Free FCTC Numerical Reasoning Question and Answers 1 — Questions 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?
- 9 oz.
- 19.26 oz. (Correct answer)
- 55 oz.
- 2oz.
Correct answer: 19.26 oz.
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? <br> 2, 5, 5, 15, 8, 45, X
- 9
- 12
- 11 (Correct answer)
- 5
Correct answer: 11
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?
- $50.22
- $74.22
- $52.22 (Correct answer)
- $84.22
Correct answer: $52.22
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?
- 8 minutes
- More than a million years (Correct answer)
- 10 hours
- 1000 years
Correct answer: More than a million years
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?
- $900.96
- $54.78
- $50.56 (Correct answer)
- $800.52
Correct answer: $50.56
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.
Question 6: How many euros can you buy today, at the current exchange rate of 1 USD = 0.88 EUR, with 200 USD?
- 20 EUR
- 150 EUR
- 176 EUR (Correct answer)
- 80 EUR
Correct answer: 176 EUR
To convert USD to EUR, you multiply the amount in USD by the exchange rate. With 200 USD and an exchange rate of 1 USD = 0.88 EUR, the calculation is 200 * 0.88. This results in 176 EUR.
Question 7: In the following sequence, find the missing number. <br> 3, 4, 0, 8, X, 16, -6, 32
- -3 (Correct answer)
- 4
- -4
- 1
Correct answer: -3
The sequence consists of two interleaved patterns. The numbers in the even positions (4, 8, 16, 32) follow a pattern of multiplying by 2. The numbers in the odd positions (3, 0, X, -6) follow a pattern of subtracting 3. Following this pattern, 0 - 3 gives -3, and -3 - 3 gives -6, which matches the next number in the odd sequence. Therefore, X is -3.
Free FCTC Numerical Reasoning Question and Answers 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?