Quantitative Reasoning (Level 600) - 1 - Free MCQ Practice Test with solutions,

The Pool has a capacity of 12 units, with Hose A having an efficiency of 2 units per hour and Hose B having an efficiency of 3 units per hour.

After 1 hour, Hose A completes 2 units of work, leaving 10 units remaining.

The combined efficiency of Hose A and Hose B is 5 units per hour.

To fill the remaining 10 units, it will take 10/5 = 2 hours.

Therefore, the total time required to fill the Pool is 1 hour (from Hose A) + 2 hours (to fill the remaining 10 units) = 3 hours. Thus, the answer is (D).

To find the combined work rate of A, B, and C, we first calculate their individual contributions:

1. A and B together can complete the job in 6 days, so their combined work rate is 1/6 of the job per day.

2. B and C together can complete the job in 10 days, so their combined work rate is 1/10 of the job per day.

3. C and A together can complete the job in 7.5 days, so their combined work rate is 1/7.5 of the job per day.

Let's denote the work rates of A, B, and C as a, b, and c, respectively:

a + b = 1/6, b + c = 1/10, c + a = 1/7.5

Adding these equations gives:

a + b + b + c + c + a = 1/6 + 1/10 + 1/7.5

2(a + b + c) = 0.4

a + b + c = 0.2

The combined work rate of A, B, and C is 0.2 of the job per day.
Therefore, they will complete the job in 1/0.2 = 5 days.

In order to maximize Dan's votes, we need to ensure that Bill, Charlie, and Dan receive as many votes as possible while minimizing the difference between their vote counts, with a minimum difference of 1. Additionally, we aim to minimize the number of votes received by Ernie to just 1 vote.

Given that Alexa received 40 votes, let's denote the number of votes received by Dan as x. Thus, the number of votes received by Bill would be x+2, Charlie would receive x+1 votes, and Dan himself would receive x votes. Lastly, Ernie's vote count is represented by d.

The total number of votes is calculated as follows: 40 + (x+2) + (x+1) + x + d = 100

Simplifying the equation, we have: 43 + 3x + d = 100

To further analyze the situation, we note that 3x is equivalent to 57 - d. Therefore, x is determined as follows: x = 18

Since d cannot be 0 and must be at least 3, we arrive at the conclusion that x equals 18.

Let's assume the duration of the call is "x" minutes.

Under plan A, the total cost for the call would be $0.60 for the first 7 minutes and $0.06 per minute thereafter. Therefore, the total cost under plan A would be:

Cost under plan A = $0.60 + ($0.06 * (x - 7))

Under plan B, the cost for the call would be $0.08 per minute. Therefore, the total cost under plan B would be:

Cost under plan B = $0.08 * x

To find the duration of the call for which the charges are the same under both plans, we can set up the equation:

$0.60 + ($0.06 * (x - 7)) = $0.08 * x

Simplifying the equation, we have:

0.60 + 0.06x - 0.42 = 0.08x

0.06x - 0.08x = 0.42 - 0.60

-0.02x = -0.18

Dividing both sides of the equation by -0.02, we get:

x = 9

Therefore, the duration of the call for which the company charges the same amount under plan A and plan B is 9 minutes. Hence, the answer is B.

Let the keys be name as A B C D E F G H I [H and I being the two new keys]

Probability of H and I being together = 

Total number of arrangements possible in a circle with the 9 keys = (n-1)! = 8!

Total number of arrangements where H and I are together = 7! x 2 [Consider H and I as one unit. In addition, there are 7 other units i.e. A B C D E F G. Total number of ways to arrange the 8 units in a circle is (n-1)! = 7!. Further, H and I can be arranged in 2 ways i.e. H I or I H.]

Probability = (7! x 2)/8! = 1/4.

To find the sum of the reciprocals of all the positive factors of the perfect number 28, we first need to determine the factors of 28.

The factors of 28 are 1, 2, 4, 7, 14, and 28.

Now, let's calculate the sum of the reciprocals of these factors:

1/1 + 1/2 + 1/4 + 1/7 + 1/14 + 1/28

To simplify this expression, we can find a common denominator:

28/28 + 14/28 + 7/28 + 4/28 + 2/28 + 1/28

Combining the fractions, we have:

(28 + 14 + 7 + 4 + 2 + 1) / 28

Simplifying the numerator, we get:

56 / 28

Dividing both the numerator and denominator by 28, we obtain:

2 / 1

Therefore, the sum of the reciprocals of all the positive factors of the perfect number 28 is 2.

Hence, the correct answer is (C) 2.

We need to determine
•    The percentage of the same distribution, which is less than A + 2SD.

As it is given that 95% of the distribution falls within two standard deviation (SD) of the mean, we can conclude that 5% lies outside this given range.

Now, as the distribution is symmetric about the mean A, we can also say that
•    Half of 5% or 2.5% lies to the right of A + 2SD
•    Therefore, the remaining (100 – 2.5) = 97.5% lies to the left of A + 2SD, or less than A + 2SD.

Hence, the correct answer is option D.

To determine the units digit of the product 2 * 3^x, we need to focus on the units digits of the factors involved.

The units digit of 2 is always 2.

Now, let's consider the units digit of the powers of 3:

3^1 = 3 3² = 9 3³ = 27 3⁴ = 81 3⁵ = 243 3⁶ = 729 ...

We observe that the units digit of the powers of 3 cycles in the pattern: 3, 9, 7, 1. So, the units digit of 3^x depends on the remainder when x is divided by 4.

Now, we can consider the possible values of x and check the units digit of 3^x:

For x = 12: 3¹² has a units digit of 1. For x = 13: 3¹³ has a units digit of 3. For x = 14: 3¹⁴ has a units digit of 9. For x = 15: 3¹⁵ has a units digit of 7. For x = 16: 3¹⁶ has a units digit of 1.

From the calculations above, we see that the only value of x for which the units digit of 3^x is equal to 4 is x = 15.

Therefore, the correct answer is (D) 15.

To determine the number of distinct positive integer factors of 2xy, we need to consider the prime factorization of 2xy.

The prime factorization of 2xy can be written as 2 * x * y.

Since x and y are both odd prime numbers, they cannot be divided further.

The number of distinct positive integer factors can be calculated by multiplying the powers of each prime factor plus 1. In this case, we have:

Number of factors = (power of 2 + 1) * (power of x + 1) * (power of y + 1)

Since the power of 2 is 1, and both x and y are raised to the power of 1, the number of factors is:

Number of factors = (1 + 1) * (1 + 1) * (1 + 1) = 2 * 2 * 2 = 8

Therefore, the number of distinct positive integer factors of 2xy is 8.

Hence, the correct answer is (D) 8.

To find the remainder when x³ + x² + x is divided by 101, we need to consider the properties of remainders.

Given that the remainder is 5 when x is divided by 101, we can express x as:

x = 101k + 5

where k is an integer.

Now, let's substitute this expression for x into the expression x³ + x² + x:

(x³ + x² + x) = (101k + 5)³ + (101k + 5)² + (101k + 5)

Expanding and simplifying this expression, we get:

(x³ + x² + x) = 101³k³ + 3 * 101²k² * 5 + 3 * 101k * 5² + 5³ + 101^2k² + 2 * 101k * 5 + 5^2 + 101k + 5

The terms involving k and its powers are all divisible by 101 since they have a factor of 101. Therefore, we can ignore those terms and focus on the constant terms:

(x³ + x² + x) = 125 + 25 + 5

Simplifying further, we find:

(x³ + x² + x) = 155

Therefore, the remainder when x³ + x² + x is divided by 101 is 155 % 101, which is 54.

Hence, the correct answer is (D) 54.

The minimum values for m and n are 14 and 9 respectively, with m being greater than n. Therefore, the difference between m and n is 5. In other words, when we divide the difference between m and n by 6, the result is 5. Hence, the correct answer is (E) 5.

The least common multiple of 2, 3, 5, and 7 is 210. Therefore, if we express a number N as 210q + 1, where q is an integer, we can find a series of numbers that satisfy this equation.

The first number that satisfies this equation is N = 1 when q = 0.

The second number that satisfies this equation is N = 211 when q = 1.

The third number that satisfies this equation is N = 421 when q = 2.

Hence, we observe that these numbers form an arithmetic progression with a common difference of 210.

The number of terms below 1000 that satisfy the equation N = 210q + 1 is 5.

Therefore, the total number of terms in the sequence is 4 + 5 = 9.

The absolute value of a number represents its distance from zero on the number line. In this case, we want to represent the possible values of x, the height of a child who can ride the roller coaster, which must fall between 24 and 52 inches.

To represent this, we need an absolute value inequality that ensures the distance between x and a certain value is less than a given range.

Let's analyze the options:

A. |x – 24| < 52: This option represents the distance between x and 24 being less than 52, but it does not restrict the upper limit to 52. Therefore, it is not a correct representation of the given conditions.

B. |x – 28| < 14: This option represents the distance between x and 28 being less than 14, but it does not reflect the lower limit of 24. Thus, it does not accurately represent the given conditions.

C. |x – 38| < 14: This option represents the distance between x and 38 being less than 14, which fits the given conditions. If we consider x = 38, the absolute value of (x - 38) is 0, indicating that x is exactly 38. This option correctly represents the range from 24 to 52.

D. |x – 14| < 38: This option represents the distance between x and 14 being less than 38, but it does not capture the upper limit of 52. Therefore, it does not satisfy the given conditions.

E. |x – 28| < 52: This option represents the distance between x and 28 being less than 52, but it does not restrict the lower limit to 24. Thus, it is not an accurate representation of the given conditions.

Based on the analysis, option C, |x – 38| < 14, correctly represents all possible values of x that fall within the range of 24 to 52 inches.

If x < y, we can analyze each option to determine which one must be true:

A. 2x < y: We can't determine whether this is true or false since we don't have any information about the relative magnitudes of x and y.

B. 2x > y: We can't determine whether this is true or false since we don't have any information about the relative magnitudes of x and y.

C. x² < y²: This inequality does not hold true for all values of x and y when x < y. For example, if x = -2 and y = 1, then x² = 4 and y^2 = 1, which violates the inequality.

D. 2x - y < y: Let's substitute x = 1 and y = 2 to test this inequality. We have 2(1) - 2 < 2, which simplifies to 0 < 2. Since x < y, this inequality is true for the given values of x and y. Since the inequality holds true for at least one case, it must be true.

E. 2x - y < 2xy: We can't determine whether this is true or false since we don't have any information about the relative magnitudes of x and y.

Based on the analysis above, the only option that must be true when x < y is option D.

Therefore, the correct answer is (D).

Let WX = a, XY = b, YZ = c
So, we have to find the value of b.
From the diagram given in the question stem, we can deduce the following information :
a+b = 21
b+c = 26
c = 2a
Substituting this value of c in the equation, we will get the following equations
2a + b = 26
a + b = 21
Solving for a = 5.
From this information, we can say b = 16(Option D)

We need to find the population of males in 1993 who are not enrolled. 
Thus it is the "total male population - the number of males who are enrolled"
Total male population = 37 + 88 = 125 million
The number of males who are not enrolled = (16% + 29%) of total enrollment = 45% of  13.9 million
45% of  13.9 million = 50% of 13.9 - 5% 13.9 = 7 - 0.7 = 6.3 (We can ignore the 0.05 as the answer options are 2-3 million apart so it won't create any issues) 
Thus the answer = 125 - 6.3 = 118.7
The answer option E.

Let s =2 and t = 3 and n =6 {Where s and t are integers greater than 1 and each is a factor of the integer 6}
n^st = 6⁶ =>2⁶3⁶ 
Now check for the options
1) s^t = 2³(Can be a factor of 2⁶3⁶)
2) (st)² = s²t²  => 2²3² (Can be a factor of 2⁶3⁶)
3) s+ t = 2 + 3 = 5 (Can not be a factor of 2⁶3⁶)
Hence only option D) 1 and 2 follows.

If the distance between 2 consecutive trees is x, then distance between 3 consecutive trees must be 2x.
similarly distance between 26 consecutive trees must be 25x = 225
x = 225/25 = 9
C is correct.­

Given that  Notice that 1/43 is the larges term and 1/48 is the smallest term.
If all 6 terms were equal to 1/43, then the sum would be 6/43=~1/7, but since actual sum is less than that, then we have that K<1/7.
If all 6 terms were equal to 1/48, then the sum would be 6/48=1/8, but since actual sum is more than that, then we have that K>1/8.
Therefore, 1/8<K<1/7. So, K must be closer to 1/8 than it is to 1/6.
Answer: C.

Let n = the number of litres in the 70% ammonia solution. We can create the equation:
0.2(120) + 0.7n = 0.5(120 + n)
24 + 0.7n = 60 + 0.5n
0.2n = 36
n = 36/0.2 = 360/2 = 180
Therefore, the volume of the 50% ammonia solution is 120 + 180 = 300 litres.
Answer: E