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GMAT Fractions - Don't get lost in the calculations
Categories : Data Sufficiency, Fractions, Problem Solving

Have you wondered how writers can make a seemingly simple GMAT topic like fractions into time-consuming calculations. One strategy that GMAT test takers must adopt to simplify the calculations. For example

Dividing by 5 is the same as multiplying by 2/10. For example:

• 840/5 = ?
• 840/5 = 840*(2/10) = 84*2 = 168

Multiplying or dividing by 10’s and 2’s is generally easier than using 5’s. 90% of the time, fractions will be easier to perform arithmetic. Decimals are sometimes more useful when comparing numbers relative to one another, such as in a number line, but these questions are the exception. Even if given a decimal (or percent) looks easy, quickly convert to a fraction. Some common ones to memorize:

• 1/9 = 0.111 repeating
• 1/8 = 0.125
• 1/7 = ~0.14
• 1/6 = 0.166 repeating
• 1/5 = 0.20
• 1/4 = 0.25
• 1/3 = 0.333 repeating
• 1/2 = 0.5 repeating

Note: Multiples of these, such as 3/8 (0.375) are also important to remember, but can easily be derived by multiplying the original fraction (1/8 * 3 = 3/8 = 0.125 * 3 = 0.375)

Denominators are super important. A denominator of a reduced fraction with a multiple of 7 will not have a finite...

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How many inches are in a mile? (There are 5,280 feet in 1 mile and 12 inches in one foot)
Categories : Fractions

How many inches are in a mile? (There are 5,280 feet in 1 mile and 12 inches in one foot)

A. 12/5,280
B. 5,280/12
C. 2740
D. 12(5,280)
E. 122(5,280)

Answer

We are given two conversion factors and are asked to start with 1 mile and convert it to inches. The first conversion relates miles to feet: 1 mile = 5,280 ft. Thus, the 1 mile we began with is equivalent to 5,280 feet. In order to convert from feet to inches, we must set up a conversion ratio.

Since 12 in = 1 ft, (12 in)/(1 ft) = 1.

Likewise, (1 ft)/(12 in) = 1 since 1ft = 12in. 5,280ft * (12in/1ft) = 5,280(12) in The equation below aligns the units wrong.

Do not make this mistake: 5,280ft * (1ft/12in) = 5,280*1 ft2/in.

The first calculation yields the units we are looking for. Thus, the answer is C, 12*5,280

Correct Answer - Choice C

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If Y < 0 and -1 < -1 + X/Y < 0, which must be true?
Categories : Number Properties, Equations, Fractions

If Y < 0 and -1 < -1 + X/Y < 0, which must be true?

1. X < 0
2. Y/X>1
3. Y^2-X^2 > 0

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Answer

If X is negative, and we already know that Y is negative, than X/Y would have to be positive (a negative divided by a negative is always positive). This means that for all values in which Y is smaller than X, X/Y would be between 0 and 1.

More importantly, X must be negative, because if it were positive, the fraction X/Y would be negative. Statement I must be true. Statement II claims that Y/X>1.

We already know that both X and Y are negative. We also know that Y has a larger absolute value. Statement II must also be true.

On statement III, since we're talking about numbers squared, we can forget about the signs. We only need to figure out which of the two variables is greater. Statement III is true as well.

Correct Answer - Choice E

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Exactly 5/6 of the cows on a certain farm have cow bells
Categories : Fractions

Exactly 5/6 of the cows on a certain farm have cow bells. If exactly half of the cows with bells are
brown, what is the minimum possible number of cows on the ranch?

A. 6
B. 8
C. 12
D. 18
E. 24

Answer: The trick to this question is that the number of cows cannot be fractional; it must be an integer.

The number of brown cows is: (1/2) × (5/6) × the number of cows.

12 is the smallest positive integer that yields another integer when multiplied by 5/12, so it is the minimum possible number of cows.

Correct Answer: Choice C

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