PSAT Math - How to add integers

What is the sum of multiples of 10 from 10 to 140 inclusive?

900

950

1000

1050

1100

Explanation

Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.

What number replaces the circle in the following sequence?

$1, 6, 31, 156, 781, \bigcirc...$

Explanation

The sequence is formed by starting with 1 and adding successive powers of 5. The numbers are obtained as follows:

$1 + 5^{1} = 1 + 5 = 6$

$6 + 5^{2} =6 + 25 = 31$

$31 + 5^{3} = 31 + 125 = 156$

$156 + 5^{4} = 156 + 625 = 781$

$781 + 5^{5} = 781 + 3, 125 = 3,906$ - the correct response.

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

Explanation

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

Suppose you know the values of the variables in the expression

$a - b^{2} \cdot c \div e +f$

and you wish to evaluate it.

Which operation do you execute last?

Addition

Subtraction

Multiplication

Division

Squaring

Explanation

In the absence of grouping symbols, the first operations that should be carried out are exponentiations, followed by multiplications and divisions, followed by additions and subtractions.

The additions and subtractions are carried out from left to right. Since the addition is the one to the right, it is performed last.

Histogram

Refer to the above graph. Francie, a sixth grader at Polk, scored a 372 on the math portion of the SCAT. Which of the following could have been her rank among the students?

$100\textup{th}$