MSA Math Reviewer

What is the formula for this problem? The product of a and b is constant.. If the value of a is decreased by 25%, by how many percent must the value of b be decreased to have the same product?

(100-25)a * (100-x) = ab

How many positive two digit numbers are possible such that the number AND the sum of its digits are divisible by 7?

The only numbers whose value and digits are all divisible by 7 is 70 and 77.

Find all possible values of x to make the expression √x√x-x a real no.

√x - x ≥ 0 (because in order for the expression to be a real number, it cannot be negative) √x ≥ x x ≥ x^2 x^2 - x ≤ 0 x(x-1) ≤ 0 Ans: 0 ≤ x ≤ 1

P is a positive integer. When P+3 is divided by 8, the remainder is 5. What is the remainder when P is divided by 8?

1) Find a value for P that isn't 0 that produces a remainder of 5. (Divide using a number bigger than 8)

What is the maximum number of squares that can be made from a piece of wire 100 meters long if the area of each square is 9 square meters?

1) Find the sides using the area Area = s^2 9 sqm = s^2 3 = s 2) Get the perimeter Perimeter = 4s P = 4(3) P = 12 100/12 = 8 squares

How do you solve x+1/3(x+1)+3/8(x+2)=25?

1) Get the LCD of 1/3 and 3/8 and multiply it to both sides of the equation to get x

Glenly unwound a new bathroom tissue and found out that there are 300 sheets in a roll with each sheet measuring 11 cm. A full roll has a diameter of 10.5 cm and the diameter of the cardboard is 4cm. How many times does the paper wind around the cardboard?

1) Get the total length of the 300 sheets 300 x 11 = 3300cm 2) get the average circumference of the roll = outer circumference + inner circumference/2 = pi(10.5)+pi(4)/2 = 22.765cm 3) divide the average circumference with the total length 3300/22.765 Total no. wounds = 145

What is the formula for this problem?: A freight train leaves a station and travels at a rate of 30kph. two hours later, an express train leaves the same station traveling in the same direction at a rate of 50 kph. In how many hours will the express train overtake the freight train?

1) since both trains cover the same distance, d(freight) = d(express) rt(freight)=rt(express) 2) 50t = 30(t+2)

What is the formula for the ff: Manshine City has won 8 games and lost 4 games. If they win the next x games, it would have won 75% of all the games it played. What is the value of x?

1) use the average formula games won/total games played ⋅ 100% 8+x/8+4+x ⋅ 100% = 75%

If d is a positive integer greater than 5 and the remainders are the same when 11 and 19 are divided by d, then d=?

19-11=d

Joshua had a flat tire after biking 2/3 of his way home. He walked the rest of the way home. If his walking time was 3 times his biking time, how many times faster is his biking speed than his walking speed?

6 times

What is the formula for this problem?: A positive number is mistakenly divided by 6 instead of being multiplied by 6. Based on the correct answer, what is the percent error?

6x-x/6/6x x 100

how many multiples of 5 are there from 1 to 9999?

An = A1 + (n-1)d An: 9995 A1: 5 d: 5

How do you find the greatest among small numbers with big exponents?

Break down the exponent into a smaller value x GCF. Raise the base by the smaller exponent and whichever has the bigger value is the greatest.

The positive integers are written in order starting with 1: 12345678910111213141516171819202122232425262728... What is the digit in the 5000th position?

Count the digits from 1-9, then 10-99 (10 subtracted by 99 subtracted by 1 multiplied by two), then 100-999 (100 subtracted by 999 subtracted by 1 multiplied by three), then 1000-1525 (1000 subtracted by 1525 subtracted by 1 multiplied by 4) and add 7 more digits (1 5 2 6 1 5 2) to make it into 5000 digits

How many perfect square integers can be displayed on a 12 digit calculator?

Get the square root of 1 000 000 000 000 and subtract it by 1 to make it 12 digits.

How do you find the area of a triangle given its 3 sides?

Heron's formula first, s = a+b+c/2 then, using the value gotten from earlier, Area = √s(s-a)(s-b)(s-c)

How do you know if an infinite geometric progression has a sum?

If its common ratio is less than 1

What is the formula for this question: Two candles of the same height and diameter burn at the same rate. Each takes 6 hours to be consumed. if the first candle is lit at 6pm and the other at 8pm, what time will the second candle be twice as tall as the first?

L-1/6L(t-2) = 2[L-1/6L(t)] the right side is multiplied by 2 because of the sentence "what time will the second candle be twice as tall as the first?"

A group of more than ten and fewer than thirty people paid the same amount for a concert. The total cost was P16490. How many people are in the group?

Take the given and divide them one by one with 16490

How many numbers between 1/4 and 1/2 can be displayed on an 8 digit calculator?

Turn 1/4 and 1/2 into decimals with 8 figures and subtract them.

How do you get the difference of two unknown numbers given their product and sum?

Use the Perfect Square Trinomial formula ( (a+b)^2 = a^2 + 2ab + b^2) then subtract both sides by 4ab

how do you get the average of multiples of 5 from 1 to 9999?

ave= first+last/2

What is the formula for the ff: The average weight of 8 boxes is 4.8 pounds. If each box weighs at least 4.3 pounds, what is the greatest possible weight of one of these boxes?

max weight = (8⋅4.8)-(7⋅4.3)

The radius of a unicycle wheel is 30cm. When the unicycle travels continuously in one direction for 1 km, the wheel makes n revolutions. what is n?

use the formula n = 1 rev/2 x distance and multiply by 100 000 cm/1km