When four is added to six times a number and the result squared, the result obtained is four times the square of the sum of the number and its next multiple. What is the number?Explanation:The question can be directly converted to an equation as follows.Let ‘n’ be the number.(4 + 6n)2= 4(n + 2n)222(2 + 3n)2 = 4(3n)24 + 12n + 9n2= 9n2n = … [Read more...] about GRE Algebra – Word Problems

# GRE Algebra Theory & Practice Questions

## Algebra – Inequalities and Exponents

Solve: (a) 7^(4-16x) > 1 (b) 2/(x-1) < 1 (a) For any a^b > 1, if a > 1 then b should be greater than 0. Hence 4 – 16x > 0 Therefore, x<1/4. (b) 2/(x-1) < 1 2/(x-1) - 1< 0 [2-(x-1)]/(x-1) < 0 (3-x)/(x-1) < 0 (x-3)/(x-1) > 0 Hence ‘x’ lies outside the roots ‘1’ and ‘3’. Therefore, x € (-∞ , 1) U (3, ∞) … [Read more...] about Algebra – Inequalities and Exponents

## Algbera Practice: Functions

A function is defined as f(x+2) = 3 + f(x) when x is even f(x+2) = x + f(x) when x is odd f(1) = 4 and f(2) = 3 Find f(f(f(1))) + f(f(f(2))) Answer: 17 Explanation: f(f(f(1))) + f(f(f(2))) = f(f(4)) + f(f(3)) Now f(4) can be found by using the definition of the function when x is even. Take x = 2. f(2+2) = 3 + f(2) f(4) = 3 + 3 f(4) = 6 Likewise, f(3) can be … [Read more...] about Algbera Practice: Functions

## Inequalities and Absolute Values

The solution set for the inequality |x+2| < |4x+1| (a) -3/5 < x < 1/3 (b) -1/3 < x < 3/5 (c) 0 < x < 1/3 (d) -1/3 < x < 1/3 (e) None of these Correct Answer: (E) Explanation Since the expressions on both sides of the inequality are under modulus, you can square on both sides without disturbing the inequality. (x+2)2 < … [Read more...] about Inequalities and Absolute Values

## More Than One Answer – Equations

The cumulative expense of a group comprising 43 people was 229 cents. If each man spent 10 cents, each woman 5 cents and each child 2 cents, which of the following can be the total contribution made by the women? (a) 185 cents (b) 145 cents (c) 105 cents (d) 225 cents (e) 25 cents (f) 15 cents Correct Answer: (a), (b), (c), (e) Explanation: Let x, y, z be the … [Read more...] about More Than One Answer – Equations