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GMAT Test 2_DS Digits #20

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Source: — Data Sufficiency |
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by Bill@VeritasPrep » Tue Apr 03, 2012 8:23 pm
1) When we multiply by 10, we move the decimal one place to the right. If 10d has a tenths digit of 7, then when we divide by 10 the decimal moves one place to the left, meaning that the hundredths digit of d must be 7. Sufficient.

2) Using the same logic, if d/10 has a thousandths digit of 7, multiplying by 10 to get rid of the denominator moves the 7 to the hundredths place. Sufficient.
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by Anurag@Gurome » Tue Apr 03, 2012 8:52 pm
kwah wrote:Attached is a question from GMAT Prep Test 2.

Please advise how to achieve the result.

Answer: D

Thanks,
K
Let us assume that d = pq.rs (note that we can take as many numbers before or after the decimal point).
Question is: Is s > 5?

(1) The tenths digit of 10d is 7.
10d = pqr.s implies tenths digit of 10d is s.
So, s = 7 > 5; SUFFICIENT.

(2) The thousandths digit of d/10 is 7.
d/10 = pq.rs/10 = p.qrs implies thousand digit of d/10 is s.
So, s = 7 > 5; SUFFICIENT.

The correct answer is D.
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by Kemmy G » Sat Apr 14, 2012 9:05 pm
Hello everyone!
I've read and re-read the replies and solutions to this particular question and I'm sorry to say I still don't understand it. Moving a decimal forward, moving it back... I've studied FDP but the question still has me confused! Can anyone please give a simpler explanation? I was beginning to understand the second instructor when he said is s>5, but after that he lost me.
Thanks for a quick response!
K
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by meetleo09 » Sat Apr 21, 2012 10:19 am
Let me try

Lets say you have $10.75. As you would know, it has 7 in the 10ths digit and 5 in the 100ths digit.

Lets say, you multiply this amount with 10. So, now you have $107.5. Now, your 7 and 5 have moved up in the digits. i.e. 5 is in the 10ths digit now and 7 has moved to units place. Similarly, if you divide $10.75 by 10, you would have $1.075. Which means, 7 has moved to 100ths place and 5 has moved to 1000ths place.

So, in the problem,
Statement 1 - when d is multiplied by 10 (10d), its 10th digit is 7. This means, 7 was in 100ths place before multiplying by 10. So, 7 is greater than 5. SUFFICIENT

Statement 2 - when d is divided by 10, (d/10), its 1000ths digit is 7. Which means, 7 was in 100ths place before dividing by 10. So, 7 is greater than 5. SUFFICIENT

Answer is D

Hope this helps.
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by aneesh.kg » Sat Apr 21, 2012 10:53 am
Let d = 0.xyz
Here x= Tenths digit, y = Hundredths digit, z = Thousandths digit

Based on our 'd', The question is: Is y > 5?

Statement (1) talks about '10d'
Multiplying our 'd' by 10, we get
10d = x.yz

The tenths digit of the above decimal is y.
This statement tells that the Tenths place of this 10d is 7, So y = 7.
Statement (1) is SUFFICIENT.

Statement (2) talks about 'd/10'
Dividing our 'd' by 10,
d/10 = 0.0xyz

The thousandths digit in this decimal is y.
The statement tells that the thousandths digit of d/10 is 7, So y = 7.
So, the Statement is SUFFICIENT.

(D) is the answer.
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