GMAT questions and answers.

GMAT
An argument is made up of premises (data) and a conclusion which was drawn on the
basis of these premises. - Answer An argument is comprised of:

Premise(s) - factual data or a given;
Conclusion - statement, opinion, or judgment based on the premise(s). The conclusion
may be logical (Example 1) or flawed (Example 2):

1. All cars have wheels. Therefore, John's car has wheels.

Ballparking π≅3+ will become extremely useful when solving geometry questions
involving circles. - Answer Replace π with ≅3+, or " a little more than 3"

the only way to add or subtract powers is by extracting a common factor. - Answer -->
2·3m·31 - 3m = 135
31 is essentially 3, so
--> 2·3·3m - 3m = 135
--> 6·3m - 3m = 135
Now, extract 3m as a common factor. 3m needs to be multiplied by 6 to reach in 6∙3m,
and by 1 to reach 3m:
--> 3m·(6-1) = 135
--> 3m∙5 = 135
Divide by 5, and:
--> 3m = 135/5 = 27

Yes/No Data Sufficiency
- Issue
- Plug In
- Plug Into Stem
- DOZEN F - Answer - Issue: Figure out the issue before diving deeper into the stmt.
- Yes/No or must be:
- Definite "yes" or "no" = Sufficient (S)
- "maybe" = Insufficient (IS)
-Plug in
- Find #'s that don't contradict the stmts.
- Regard the stmts as facts.
- Once you find the # that completes the stmt, plug that into the ? stem. Test for Y/N.
- "Is it true for any #?". DOZEN F

DOZEN F - Answer Different
One
Zero
Equal #'s for different variables
Negative

,Factors

Anything raised to the power of 1 equals - Answer itself.
423 raised to 1 = 423

1 raised to any power equals - Answer = 1

1 raised to 3 = 1

Any number (except 0) raised to the power of 0 equals - Answer = 1

423 raised to 0 = 1

0 raised to any power (except 0) equals - Answer = 0

0 raised to 423 = 0

When dividing powers of the same base, ????? the exponents - Answer subtract the
exponents.

a^5 / a ^3 = a^5-3 = a^2

reverse
3^x - 2 = 3^x / 3^2

any number raised to a negative power = - Answer the inverse.
2^-2 = 1 / (2^2) = 1/ 4

is (y) to the power of (-x) negative?

stmt: Y is positive - Answer No. There is no power that can turn a positive base into a
negative result.

plug in 2 for y and -3 for x
2 to the power of -3 = 1 / (2 to the power of 3) = 1/8 = positive

is y to the power of (x) negative?

stmt: x is even. - Answer No. An even power will always be non-negative.

plug in -3 for y and 2 for x
-3 to the power of 2 = (-3)(-3) = 9 (non-negative)

is (y) to the power of (-x) positive?

stmt: y is negative

, stmt: x is odd - Answer No. An odd power will maintain the bases original sign.

plug in -2 for y and 3 for x
-2 to the power of -2 = 1/-2 to the power of 3 =
1 / (-2)(-2)(-2) = 1/-8

An even power will always be non-negative.

(y) to the power of (-x)

If y=-3 and x=2, then y to -x = (-3) to -2 = 1/(-3) to 2 = 1/9, which is positive - Answer An
odd power will maintain the base's original sign.

(y) to the power of (-x)

If y=-3 and x=1, then y to -x = (-3) to -1 = 1/(-3) to 1 = 1/-3, which is negative

Integer - Answer an integer is simply a non-fraction or a non-decimal.
Integers can be positive or negative.
0 is an integer.

Real Number - Answer A real number can be anything: positive, negative, integer,
fraction.

Power is made up of a base and an exponent.
x to the power of 5. (x) is the base and 5 is the exponent. - Answer which is the base?
which is the exponent?

(Y) to the power of (-x)

base - Answer Power is made up of a base and an exponent.
x to the power of 5. (x) is the base and 5 is the exponent.

exponent - Answer Power is made up of a base and an exponent.
x to the power of 5. (x) is the base and 5 is the exponent.

How do you divide powers of the SAME BASE? - Answer Subtract the exponents.

(a) to the power of 5 divided by a to the power of 3
(a to 5) / (a to 3) = a to (5-3) = a to 2

reverse:
3 to (x-2) = 3 to x / 3 to 2

m to 3 = m to (5-2) = m to 5 / m to 2