HSPT Quantitative : How to make non-geometric comparisons

Example Questions

Example Question #91 : Non Geometric Comparison

Examine (a), (b), and (c) to find the best answer:

a)  of

b)  of

c)  of

Explanation:

Calculate the expressions to compare the values:

a)  of

b)  of

c)  of

Therefore (b) is smaller than (a), which is smaller than (c).

Example Question #92 : Non Geometric Comparison

is 30% of 12.

is 40% of 9.

is 50% of 6.

Which of the following is correct?

Explanation:

is 30% of 12, and the decimal equivalent of 30% is 0.3. Therefore,

is 40% of 9, and the decimal equivalent of 40% is 0.4. Therefore,

is 50% of 6, and the decimal equivalent of 40% is 0.4. Therefore,

Therefore, .

Of the four choices, only  is a correct statement.

Example Question #93 : Non Geometric Comparison

Which of the following is correct?

Explanation:

To add two fractions, first express them in terms of the same denominator; the least common denominator of 3 and 6 is 6, so multiply both halves of the first fraction by 2:

Add the numerators and preserve the common denominator:

Reduce by dividing both halves by their greatest common factor, 3:

To multiply two fractions, multiply numerators and multiply denominators:

To divide two fractions, multiply the first number by the reciprocal of the second number - switch the two halves of the latter:

Again, multiply numerators and multiply denominators:

Compare the fractions by expressing them in terms of the same denominator. The least common multiple of 2, 3, and 6 is 6; rewrite each fraction by multiplying whatever number yields this common denominator:

Compare fractions with the same denominator by comparing numerators:

, so

, and

.

Of the four choices, only  is a correct statement.

Example Question #91 : Non Geometric Comparison

is ten added to the square of ten.

is twenty added to the square of nine.

is thirty added to the square of eight.

Which of the following is correct?

Explanation:

is ten added to the square of ten - that is,

Evaluate this according to the order of operations by squaring, then by adding.

Evaluate the other two expressions using the same order:

is twenty added to the square of nine, so

is thirty added to the square of eight, so

, so the only correct statement of the four is .

Example Question #95 : Non Geometric Comparison

Which of the following is correct?

Explanation:

By the order of operations, multiplication precedes either addition or subtraction, so calculate accordingly:

so the only correct statement among the choices is .

Example Question #96 : Non Geometric Comparison

Which is a true statement?

Explanation:

.

Example Question #97 : Non Geometric Comparison

Which of the following is correct?

Explanation:

Each expression can be calculated according to the order of operations: Multiplication and division in left to right order, then addition and subtraction in left to right order.

Divide first:

Multiply second:

Multiply first:

Divide second:

Multiply first:

Divide second:

The only correct statement among the choices is .

Example Question #98 : Non Geometric Comparison

is 30% of 40.

is 20% of 60.

is 10% of 80.

Which of the following is correct?

Explanation:

30% of a number is equal to that number multiplied by the decimal equivalent of 30%, which is 0.30, or 0.3:

is 30% of 40, so

Similarly,

is 20% of 60, so

is 10% of 80, so

.

The only correct statement of the four is .

Example Question #99 : Non Geometric Comparison

Which of the following is correct?

Explanation:

In each expression, substitute, then evaluate. Follow the order of operations, which dictates that multiplication precedes subtraction:

The only correct choice is .

Example Question #92 : Non Geometric Comparison

Which of the following is correct?