GMAT Math : Understanding fractions

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Example Question #1 : Understanding Fractions

If $\dpi{100} \small x=\frac{1}{2}$ and $\dpi{100} \small y=\frac{1}{3}$ , which of the following is the smallest?

Possible Answers:

$\dpi{100} \small (x+y)^{2}$

$\dpi{100} \small x^{2}+y^{2}$

$\dpi{100} \small (xy)^{2}$

$\dpi{100} \small x-y$

$\dpi{100} \small x+y$

Correct answer:

$\dpi{100} \small (xy)^{2}$

Explanation:

It can be solved by calculating all five answers:

$\dpi{100} \small x+y = \frac{5}{6}$

$\dpi{100} \small x-y=\frac{1}{6}$

$\dpi{100} \small (xy)^{2}=\frac{1}{36}$

$\dpi{100} \small x^{2}+y^{2}=\frac{13}{36}$

$\dpi{100} \small (x+y)^{2}=\frac{25}{36}$

The smallest is $\dpi{100} \small \frac{1}{36}$ .

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Example Question #1 : Understanding Fractions

What is $\dpi{100} \small 66\frac{2}{3}$ % of 18?

Possible Answers:

Correct answer:

Explanation:

We need to convert this percentage into a fraction. This is one of the conversions you should remember.

$\dpi{100} \small 66\frac{2}{3}$ % = 0.666666 = $\dpi{100} \small \frac{2}{3}$

$18 \ast \frac{2}{3} = 6 \ast 2 = 12$

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Example Question #3 : Understanding Fractions

Which of the following is less than $\small \frac{3}{8}$ ?

Possible Answers:

$\small 0.40$

$\small \frac{2}{5}$

$\small \frac{2}{4}$

$\small 0.25$

Correct answer:

$\small 0.25$

Explanation:

It's easiest to convert the fractions into decimals.

$\small \frac{3}{8}\ =\ 0.375$

$\small \frac{2}{4}\ =\ 0.50$

$\small \frac{2}{5}\ =\ 0.40$

Therefore, the correct answer is 0.25.

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Example Question #4 : Understanding Fractions

Given that $\small 4 \leq A \leq 5$ and $\small \small 2 \leq B \leq 3$ , what is the range of possible values for A - B ?

Possible Answers:

$\small \small 1 \leq A -B \leq 7$

$\small 1 \leq A -B \leq 3$

$\small \small 2 \leq A -B \leq 6$

$\small \small 2 \leq A -B \leq 8$

$\small \small 0 \leq A -B \leq 2$

Correct answer:

$\small 1 \leq A -B \leq 3$

Explanation:

To get the smallest possible A - B , subtract the greatest possible from the smallest possible ; this is 4 - 3 = 1 .

To get the greatest possible A - B , subtract the smallest possible from the greatest possible ; this is 5 - 2 = 3 .

$\small 1 \leq A -B \leq 3$

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Example Question #5 : Understanding Fractions

If $\small x + y = 10$ and $\small xy = 20$ , then evaluate $\small x-y$ .

Possible Answers:

$\small -2\sqrt{5}$

$\small -5\sqrt{2}$

It cannot be determined from the information given.

$\small 2 \sqrt{5}$

$\small 5 \sqrt{2}$

Correct answer:

It cannot be determined from the information given.

Explanation:

$\small x + y = 10$

$\small (x + y )^{2} = 10^{2}$

$\small x^{2} + 2xy + y^{2} = 100$

$\small \small x^{2} + 2xy + y^{2} - 4xy= 100 - 4xy$

$\small \small x^{2} - 2xy + y^{2} = 100 -4xy$

$\small (x - y)^{2} = 100 - 4 (20)$

$\small \small (x - y)^{2} = 20$

Either $\small \small \small x - y = \sqrt{20} = 2 \sqrt{5}$ or $\small \small x - y = - \sqrt{20} = - 2 \sqrt{5}$

But without further information, it is impossible to tell which is true. Therefore, the correct choice is that it cannot be determined from the information given.

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Example Question #6 : Understanding Fractions

Galactic Bounty Hunters, Inc has two departments: Trainees and Veterans. If on an average week, the each member of the Trainee department arrests $\frac{3}{5}$ as many criminals as each member of the Veteran department, but the Veteran department has $\frac{1}{3}$ as many members as the Trainee department, what fraction of the arrests were made by the members of the Veteran department?

Possible Answers:

$\frac{1}{5}$

$\frac{17}{39}$

$\frac{2}{11}$

$\frac{5}{14}$

$\frac{1}{2}$

Correct answer:

$\frac{5}{14}$

Explanation:

What we want to do is pick numbers for the number of arrests made during the week and for the number of members in each department.

Let's take the number of arrests first. Let's say each Trainee arrests 3 criminals. Then, since the Trainees make 3/5 the number of arrests the Veterans make, we have:

$\frac{3}{5}v_a=3$

$v_a=3\bigg(\frac{5}{3}\bigg)=5$

So, each Veteran would arrest 5 criminals.

Next, we know that there are 1/3 as many Veterans as Trainees. There if we have 3 Trainees, then we have 1 Veteran.

Using this information we can create the following equation for total arrests made by each department:

$\frac{t_a(t)}{v_a(v)}$

Where t_a(t) is the number of Trainee arrests times the number of Trainees and v_a(v) is the number of Veteran arrests times the number of Veterans

$\frac{t_a(t)}{v_a(v)}=\frac{3(3)}{5(1)}=\frac{9}{5}$

We're almost done. Since we have 3 Trainees, and each arrests 3 criminals, the total number of Trainee arrests is 9.

Since we have 1 Veteran, and each arrests 5 criminals, the total number of Veteran arrests is 5.

The total number of arrests is 9+5=14

The fraction of the arrests made by the Veterans is:

$\frac{5}{14}$

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Example Question #7 : Understanding Fractions

Find the result and simplify the following expression: $\frac{1}{1-\frac{2}{5}}+ \frac{1}{1+\frac{1}{5}}$

Possible Answers:

$\frac{9}{5}$

$\frac{5}{2}$

$\frac{15}{6}$

$\frac{10}{9}$

$\frac{5}{6}$

Correct answer:

$\frac{5}{2}$

Explanation:

We start by simplifying the denominators:

$\frac{1}{1-\frac{2}{5}}=\frac{1}{\frac{5}{5}-\frac{2}{5}} = \frac{1}{\frac{3}{5}}$ and $\frac{1}{1+\frac{1}{5}} = \frac{1}{\frac{5}{5}+\frac{1}{5}}=\frac{1}{\frac{6}{5}}$

We know that: $\frac{1}{\frac{3}{5}}+\frac{1}{\frac{6}{5}} = \frac{5}{3}+\frac{5}{6}$

Then we put both fractions to the same denominator, and don't forget to simplify the fraction:

$\frac{5}{3}+\frac{5}{6}=\frac{10}{6}+\frac{5}{6}=\frac{15}{6}=\frac{5}{2}$

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Example Question #8 : Understanding Fractions

Which of the following is false?

Possible Answers:

$\frac{m}{n} +\frac{p}{q} = \frac{qm+pn}{qn}$

None of the other answers.

$\frac{a}{b}\times\frac{c}{d} = \frac{ac}{bd}$

$\frac{p}{mn}$

$\frac{a}{b}+\frac{c}{d} = \frac{a+c}{bd}$

Correct answer:

$\frac{a}{b}+\frac{c}{d} = \frac{a+c}{bd}$

Explanation:

$\frac{a}{b} +\frac{c}{d} = \frac{a+c}{bd}$ is false because is not displaying the correct way to add two fractions together. When adding fractions we must find a common denominator before adding the numerators.

For example, if a=1, b=2, c=1, d=2 , then the above expression would read

$\frac{1}{2} +\frac{1}{2} = \frac{1}{2}$ This we know is absurd!

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Example Question #9 : Understanding Fractions

What is the least common denominator of the following fractions?

$\frac{7}{5}, \frac{8}{15},\frac{2}{3}$

Possible Answers:

Correct answer:

Explanation:

The least common denominator (LCD) is the lowest common multiple of the denominators.

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Multiples of 15: 15, 30, 45, 60, 75, 90,105,120, 135, 150

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

The least common denominator is 15.

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Example Question #151 : Algebra

What value must take in order for the following expression to be greater than zero?

$\frac{3}{k}-\frac{5}{7}$

Possible Answers:

Correct answer:

Explanation:

is such that:

$\frac{3}{k}-\frac{5}{7}>0$

Add $\frac{5}{7}$ to each side of the inequality:

$\frac{3}{k}>\frac{5}{7}$

Multiply each side of the inequality by :

$\frac{21}{k}>5$

Multiply each side of the inequality by :

21>5k

Divide each side of the inequality by :

$k< \frac{21}{5}$

You can now change the fraction on the right side of the inequality to decimal form.

$k<\frac{21}{5}=\frac{20}{5}+\frac{1}{5}= 4.2$

The correct answer is , since k has to be less than 4.2 for the expression to be greater than zero.

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GMAT Math : Understanding fractions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Understanding Fractions

Example Question #1 : Understanding Fractions

Example Question #3 : Understanding Fractions

Example Question #4 : Understanding Fractions

Example Question #5 : Understanding Fractions

Example Question #6 : Understanding Fractions

Example Question #7 : Understanding Fractions

Example Question #8 : Understanding Fractions

Example Question #9 : Understanding Fractions

Example Question #151 : Algebra

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