Quantitative Reasoning Basic
Knowledge Questions and
Complete Solutions Graded A+
6 x 7 - Answer: 42
6 x 8 - Answer: 48
7 x 8 - Answer: 56
12 x 5 - Answer: 60
12 x 6 - Answer: 72
12 x 7 - Answer: 84
12 x 8 - Answer: 96
12 x 9 - Answer: 108
12 x 11 - Answer: 132
How to divide any number by 5. - Answer: Double the number and divide it by 10 in either order
How to square a multiple of 10. - Answer: Square the digits without the zeros, then put 2 zeros
after the nonzero numbers.
,How to square a number ending in 5. - Answer: 1. Remove the 5, leaving the remaining digit(s)
2. Add 1 to the remaining digit(s)
3. Multiply the numbers (n)(n+1)
4. Put this product in front of 25.
1. If we know the value of n², then how can we get the next square up (n+1)²? - Answer: Add n
and (n+1) to n²
2. When a multiple of 10 greater than 1 is written in standard form, the exponent next to the 10
equals what? - Answer: The number of zeros after the 1. (10,000 = 10⁴)
For powers of 10 less than 1, the negative exponent next to the 10 equals what? - Answer: The
number of decimal places to the right of the decimal. (10^-2 =.01)
2. How to multiply with decimals? - Answer: 1. Count the number of digits to the right of the
decimal of each number. The sum of these is the amount of decimal places in your product
2. Find the product without worrying about the decimals
3. Put the correct number of decimal places into the final produce
How to divide with decimals? - Answer: move the decimals of both numbers one place to the
right until the denominator is a whole number.
2. How to find the power of a decimal? - Answer: Multiply the amount of digits to the right of
the decimal with the exponent and that is the amount of decimal places will be in your answer.
(.03)³=.000027
2. What is 1/6 in decimal form? - Answer: 0.166666....
,What is 1/7 in decimal form? - Answer: ~0.143
What is 5/6 in decimal form? - Answer: 0.83333333.....
What is 1/8 in decimal form? - Answer: 0.125
What is 3/8 in decimal form? - Answer: 0.375
What is 5/8 in decimal form? - Answer: 0.625
What is 7/8 in decimal form? - Answer: 0.875
2. How to simplify a complex fraction? - Answer: Multiply the numerator and denominator of
the big fraction by each denominator of the inner fractions.
2. How to quickly compare 2 fractions that are relatively close? - Answer: 1. 7/11 ?? 5/8
2. (7)(8) ?? (11)(55)
3. 56 > 55
4. So, 7/11 > 5/8
3. What is the equation for simple interest? - Answer:
3. What is the equation for compound interest? - Answer: V=P[1+(r/100n)]^nt
3. The equation for finding the % increase/decrease. - Answer: 100 (difference)/ original value
, 4. How to determine if an integer is divisible by 3? - Answer: If the sum of the digits are a
multiple of 3, then it is divisible by 3.
How to determine if an integer is divisible by 4? - Answer: If its last 2 digits are a multiple of 4
then it is divisible by 4.
Ex: 6,932 is a multiple of 4, since 32 is a multiple of 4.
How to determine if an integer is divisible by 6? - Answer: If it is divisible by 2 and 3, then it
divisible by 6.
How to determine if an integer is divisible by 9? - Answer: If its digits add up to a multiple of 9,
then it is divisible by 9.
How to test whether any number less than 100 is prime? - Answer: check whether it is divisible
by one of the prime numbers less than 10. If a number less than 100 is not divisible by any
prime divisor less than 10, then the number has to be prime.
11^2? - Answer: 121
12^2? - Answer: 144
13^2? - Answer: 169
14^2? - Answer: 196
15^2? - Answer: 225
Knowledge Questions and
Complete Solutions Graded A+
6 x 7 - Answer: 42
6 x 8 - Answer: 48
7 x 8 - Answer: 56
12 x 5 - Answer: 60
12 x 6 - Answer: 72
12 x 7 - Answer: 84
12 x 8 - Answer: 96
12 x 9 - Answer: 108
12 x 11 - Answer: 132
How to divide any number by 5. - Answer: Double the number and divide it by 10 in either order
How to square a multiple of 10. - Answer: Square the digits without the zeros, then put 2 zeros
after the nonzero numbers.
,How to square a number ending in 5. - Answer: 1. Remove the 5, leaving the remaining digit(s)
2. Add 1 to the remaining digit(s)
3. Multiply the numbers (n)(n+1)
4. Put this product in front of 25.
1. If we know the value of n², then how can we get the next square up (n+1)²? - Answer: Add n
and (n+1) to n²
2. When a multiple of 10 greater than 1 is written in standard form, the exponent next to the 10
equals what? - Answer: The number of zeros after the 1. (10,000 = 10⁴)
For powers of 10 less than 1, the negative exponent next to the 10 equals what? - Answer: The
number of decimal places to the right of the decimal. (10^-2 =.01)
2. How to multiply with decimals? - Answer: 1. Count the number of digits to the right of the
decimal of each number. The sum of these is the amount of decimal places in your product
2. Find the product without worrying about the decimals
3. Put the correct number of decimal places into the final produce
How to divide with decimals? - Answer: move the decimals of both numbers one place to the
right until the denominator is a whole number.
2. How to find the power of a decimal? - Answer: Multiply the amount of digits to the right of
the decimal with the exponent and that is the amount of decimal places will be in your answer.
(.03)³=.000027
2. What is 1/6 in decimal form? - Answer: 0.166666....
,What is 1/7 in decimal form? - Answer: ~0.143
What is 5/6 in decimal form? - Answer: 0.83333333.....
What is 1/8 in decimal form? - Answer: 0.125
What is 3/8 in decimal form? - Answer: 0.375
What is 5/8 in decimal form? - Answer: 0.625
What is 7/8 in decimal form? - Answer: 0.875
2. How to simplify a complex fraction? - Answer: Multiply the numerator and denominator of
the big fraction by each denominator of the inner fractions.
2. How to quickly compare 2 fractions that are relatively close? - Answer: 1. 7/11 ?? 5/8
2. (7)(8) ?? (11)(55)
3. 56 > 55
4. So, 7/11 > 5/8
3. What is the equation for simple interest? - Answer:
3. What is the equation for compound interest? - Answer: V=P[1+(r/100n)]^nt
3. The equation for finding the % increase/decrease. - Answer: 100 (difference)/ original value
, 4. How to determine if an integer is divisible by 3? - Answer: If the sum of the digits are a
multiple of 3, then it is divisible by 3.
How to determine if an integer is divisible by 4? - Answer: If its last 2 digits are a multiple of 4
then it is divisible by 4.
Ex: 6,932 is a multiple of 4, since 32 is a multiple of 4.
How to determine if an integer is divisible by 6? - Answer: If it is divisible by 2 and 3, then it
divisible by 6.
How to determine if an integer is divisible by 9? - Answer: If its digits add up to a multiple of 9,
then it is divisible by 9.
How to test whether any number less than 100 is prime? - Answer: check whether it is divisible
by one of the prime numbers less than 10. If a number less than 100 is not divisible by any
prime divisor less than 10, then the number has to be prime.
11^2? - Answer: 121
12^2? - Answer: 144
13^2? - Answer: 169
14^2? - Answer: 196
15^2? - Answer: 225
