What is the thousandths digit of the decimal p ?

What is the thousandths digit of the decimal p ?

(1) p is equivalent to the fraction 4/7. We are given the exact value of p, thus we can find its thousandths digit. Sufficient.

(2) The units digit of 100p is 2. Say p=a.bcd, the thousandths digit would be d. Given that the units digit of 100p=abc.d is 2, thus we have that c=2, but we need d. Not sufficient.

Answer: A.

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For Decimal numbers, such as 0.abcd Each digit has a different place value.

The first digit after the decimal point is called the tenths place value.
The second digit tells you how many hundredths there are in the number.
The third digit is the thousandths place.
The fourth digit is the ten-thousandths place , and so on.

Now back to the question :
let p=0.abcd, we need to know the value of c

(1) p=4/7
Well we have been given the entire no, who cares what is asked, any digit of the resultant decimal number can be answered =>Definitely sufficient

(2)units digit of 100p is 2
i.e. for ab.cd, b=2
we still dont know c though =>Clearly insufficient

Ans: A

Here is the Official Explanation from the GMAT Hacks website.

Answer: A
Statement (1) is sufficient. It would require long division to determine the thousandths digit of 4/7, but since 4/7 is a specific real number, we should realize that we could do so.

Statement (2) is insufficient. Say that 100p = 112.11, for one example when the units digit is 100p is 2. We're interested in p, so divide both sides by 100:
p = 112/100 = 1.1211

The thousandths digit is 1--but remember that we invented that digit for the purpose of an example. It could just as easily have been any other integer. Choice (A) is correct.

The first digit after decimal is "tenth", 2nd is "hundredth" and the third digit is "thousandth" and so on.

So \(p = XX.abcd\) where c is the thousandth digit.

Statement 1 :-
If p = 4/7 then we can certainly know what is the thousandth digit.
Even if it ends at tenth digit or hundredth digit (eg in case of 2/5 which is equal to 0.4) we know that the thousandth digit will be "0" in that case. So no need to actually calculate here.

Statement 2 :-
If we multiply p which is \(p = XX.abcd\) by 100 then we get \(XXab.cd\).

It is given what b is but we are interested in thousandth digit which is c. Hence Not sufficient.

Answer A.

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