TTP Essential GMAT Quant Skills

Why doesn't zero have a reciprocal?

If a number has a reciprocal, then the product of that number and its reciprocal will equal 1 (ex. 2 x 1/2 = 1). Thus, zero does NOT have a reciprocal because there does not exist a number such that the product of 0 and this number equals 1.

How would you know if two fractions, a/b and c/d, are equivalent?

If a x d = b x c

In a fraction where the numerator is lesser than the denominator (4/5), what happens when you add 1 to both the numerator and denominator by 1?

It will result in a number that is greater in value than the original.

In a fraction where the numerator is greater than the denominator (5/4), what happens when you add 1 to both the numerator and denominator by 1?

It will result in a number that is lesser in value than the original.

If there are two fractions and one can be expressed as a terminating decimal, can their sum be expressed as a terminating decimal?

No

Is 13,522 a perfect square?

No. A perfect square cannot have a units digit of 2, 3, 7 or 8.

Is 4,398 a perfect square?

No. A perfect square cannot have a units digit of 2, 3, 7 or 8.

Is √-4 a real number?

No. The square root of a negative value is non-real number.

In the equation a/b = 1/3, does a = 1?

No. The variable a does not necessarily equal 1. If b = 3, then a = 1. If b = 6, then a = 2, and so on.

Will a fraction that has an integer numerator and non-zero integer denominator terminate or repeat?

Not necessarily. Only fractions that are in lowest terms and has an integer numerator and non-zero integer denominator will always terminate or repeat.

How many numbers are both a perfect square and a perfect cube, and also greater than 10 but less than 100?

Only one. The number is 64.

If there are two fractions and both cannot be expressed as a terminating decimal, can their sum be expressed as a terminating decimal?

Sometimes. Ex. 1/3 + 1/6 = 1/2

How does TTP recommend to approach the comparison of a set of fractions?

TTP recommends that you check to see if you can change the fractions to get a common numerator or denominator

What is one helpful rule when evaluating whether two values are reciprocals of each other?

The product of a number and its reciprocal will equal 1.

If there are two fractions and both can be expressed as a terminating decimal, can their sum be expressed as a terminating decimal?

Yes

If x = 1/4, is √x greater than x?

Yes. √x = 0.5 When x is between 0 and 1, then x^2 < x < √x.

If x = 1/2, is √x greater than x?

Yes. √x = 0.71 When x is between 0 and 1, then x^2 < x < √x.

Is 1! and 0! equal?

Yes. They both equal 1.

If a fraction's denominator only has factors of only 5 or 2, what can you immediately infer about this fraction?

You can immediately infer that this fraction is a terminating decimal.

For two fractions, a/b and c/d, how do you quickly know whether or not a/b is greater than c/d?

You will quickly know if a/b is greater than c/d, if ad > cb

1/ (a/b) = ?

b/a

What is another way to rephrase the addition of the fraction, b/c, to the whole number, A? A + (b/c) = ?

(A x c + b) / c

What is another way to rephrase the subtraction of the fraction, b/c, to the whole number, A? A - (b/c) = ?

(A x c - b) / c

What are the five major types of numbers that you want to test in the GMAT Quant section?

- Negative Integers - Negative Proper Fractions (between -1 and 0) - Zero - Positive Proper Fractions (between 0 and 1) - Positive Integers

What is the opposite of the number 2?

-2

Convert 32/1000 to a decimal.

.032

Convert 2/7 to a decimal.

.286

Convert 3/7 to a decimal.

.429

Convert 4/7 to a decimal.

.571

Convert 5/7 to a decimal.

.714

Convert 5/6 to a decimal.

.833

Convert 6/7 to a decimal.

.857

What is a number such that its opposite is equal to itself?

0

What is the square root of 0?

0

What is the only number that does not have a reciprocal?

0 because 1/0 is undefined.

What are all the possible digits that can be the units digit of a perfect square?

0, 1, 4, 5, 6, and 9

Convert 56/10000 to a decimal.

0.0056

Convert 1/9 to a decimal.

0.111

Convert 1/8 to a decimal.

0.125

Convert 1/7 to a decimal.

0.143

Convert 1/6 to a decimal.

0.167

Convert 2/9 to a decimal.

0.222

Convert 3/8 to a decimal.

0.375

Convert 4/9 to a decimal.

0.444

Convert 5/9 to a decimal.

0.555

Convert 5/8 to a decimal.

0.625

Convert 7/9 to a decimal.

0.777

Convert 7/8 to a decimal.

0.875

Convert 8/9 to a decimal.

0.888

0! =

1

1! =

1

What are numbers such that its reciprocal is equal to itself?

1 and -1

b/a = ?

1/ (a/b)

8 x 125 =

1000

5! =

120

Convert 1.47 to a fraction.

147/100

9,992 + 6,889

16,881

What are the four digits that cannot be a units digit of a perfect square?

2, 3, 7 and 8

What is 6^3?

216

4! =

24

What is the opposite of the number -3

3

Convert 0.3 to a fraction.

3/10

Convert 0.30 to a fraction.

3/10

What is 7^3?

343

12 x 3

36

9! =

362,880

∛64

4

What is √16?

4 (Not +/- 4)

8! =

40,320

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 =

45

9 x 5

45

What is the sum of all single digit numbers?

45

12 x 4

48

Factor out 5.000005

5 x 1.000001

5 x 1.00001 =

5.00005

Simplify 120/144

5/6

7! =

5040

What is 8^3?

512

Convert 0.0056 to a fraction.

56/10000

3! =

6

Convert 0.697 to a fraction.

697/1000

6!

720

What is 9^3?

729

5 x 15

75

Solve the following expression by combining like terms: = -3 + 7 - 8 + 9 + 12 - 5 - 6 + 4

= (-3 - 8 - 5 - 6) + (7 + 9 + 12 + 4) = (-22) + (32) = 32 - 22 = 10

1000 - 857 =

= (999+1) - 857 = (999 - 857) + 1 = 142 + 1 = 143

Simplify the following expression: x% + y% = ?

= (x/100) + (y/100) = (x+y)/100

Factor out 368 from 0.368368368.

= 0.368368368. = 0.368 + 0.000368 + 0.000000368 = 368 x (0.001 + 0.000001 + 0.000000001)

Define a proper fraction.

A proper fraction is when a fraction's numerator is less than its denominator.

How should absolute value bars and square roots be treated as it relates to PEMDAS?

Absolute value bars and square roots should be treated like a parenthesis in terms of priority

Define an improper fraction.

An improper fraction is when a fraction's numerator is greater than its denominator.

How does TTP recommend to simplify a complex fraction?

By multiplying the numerator and denominator by their least common denominator.

What two types of numbers should you watch out for if a question is asking whether an expression results in a real number?

Check for non-real numbers such as the square root of a negative number and an undefined value (denominator of zero)