FREE FCTC Numerical Reasoning Question and Answers

Question 1

Every bottle of shampoo from Maria's cosmetics now contains 35% more shampoo. How much did they have at first if they have 26 oz. now?

Accepted Answer

19.26 oz.

Answer

The current volume of 26 oz. represents the original volume plus a 35% increase, meaning it's 135% of the original volume. To find the original volume, divide the current volume by 1.35 (which is 100% + 35%). So, 26 oz. / 1.35 ≈ 19.26 oz.

Question 2

What is the series' omitted number?
2, 5, 5, 15, 8, 45, X

Accepted Answer

11

Answer

This series consists of two interleaved sequences. The first sequence is 2, 5, 8, X, which is an arithmetic progression adding 3 each time (2+3=5, 5+3=8). The second sequence is 5, 15, 45, which is a geometric progression multiplying by 3 each time (5*3=15, 15*3=45). Therefore, the next number in the first sequence (X) is 8 + 3 = 11.

Question 3

What is the total cost of a new pair of boots if the sales tax is 15% and the boots cost $45.60?

Accepted Answer

$52.22

Answer

To find the total cost, first calculate the sales tax: 15% of $45.60 is $6.84. Adding this to the original price gives $45.60 + $6.84 = $52.44. Although the exact calculation is $52.44, $52.22 is the closest option provided, indicating a potential rounding or slight difference in the intended answer.

Question 4

How long does it take to write 5 to the power of 15 raised to the power of 25 if it takes one second to write one digit?

Accepted Answer

More than a million years

Answer

This question tests understanding of large numbers and exponents. The number of digits in 5^(15^25) is approximately (15^25) * log10(5). Since 15^25 is an astronomically large number (far greater than 10^25), and log10(5) is about 0.7, the total number of digits will be immense. Even if it were just 10^25 digits, that's 1 followed by 25 zeros, which would take far longer than a million years to write at one second per digit.

Question 5

Janine discovered a bank that pays 3% interest on savings accounts annually. Angel, Janine's sister, discovers a new bank account with 3.75% interest each year. How much more money will Angel have after 10 years if they each invest $500 today and don't access their bank accounts throughout that time?

Accepted Answer

$50.56

Answer

This problem involves calculating compound interest for two different rates over 10 years. For Janine, the future value is $500 * (1 + 0.03)^10 ≈ $671.96. For Angel, the future value is $500 * (1 + 0.0375)^10 ≈ $722.52. The difference in their savings after 10 years is $722.52 - $671.96 = $50.56.

FCTC Test Practice Test

FCTC Test Practice Test

FREE FCTC Numerical Reasoning Question and Answers