What is the tenths digit of the quotient when thirty-five hundredths

Yes, we definitely want to be clear on what hundredths and thousandths are!

One hundredth = 1/100 = 0.01
One thousandth = 1/1000 = 0.001

So, we could do this either with fractions or decimals. With fractions:

Thirty-five hundredths = 35/100
Four thousandths = 4/1000

This is what hmasand did above, calculating \(\frac{35}{100}\) / \(\frac{4}{1000}\) = \(\frac{35*1000}{4*100}\) = \(\frac{350}{4}\) = 87.5

With decimals:

Thirty-five hundredths = 0.35
Four thousandths = 0.004

We would then be calculating \(\frac{0.35}{0.004}\), which we can multiply by \(\frac{1000}{1000}\) to get rid of the decimals, giving us \(\frac{350}{4}\) = 87.5 again.

Please let me know if you have any questions!

I believe the solution is as follows.

35/100 / 4/1000 (35/100 and 4/1000)

35 * 1000 / 4 * 100

350 / 4

87.5 (got the clue from tenTHS-after decimal not teNS-before decimal)

E is the answer.

Posted from my mobile device

If i am not wrong , i think question means the following
3500/4000= 0.875 so the tents digit of decimal would be '5' .. IMO E

I assumed that this means decimal calculation: 35/100/4/1000 -> 35/100*1000/4 -> 87,5. As you can see, my result would be 0, which is incorrect. Any ideas? Did I wrongly assume that its decimal, albeit it actually says 3500/4000=0,875 (which seems to be incorrect).

Best, gota900

Bunuel please provide official explanation for this.

thirty-five hundredths =.035?
four thousandths=.004?

thanks a lot.I have a question.How did u write:

Thirty-five hundredths = 0.35

hundredth position is 2nd postion aftr decimal so should not 3 come in 100th postion.Please clarify

Sure! You are correct that the hundredths position is the second position after the decimal, so one hundredth is 0.01. However, if we have 35 hundredths, this means that we need to multiply 0.01 by 35:

35*0.01 = 0.35.

In this case, the 3 ends up in the tenths position, instead of the hundredths position. If it were just 9 hundredths, for example, it would be:

9*0.01 = 0.09

However, if we are talking about more than 9 hundredths, the first digit won't be in the hundredths place.

Please let me know if you have more questions!

That is really appreciable.Thanks a lot Sir

Bunuel EducationAisle
How do we know that quotient includes the remainder? While the definition of quotient is "the result obtained by dividing quantity by another", we do use the formula: Dividend = Quotient * Divisor + Remainder.

If we use that formula, then tenths digit would always be 0, leading to answer equal to A. But if we include the remainder in the quotient, then we get E. I believe we can infer from "tenths digit of the quotient" that the remainder is included in the quotient or else this Q would be meaningless since tenth digit would always be 0?

Solution:

Translating the problem, we have:

(35/100) / (4/1000)

35/100 x 1000/4

35 x 10/4 = 35 x 2.5 = 87.5

So the tenths digit is 5.

Answer: E

_________________

thirty-five hundredths = 35/100
four thousandths = 4/1000

(35/100) / (4/1000)
= (35/100) * (1000/4)
= 35/1 * 10/4
= 350/4
= 87.5

Tenths digit is 5. Answer is E.
_________________

0,35/0,004

0,004 will go 250 times in 1.

0,35*250 = 3,5*25 = 87,5

"Thirty-five hundredths divided by four thousandths" = 35/100 ÷ 4/1000
= (35/100)(1000/4)
= 35,000/400
= 350/4

Mental math tip: One way to divide by 4 is to divide by 2 and then divide the result by 2
So, take 350, and divide by 2 to get 175
Then divide 175 by 2 to get 87.5


Answer: E

BrentGMATPrepNow avigutman KarishmaB

The language of this official question threw me off.



My understand is that whenever we use the term quotient, it inherently refers to an integer. For example lets the consider the statement

When 5 is divided by 4, the quotient is 1 and the remainder is 1.

The representation that I am considering in here -

Dividend = Quotient * Divisor + Remainder

However, in this question we are asked to find the tenths digit of the quotient. Wanted to check if the verbiage is correct or do we in general represent quotient as numbers (and not integers)

To make things worse we also have 0 as an option. How do we distinguish in the exam that GMAC is not testing us on basic (definition) and is referring to the tenths digit of the number when thirty-five hundredths divided by four thousandths.

Please share your thoughts on this.

P.S - My apologies if the question seem silly
_________________

I got a similar question from Braintree recently, gmatophobia. See their post here and my response below it.
The GMAC wouldn't ask you for the tenths digit of a number that is by definition an integer.

Yes, I would normally expect to see the term 'quotient' in the 'quotient-remainder' format. In other cases, one could say 'the result obtained when a number is divided by another etc.' but by definition, quotient is not necessarily an integer. Until and unless the question specifically talks about a remainder, we shouldn't assume that there will be one. And one thing is sure - a question wouldn't ask for a tenths digit if a number is supposed to be an integer. An integer doesn't have a tenths digit. 5 is an integer. 5.0 is a decimal number.
Hence we know exactly what the GMAT is asking for here - quotient as the result obtained when a number is divided by another.
_________________