Fractions

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GRE Quantitative Reasoning › Fractions

Questions 1 - 10

Abe, Bob, and Carol went to lunch together and their total bill was 60 dollars. They first decided to split the bill , respectively. Unfortunately, Abe was short on cash and they decided to split the bill . How much more did Carol have to spend on the under the new system of splitting the bill?

Explanation

Since the problem is focusing on Carol, we will only worry about Carol's contribution to the bill.

The original split on the bill was with Carol paying the smaller portion. With parts, each one was $\$10$ . This was originally the amount Carol was responsible for.

With the the ratio of , this meant there are parts with each being $\$6$ . Carol pays instead $\$30$ .

The difference is then or $\$20$ .

Which fraction is the SMALLEST?

47/100

1/2

35/50

4/9

6/11

Explanation

estimate or calculate decimals after simplifying

Happy Harold's Creamery offers specials during the week on particular sundaes. Monday they offer the Triple Trouble, in which three different scoops may be chosen from the full thirty-one that HHC offers. Tuesday features, for the same price, the Fearsome Four, which is a sundae of four scoops; however, only twenty-one flavors may be chosen from.

Quantity A: The amount of sundae options available for the Triple Trouble.

Quantity B: The amount of sundae options available for the Fearsome Four.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

The relationship between the two cannot be determined.

Explanation

Both of these sundae options are dealing with combinations, i.e. the order the scoops are chosen does not matter, and so the amount of possible combos is given by the formula:

$C(n,k)=\frac{n!}{(n-k)!k!}$

Where is the total number of options and is the size of the combination created.

For the Triple Trouble, the total amount of possible sundaes is:

$\frac{31!}{(31-3)!3!}=4495$

And for the Fearsome Four:

$\frac{21!}{(21-4)!4!}=5985$

For how many integers, , between 26 and 36 is it true that

$\frac{3}{x}_{,}\frac{4}{x}_{,}$ and $\frac{5}{x}$ are all in lowest terms?

Explanation

If is even, then $\frac{4}{x}$ is not in lowest terms, since both and 4 are divisible by 2. Therefore, the only possibilities are 27,29,31,33, and 35. But $\frac{3}{27}= \frac{1}{9}$ , $\frac{3}{33}= \frac{1}{11}$ , and $\frac{5}{35}= \frac{1}{7}$ , so only two integers satisfy the given condition: 29 and 31.

Quantity A: The amount of sundae options available for the Triple Trouble.

Quantity B: The amount of sundae options available for the Fearsome Four.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

The relationship between the two cannot be determined.

Explanation

Both of these sundae options are dealing with combinations, i.e. the order the scoops are chosen does not matter, and so the amount of possible combos is given by the formula:

$C(n,k)=\frac{n!}{(n-k)!k!}$

Where is the total number of options and is the size of the combination created.

For the Triple Trouble, the total amount of possible sundaes is:

$\frac{31!}{(31-3)!3!}=4495$

And for the Fearsome Four:

$\frac{21!}{(21-4)!4!}=5985$

If Jill, Jack and John found $\$1000$ and decided to split it respectively, how much more did Jack get than John?

Explanation

If Jill, Jack and John get , that means there are parts.

Because they found , each part gets $\frac{1000}{20}$ or $\$50$ .

Jack gets $50\cdot9$ or $\$450$ .

John gets $50\cdot5$ or $\$250$ .

Since the question is asking how much more did Jack get than John, we subtract and to get .

Quantity A: $\frac{490}{12}$

Quantity B: $40\frac{5}{6}$

Which of the following is true?

The two quantities are equal

The relationship of the two quantities cannot be determined based on the information provided.

Quantity B is larger.

Quantity A is larger.

Explanation

Though there are several ways you could solve this, let's convert the improper fraction into a mixed one so we can compare them. Start by dividing by . This gives you

Now, since we know that the two numbers have the same whole-number value, we need to compare their decimal portions. Compare to $\frac{5}{6}$ . The latter is indeed Therefore, the two values are equal.

Quantity A: $\frac{490}{12}$

Quantity B: $40\frac{5}{6}$

Which of the following is true?

The two quantities are equal

The relationship of the two quantities cannot be determined based on the information provided.

Quantity B is larger.

Quantity A is larger.

Explanation

Though there are several ways you could solve this, let's convert the improper fraction into a mixed one so we can compare them. Start by dividing by . This gives you

A clothing store can only purchase socks in crates. Each crate has 200 socks and costs \$2091.

Quantity A: The amount of socks that can be bought with \$12651.

Quantity B: The amount of socks that can be bought with \$14574.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined.

Explanation

For this problem, realize that the store cannot buy part of a crate of socks. If they only have enough to pay for part of a crate, they might as well not have any money at all.

For the amount of money listed, figure out how many crates can be purchased:

Quantity A

$\frac{12651}{2091}=6.05$