmt will not be correct. 
BUT in this case, they say that  YOU have to pick a value that makes the stmt (2) TRUE. Discard the case of 46 ?????

I am so confused because that logic of discarding the #46 for stmt 2 but NOT discarding the #54 for Stmt 1) makes no sense. Why didnt they discard 54 for stmt 1? Why are they NOT trying to prove stmt 1 Correct?

Then they say that When you multiply x by 10,  units  digit becomes  tens.  if you know the tens digit of the new number is 5, then the units digit of the original number also has to be 5.

BUT we can say the same thing about stmt 1) when you divide x by 10,  tens digit becomes units . if you know the units digit of the new number is 4, then the tens digit of the original number also has to be 4.

Correct answer is B

What am I not understanding ?

mikemcgarry · Answer

Dear serena32 I'm happy to respond. :-)

Part of the point the MGMAT folks are making on that page is as followings. Picking numbers on DS can be a way to disprove a statement, to demonstrate that a statement is insufficient. We CANNOT use picking numbers as a way to prove a statement. If a statement IS sufficient, the only thing that picking numbers can do, at most, is to suggest a pattern. For proof of sufficiency, we need to use logic or a formula or something other than picking numbers . That is all extremely important. Also, the way picking numbers on DS works is as follows. If I want to check whether statement #1 is sufficient, I have to pick numbers that are consistent with statement #1. We want to know, when Statement #1 is true and in effect, does this determine a unique answer to the prompt question? That's sufficiency. Any number that is not consistent with Statement #1 is purely irrelevant. If Statement #1 is not true, then we don't care what happens. The whole point is to figure out what it means if Statement #1 IS true. That's why we only pick numbers consistent with the statement. Furthermore, all we need are two numbers consistent with Statement #1 that give us two different answers to the prompt question, and we are done. As soon as two different numbers are consistent with the prompt statement lead to two different answers to the prompt statement, automatically that means that this statement by itself is not going to be sufficient in determining a unique answer to the prompt question. As soon as they test 45 and 46 and get two different answers, they are done: statement #1, alone and by itself, has been shown to be insufficient. Now, statement #2 is sufficient, so while they pick a few numbers, it is 100% impossible to prove that a number is sufficient purely by picking numbers. It looks as if they picked 46 purely to demonstrate something that we shouldn't pick . Right after that, they made a point of saying: " You have to pick numbers that make statement #2 true. Discard this case. (Literally cross it off on your scrap paper.) " They were "pedagogically" breaking the rule, showing you what not to do by doing it. That's the only reason they picked 46 at all. In solving a DS, you NEVER should pick numbers that don't make the statement true. Finally, picking numbers wasn't going to cut it for statement #2, so in the final paragraph, they abandoned picking numbers and used some logical argument to demonstrate that statement #2 is true. Back to your other question, we can't use that same logic on statement #1. The prompt asks: " what is the units digit of x? " Statement #1 gives us clear information about the tens digit of x, but that is not what was ask. Clear information about a question not asked is useless. Politicians don't seem to understand that point, but math students need to understand it. Whatever statement #1 does tell us, it does NOT very specifically allow us to give a clear and definitive answer to the prompt question. Giving a clear and definitive answer to the prompt question is the entire point of the DS exercise. You may find this blog helpful: GMAT Data Sufficiency Tips Does all this make sense? Mike :-)

rohit8865 · Answer

(1) x/10=4
if x=40 thus unit digit is 0
if x=41 then x/10=4.1 thus unit digit is 1
(form of a number is ......XXXX,hundreds,tens,units . tens, hundreds, xxxxx --so there could be only one unit digit for any number)

not suff...

(2) The tens digit of 10x = 5
any number multiple of 10 have unit digit 0
thus if tens digit is 5 then unit digit of x=5(number 10x= xxxx50)
 suff...

Ans B

lrous44 · Answer

Hi all,

I too am struggling with this problem and would like some guidance on it.

For statement (1), we can plug in any number from 40 - 49 in order to produce a number with a units digit of 4. Therefore, since that is more than one outcome to satisfy this statement, it has to be insufficient. I understand that reasoning, as that is how I have handled pretty much every example Value DS problem up to this point.

However, where I begin to get confused is with the MGMAT's explanation for statement (2).

For statement (2), we can use 15, 25, 35, 45, 55, 65, 75, 85, and 95 to produce a number that has a tens digit of 5 while also having a uniform units digit of 0 (which satisfies what the main question is asking for). Obviously, we could not use a number like 150, as that would contradict statement (2) (and therefore we would just throw that value out). However, those are 8 different values that end up giving you a number with 5 in the tens digit and 0 as the unit digit. So, how exactly can it be sufficient if we have more than one value at play here? Is it because we know definitively that x can only be one of these 8 two-digit numbers I listed at the beginning of this stanza? It just seems like the same situation as statement (1), yet we deem it a completely different answer.

Thanks,

lrous44

Rilo0918 · Answer

Hi how come for statement 1, the numbers tried out are in the 40s? Can it be any random numbers?

And for statement 2, I understood your explanation. All integers are going to have units digit of 0. But is the statement suggesting to use numbers that’ll have a 5 for the tenths place? And since they still end up with a 0 in all of those, that’s why it’s sufficient?

If that’s the case, why not use an integer knowing that the units digit will have a 4. Like 34,44,54 etc.

Thank you!

Posted from my mobile device

Sevigny86 · Answer

Easiest way I find doing these is the following:

1. x/10 = _ _ 4, therefore, x = _ 4 _ ---> We don't know the units, it can be anything. (NS)
2. 10x = _ 5 _, therefore x = _ _ 5 ---> This gives us the units! (S)

Answer is B

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

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GMAT Data Sufficiency (DS) Questions

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

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