The formula for distance = rate x time

Let t be the time when the two cars are 1701 kilometers apart.

DistanceA + DistanceB = RateA x timeA + RateB x TimeB

1701 = 67t + 59t

1701 = 126t

1701/126 = t

13.5 = t

The correct answer is (B) 13.5

15(3² – 5 + 2 x 6) – 4 x 2  =  15(9 – 5 + 12) – 8 = 15(16) – 8 = 240 – 8 = 232

The correct answer is (C) 232.

In solving Math problems, we follow PEMDAS, which is an acronym for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.  In any problem, we must first solve what is inside the parentheses, then the exponents, then multiplication and division, and lastly, addition and subtraction.

Tip #1:

Practice! Practice! Practice!

Tip #2:

Write down the numbers with the decimal points all lined up.

Add zeros after the decimal point to have numbers with the same length.  In this case, write down 12.6 as 12.60.  This is helpful to avoid confusion when adding.  Don’t forget to put the decimal point in the answer.

Let x be the original cost of the pair of shoes.

2500 = 80% (x)

2500 = 0.8 (x)

2500 / 0.8 = x

3125 = x

The correct answer is (E) P 3125

20% (125) = 40% (x)

25 =0.4 (x)

25 / 0.4 = x

62.5 = x

The correct answer is (E) 62.5

Average = (sum of a, b and c)/ (count of a, b and c)  = (162 + 39) / (3) = 201 / 3 = 67

The correct answer is (D) 67

Divisibility rule for 4:

If the last 2 digits is divisible by 4, then the whole number is divisible by 4.

(A) 8464, last 2 digits is 64 which is divisible by 4

(B) 4090, last 2 digits is 90 which is not divisible by 4

(C) 2008, last 2 digits is 8 which is divisible by 4

(D) 1512, last 2 digits is 12 which is divisible by 4

(E) 772, last 2 digits is 72 which is divisible by 4

The correct answer is (B) 4090.

2/18+17/45+71/2 =

20/180+68/180+105/180 = 193/180

When adding fractions with different denominators, we must first make the denominators the same.

Find the least common multiple (LCM) which will serve as the new denominator. In this case, the LCM for 18, 45 and 12 is 180.

Next, we convert the fractions using the LCM as the new denominator.

The new numerator can be obtained by dividing the LCM by the old denominator, then multiplying it with the old numerator.

Example, for 2/18.

180 ÷18 x 2 = 20

Hence, 2/18 becomes 20/180.

17/45 becomes 68/180

7/12 becomes 105/180.

Adding the three new fractions (20/180 + 68/180 + 105/180) results to 193/180.

Note: X_n is the nth term in the sequence.  In this case, the 5th term is X₅ and n=5.

X₅ = 3 (1/3)⁵ = 3 (1/243) = 3/243 = 1/81

The correct answer is (B) 1/81

Factors are numbers that we multiply together to get another number.  For example, 2 and 5 are factors of the number 10 because when we multiply 2 and 5, the result is 10.

Factors for 24:  1 and 24, 2 and 12, 3 and 8, 4 and 6

Factors for 54:  1 and 54, 2 and 27, 3 and 18, 6 and 9

Comparing the factors:

Factors for 24:  1, 2, 3, 4, 6, 8, 12, 24

Factors for 54:  1, 2, 3, 6, 9, 18, 27, 54

The common factors are 2, 3 and 6; the largest of which is 6.

Hence, the greatest common factor is (C) 6.

Tip:

Another solution for this type of question is to run through the choices and check if the two numbers can be divided by the choices. Since we are looking for the GCF, we start with the largest number among the choices, 18.  Is 24 divisible by 18?  The answer is NO, so we immediately move on to the next largest choice, 12.

Is 24 divisible by 12? YES.  But is 54 divisible by 12? NO.

So we move on to the next choice, 6.  Both 24 and 54 are divisible by 6, so we can quickly answer letter (C) 6.