Is the hundredths digit of the decimal d greater than 5?

d can be any number, so it's not necessary to be of the form 0.12345, it can be 12345.12345 or any other real number in decimal representation. But for this particular question it really doesn't matter so we can take d to be \(a.bc\) (it does not matter how many numbers are before decimal point or after hundredth digit).

Is \(c>5\)?

(1) The tenths digit of 10d is 7 --> \(10d=ab.c\) --> tenth digit of \(10d\) is \(c\), so \(c=7>5\). Sufficient.

(2) The thousandths digit of d/10 is 7 --> \(\frac{d}{10}=0.abc\) --> thousandth digit of \(\frac{10}{d}\) is \(c\), so \(c=7>5\). Sufficient.

Answer: D.

Note:
1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS

Similar questions:
https://gmatclub.com/forum/tens-digit-10 ... hs#p787863
https://gmatclub.com/forum/arithmetic-ds ... hs#p786226
https://gmatclub.com/forum/geometry-and- ... hs#p765373
https://gmatclub.com/forum/help-solve-me ... hs#p722510
https://gmatclub.com/forum/gmat-prep-ds- ... hundredths
https://gmatclub.com/forum/hundreth-digi ... hs#p791277

Hope it helps.
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Thanks bunuel,
But what if the decimal
d=72121.212121
d/10 = 7212.12121
in this case with statement 2, the thousands digit is 7 but that information is not enough to find out the hundredth digit... please correct me where i am wrong...
Thank you very much for the reply

Is the hundredths digit of decimal d greater than 5?
(1) The tenths digit of 10d is 7
(2) the thousandths digit of d/10 is 7

There is a difference between THOUSANDS and THOUSANDTHS.

1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS
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Oh my GOD....
This is first time i have paid attention to this term thousands and thousanths

In the decimal abcd.xyz, x is the tenths digit, y is the hundredths digit, and z is the thousandths digit.

Once you know how the digits after the decimal point are named this is an easy one.

Statement 1: If the tenths digit of 10d is 7, then the hundredths digit of d is 7, which is more than 5. Sufficient.

Statement 2: The thousandths digit of d/10 is the same as the hundredths digit of d, which is 7 and more than 5. Sufficient.

(D) it is.
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Its D because you can use any number as sample:

Lets say you have .456; then .456*10= 4.56 then 5 has to be the hundredths digit before the multiplication. In the questions problem the 5 is actually a 7. (1) sufficient.

In the same way, 3.456/ 10 = .3456; thus the former hundredths digit is now the thousandths digit which is given. (2)(Sufficient)

Thus D.

Take the number as, d= 0.tHT, where t= tens digit, H= Hundred's digit, and T= Thousand's digit.

We need to find weather H is greater than 5

Now, 1) 10d= t.HT, ten's digit for this number = H= 7, which is greater than 5.

2) d by 10 = 0.0tHT, thousand's digit= H = 7, which is greater than 5.

Hence IMO d

Hi banuel,

you posted in 1234.567, 5 = 10 th digit. Will you please explain. Is it not unit digit ?

Thanks in advance.
Regardsi

Nope. In 1234.567 the units digit is 4 (the first digit to the left of decimal point) and the tenths digit is 5 (the first digit to the right of decimal point).
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the hundredths digit of the decimal d great than 5?
1) The tenths digit of 10d is 7.
2) The thousandths digit of d/10 is 7.

There is one variable (d) and 2 equations are given by the conditions, so there is high chance (D) will become the answer.
For condition 1, the hundredth digit of d=7. This is unique and the condition is hence sufficient
For condition 2, the hundredth digit of d=7. This is unique and the condition is hence sufficient
1)=2), and the answer hence becomes (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Hello Bunuel!

If 1 is THOUSANDS,
What is '0' and '-1'?

Also, if 7 is THOUSANDTH,
What is '8' and '9'?



It might be negligible, but I want to know.
Thanks!

Number 1234.567 is given as an example. Before THOUSANDS is TEN THOUSANDS, and after THOUSANDTH is ten thousandth...
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Can we solve it this way:

STATEMENT 1

For the tenth digit of 10d to be 7

d can be 0.07 then 10*d --> 10*0.07 = 0.7 = the tenth digit is 7

referring back to the question stem, d = 0.07 here and the hundredths digit = 7 therefore the hundredths digit is greater than 5

S1 is sufficient on its own (we could also plug in d=0.77 and we still find that the tens digit is 7 and the hundredths digit of d is greater than 5)

S2 tells us for d /10 --> the thousandths digit is 7

Plugging in 0.07 for d we can 0.07/10 = 0.007 --> the thousandths digit is 7

d = 0.07, the hundredths digit is greater than 5

Statement 2 is also sufficient on its own.

Answer choice D