## is the hundredths digit of the decimal d greater than 5?

Math questions from mba.com and GMAT Prep software
guest

### is the hundredths digit of the decimal d greater than 5?

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

1) The tenths digit of 10d is 7.

2) The thousandths digit of d/10 is 7.

Can anyone help? Tks in advance.
Guest

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

1) The tenths digit of 10d is 7.

2) The thousandths digit of d/10 is 7.

Can anyone help? Tks in advance.

(1) Suppose 10d=***.7***, in which each star represents a digit, whether equal or unequal.

d=**.*7***. So the hundredths digit is 7. Sufficient.

(2) Similarly, this statement is also sufficient.

D
Guest

### is the hundredths digit of the decimal d greater than 5?

Nice - tks for your help. Amazingly simple!!!
parvezshah

### Re: is the hundredths digit of the decimal d greater than 5?

guest wrote:is the hundredths digit of the decimal d greater than 5?

1) The tenths digit of 10d is 7.

2) The thousandths digit of d/10 is 7.

Can anyone help? Tks in advance.

my take is answer is E
let the digit be ***.****** or it is ********.*

stmt 1 ) says 10(***.******) tenth is 7 == ****.***7* or *******7*
so no conclusion

similarly statment 2 also is inconclusive
2) The thousandths digit of d/10 is 7.
says (***.******)/ thousandths digit is 7 == ***.**7*7* or *****7*7.*
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

### Re: is the hundredths digit of the decimal d greater than 5?

parvezshah wrote:
guest wrote:is the hundredths digit of the decimal d greater than 5?

1) The tenths digit of 10d is 7.

2) The thousandths digit of d/10 is 7.

Can anyone help? Tks in advance.

my take is answer is E
let the digit be ***.****** or it is ********.*

stmt 1 ) says 10(***.******) tenth is 7 == ****.***7* or *******7*
so no conclusion

similarly statment 2 also is inconclusive
2) The thousandths digit of d/10 is 7.
says (***.******)/ thousandths digit is 7 == ***.**7*7* or *****7*7.*

the post above yours contains the correct solution, so you should study the differences between that post and yours.
here's what you're doing wrong: you're confusing the thousandths digit and the thousands digit. those are completely different digits, and are not to be confused with one another.
the thousands digit is 4 spots to the left of the decimal point: e.g., the '1' in 1000.
the thousandths digit is 3 spots to the right of the decimal point: e.g., the '1' in 0.001.
in general, if a place value ends in '-ths', then that place value signifies a DECIMAL place; if it doesn't, then it signifies one of the INTEGER places (i.e., the ones to the left of the decimal point).

same distinction goes for the tens place (2 spots to the left of the decimal point) and the tenths place (one spot to the right of the decimal point).

watch the distinction, and try not to confuse them - each spot has a unique name!
Guest

Could someone please provide an explanation as to how one got the answer, that is D. How did the 7 move from the tenths place to the hundredths place? Did I miss something?

Greatly appreciated....
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

Anonymous wrote:Could someone please provide an explanation as to how one got the answer, that is D. How did the 7 move from the tenths place to the hundredths place? Did I miss something?

Greatly appreciated....

you shouldn't think of it as though the 7 has moved; you should think of it as though the decimal point has moved. in fact, this is precisely what has happened, as both statements involving multiplication by powers of 10 (which serves to move the decimal point while leaving the digits themselves unaffected).

here's the deal:
you are interested in the hundredths place of the original number 'd'. to wit, let's write 'd' as a succession of decimal places:
d = XXXXXX.XXXX...
in this version, the orange digit is the one in which you're interested.

statement (1) concerns the number 10d, not d. when you multiply by 10, the decimal point is shifted to the right by one spot, so that the ones digit becomes the new tens digit and so on. so, with 'd' represented as above, you can write
10d = XXXXXXX.XXX...
according to statement (1), then, the orange digit is 7, so statement (1) is sufficient.

statement (2) concerns the number d/10, not d. when you divide by 10, the decimal point is shifted to the left by one spot, so that the tens digit becomes the new ones digit and so on. so, with 'd' represented as above, you can write
d/10 = XXXXX.XXXXX...
according to statement (2), then, the orange digit is 7, so statement (2) is sufficient.

hth.
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

to the users of the forum:
color is great for problems like this one. (i actually have no idea how i would explain this problem without coloring the digits.)

if you want to learn how to use color, just hit 'quote' on my post above, look at the color tags in the quoted text, and emulate them in your own posts.

sweetness
Guest

### is the hundredths digit of the decimal d greater than 5?

Ron,

I love ur method of representing the digits with xxxxxxx.xxxxx, the reason is I have seen some of these sums before and I was always baised to take numbers which they are asking for thus and it would always satisfy the question. In the above question I was again baised to start with actually taking 7 and then work... you get the point.. But with xxx that is gone.. Thanks I think these kind of sums are newly introduced and one is sure to see one of these on the D day...thanks again
rfernandez
ManhattanGMAT Staff

Posts: 381
Joined: Fri Apr 07, 2006 8:25 am

Guest

### Re: is the hundredths digit of the decimal d greater than 5?

guest wrote:is the hundredths digit of the decimal d greater than 5?

1) The tenths digit of 10d is 7.

2) The thousandths digit of d/10 is 7.

Can anyone help? Tks in advance.

If one is not comfortable with fonts and also does not wish to use X's, here is another way.

Let d= uvw.xyz
question: is y>5?

1) 10d = uvwx.yz and, therefore, tenths digit i.e. y=7, which is greater than 5.
2) d/10 = uv.wxyz hence thousandths digit i.e. y=7, which again is greater than 5.

Hence, D. Use of distinct alphabets may make it easier to understand (in my opinion). Hope this helps.
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

### Re: is the hundredths digit of the decimal d greater than 5?

Anonymous wrote:
guest wrote:is the hundredths digit of the decimal d greater than 5?

1) The tenths digit of 10d is 7.

2) The thousandths digit of d/10 is 7.

Can anyone help? Tks in advance.

If one is not comfortable with fonts and also does not wish to use X's, here is another way.

Let d= uvw.xyz
question: is y>5?

1) 10d = uvwx.yz and, therefore, tenths digit i.e. y=7, which is greater than 5.
2) d/10 = uv.wxyz hence thousandths digit i.e. y=7, which again is greater than 5.

Hence, D. Use of distinct alphabets may make it easier to understand (in my opinion). Hope this helps.

also a good idea.