Question: Rounding Decimals

Comment on Rounding Decimals

How do you exactly find the values for x in each statement? Do you use the hundredth place numbers for k (6 and 7) and copy 6 and 7 over to the right side of the table? I wasn't clear on that.
gmat-admin's picture

For statement 1, we showed two possible cases:
case a: k = 4.27056
case b: k = 4.26956

Both of these k-values satisfy the information provided in statement 1.
In case a, the digit in the hundredths position is 7, and in case b, the digit in the hundredths position is 6,

In other words, in case a, x = 7 and in case b, x = 6

Does that help?

How would you explain statement 2 then?
gmat-admin's picture

For statement, there are still two possible cases (at least):
case a: k = 4.27056
case b: k = 4.26956

Both of these k-values satisfy the information provided in statement 2.

Hi,, do you know why most people are asking you about statement 2...

because since a very long time.. what we have learned ..

As per your cases:

Case a: K=4.27056 ----> can not be rounded..
Case b: K=4.26956 ----> can be rounded..

and for that the only option is for x to be 6 and for y to be 5 and above

and for that Majority would have statement 2 to be enough ..

Thank you
gmat-admin's picture

Sorry, I'm not entirely sure I understand what you're saying. Can you please rephrase your statement.

In the meantime, I should mention that those values can still be rounded to the nearest hundredth.
Case a: 4.27056 rounded to the nearest hundredth is 4.27
Case b: 4.26956 rounded to the nearest hundredth is 4.27

Are these sort of questions tested on the GMAT exam?

Thanks.
gmat-admin's picture

Yes, there can be questions of this nature.

Oh wow, I got so confused about this question. I read it as k = (4.2)(x)(y)(56). Not as k = the number 4.2xy56 where x and y are numbers to the right of the decimal. :P

gmat-admin's picture

That's a common mistake. The key word here is "digits"

Exactly, the second I noticed the word "digits" in the question it all of a sudden made sense. Haha, thanks for the great prep material!

When I read the question, I read the word digits but assumed it meant that X and Y would be singular digits, such as 3 rather than 28, which is a two digits number, resulting in something like k = (4.2)(3)(4)(56) . How can we know that it doesn't mean that?
gmat-admin's picture

It's important to note that a digit isn't a number; it's a building block for CREATING numbers.
So, if we say that x and y are single digits, then xy represents a 2-digit number. It does not represent the product of two digits.

For example, if x is the DIGIT 2 and y is the DIGIT 7, then xy is the 2-digit number 27. That is, xy does NOT represent the product (2)(7).

Does that help?

Cheers,
Brent

Good day

These sufficiency questions really get me. As an example for statement 1 you could've used 5,6,7,8,9 as decimal digits correct?
Or did you chose those two numbers (6 and 7) due to the second statement provided?

I get confused with sufficiency statements, should they be looked at in isolation and then together or whats the deal?

Thanks for the quality videos.
gmat-admin's picture

Hi Schalla14,

You're correct; we could have used any of the digits 5, 6, 7, 8, or 9. Once we find two different answers to the target question (What is the value of x?), we can be certain that the statement is not sufficient.

Each statement must be examined on its own. However, if we're able to use the same counter-examples for each statement (to show that each statement is not sufficient), then we can conclude that the statements COMBINED are not sufficient.

ASIDE: It's important to recognize that EVERYONE struggles with Data Sufficiency (DS) questions at first. Keep in mind that this question type is unique to the GMAT, so it's totally foreign territory.

It just takes time for the concepts and strategies to become secondary, at which point you may come to find that DS questions are actually easier than Problem Solving questions.

Cheers,
Brent

Hi Brent

Thanks so much that makes more sense now as we are looking to find a specific value for x (i.e. one digit).

Awesome thanks for the info I'll give it some time and practice for the next couple of days.

Cheers
Schalk

Hi Brent!

Would it also be correct to approach the question this way;

Statement 1: Basically tells us x is a number greater than 5, and less than or equal to 9, but does not give us an exact number: Insufficient

Statement 2: Could either be 6 or 7, completely dependent on the value next to it, which is y, which we don't know.

Both together: We know x could be 6 or 7 from statement 2, and x is greater than 5 from statement 1, without the value of y, the precise value is ambiguous.

Answer: (E)
gmat-admin's picture

Hi Swatato,

That approach is almost perfect.

The only error occurs in statement 1, when you say "Basically tells us x is a number greater than 5, and less than or equal to 9."

It should be "Basically tells us x is a number greater than OR EQUAL TO 5, and less than or equal to 9"

Cheers,
Brent

Hi Brent,
Can you please solve question PS01648?
"List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If
1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E − S?"

Thanks!
Kashaf
gmat-admin's picture

Yulia's picture

Hi Brent,

Please clarify something for me.

Question 1: https://gmatclub.com/forum/on-a-recent-trip-cindy-drove-her-car-290-miles-rounded-to-99378.html

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between

A. 290/12.5 and 290/11.5
B. 295/12 and 285/11.5
C. 285/12 and 295/12
D. 285/12.5 and 295/11.5
E. 295/12.5 and 285/11.5

I understood that they are talking about rounding which means that for 290 miles the actual miles could be 285 or 294, same for 12 gallons which could be 11.5 or 12.4. I chose C because in answer D if we round 12.5 it would be 13 gallons. What did I do wrong here?
gmat-admin's picture

Question link: https://gmatclub.com/forum/on-a-recent-trip-cindy-drove-her-car-290-mile...

Given: used 12 gallons of gasoline, rounded to the nearest gallon
This means: 11.5 ≤ gallons used < 12.5
So, it COULD be the case that Cindy used 12.49999999 gallons of gasoline.

Keep in mind that the question asks: The actual number of miles per gallon that Cindy's car got on this trip must have been BETWEEN...
So, we're not saying that 285/12.5 is possible.
Since 285/12.499999999 is BETWEEN 285/12.5 and 295/11.5, it's a valid option.

Does that help?

Yulia's picture

Hi Brent. Thank you.
Could you please tell why 285/12.5 and 295/11.5 instead of 285/11.5 and 295 12.5 if our estimation is (see bellow)?
11.5 ≤ gallons used < 12
285 ≤ miles driven < 295
gmat-admin's picture

GIVEN: Cindy....used 12 gallons of gasoline, rounded to the nearest gallon.
The this tells us that: 11.5 ≤ gallons used < 12.5 (not 12, as you have above)

We want the range with regard to miles/gallons.

To MINIMIZE the value of the fraction miles/gallons, we need to minimize the numerator (miles) and maximize the denominator (gallons).
So the smallest possible value of miles/gallons is 285/12.5

To MAXIMIZE the value of miles/gallons, we need to maximize the numerator (miles) and minimize the denominator (gallons).
So the biggest possible value of miles/gallons is 295/11.5

For more on this concept start watch the following video at 2:50 - https://www.gmatprepnow.com/module/gmat-arithmetic/video/1067

Cheers,
Brent

Yulia's picture

Hi Brent,
Thank you.
yes, I know that concept. What I cant understand why we need to go from min to max? The question asks the actual number of miles driven. There are no words indicators such as range, between, max or min.
gmat-admin's picture

The question reads: The actual number of miles per gallon that Cindy's car got on this trip must have been BETWEEN...
Here, the word BETWEEN indicates we are looking for the range of possible values.

Hi Brent,

I see the explanation for the two statements is the same ?

I can't differ k is nearest to the tenth and hundredth in this case. Please help

Thanks,
Sam
gmat-admin's picture

Sorry, but I don't understand what you're asking. Can you please rephrase your question?

Hi Brent,

Could you provide me your solution for the below? The solutions posted are not clear to me.

https://gmatclub.com/forum/list-t-consist-of-30-positive-decimals-none-of-which-is-an-integer-131755.html

For PS Question 143, how do I think about it? I think it's complex and overwhelming
gmat-admin's picture

Which GMAT resource (name and year) are you referring to?
The question will be on GMAT Club. So, if you can find it and add the link to your next post, I'll try to help.

sorry it's a wrong one, I have figured it out, thanks, I guess I'm just being a abit anxious since I'm starting at arithmetic and will keep work through everything, my next test will be on December so besides courses work I should be good.
gmat-admin's picture

Okay, sounds good!

hi!

I understood the question but I didn't understand the answer, what does it mean by "the answer is E"? does it mean that both 1 and 2 are inssufiecent ? and in the exam it will only be questions like this for this section without calculating? I mean I will only answer if 1 and 2 are sufficient or 1 is sufficient and 2 is not etc??
gmat-admin's picture

Hi Sarah!

Here's what each answer choice represents:

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

D) EACH statement ALONE is sufficient to answer the question asked.

E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Data Sufficiency questions are pretty strange at first (they're unique to the GMAT). You might want to review the Data Sufficiency module to brush up on this topic: https://www.gmatprepnow.com/module/gmat-data-sufficiency

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