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Exponents

Categories : Exponents

GMAT ExponentsThe GMAT's quantitative section is increasingly emphasizing problem solving skills over calculation abilities, and often does so in the form of "Number Properties" questions. The authors of the exam are also quite adept at recognizing "mathematical psychology", and creating questions that increase an examinee's anxiety by enough to make that process of problem solving a bit more difficult. One of the major themes that arises as a result is the use of exponents, which carry with them a number of properties extremely useful to the writers of the GMAT.

Exponents

• Inspire fear (or at least apprehension) in test takers
• Lead to cumbersome, time-consuming calculations involving large numbers
• Are actually quite pattern-driven, and reward those who seek out those patterns rather than attempt to perform the extensive calculations

How can this help you on the exam?

If you embrace the pattern-driven quality of exponents, you can rest easy on exponent questions...

Categories : Exponents, Fractions

GMAT Fraction ExponentsTo answer questions that involve negative fractions and exponents, you have to know the following rules:

1) Fraction with one in the numerator always obeys the following rule

1/High Number < 1/Low Number

What confuses test takers is the definition of High Number and Low Number when it comes to negative denominator

2) For negative numbers, remember this one rule

-5 < -3

- (Higher Positive Number) < - (Lower Positive Number)

3) When it comes to negative fraction, the rule reverses

-(1/High Number) > - (1/Low Number)

4) Even power of negative fraction is positive and odd power of negative fraction is negative

(-(a/b)) ^n is positive if n is even and negative is n is odd

Q) If a = -1/4 & b = -1/3, which of the following is true?

a) a^2 < b^3
b) a^3 > b^2
c) a^4 > b^6
d) a^3 < b^3
e) a^2 < b^4


Solution

Once you know the four rules, it becomes easier to eliminate answer choices. The question asks us to find the cube and square of two negative fractions a and b...

Categories : Exponents

If 5^A = B, what is A?

1. B = 25
2. B^3 = 15,625

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

(1) SUFFICIENT: If B = 25, we know that 5^A = 25. Thus A must equal 2.
(2) SUFFICIENT: If y^3 = 15,625, y must equal 25. The correct answer is D.

Answer - Choice D


If n and a are positive integers, what is the units digit of n^(4a+2) – n^(8a)?

(1) n = 3
(2) a is odd

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;
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 are needed.

BONUS QUESTION: What actually is the units digit (assuming the answer is not E)?


ANSWER BELOW

One important thing to note about exponents is that, by definition, they indicate “repetitive multiplication” – the multiplication of the same number over and over again.  Accordingly, they lend themselves nicely to patterns, as when you perform the  same action over and over again you’ll tend to get similar results.  When you consider statement 1, that n = 3, look at how 3 multiplies to different exponents:...




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