RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Of the 5 numbers, whose average is 75, the first is one-fourth of the sum of the last 4. The first number is?
A.75
B.80
C.78
D.56
Answer: A.75
Explanation: Total of 5 numbers = 5 * 75 = 375
Let total of last 4 numbers = x
1st number = x/4
x+ x/4 = 375
5x = 1500 => x =300
1st number = 300/ 4 = 75
Answer :A
Question: The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.
You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?
A.39%
B.41%
C.60%
D.70%
Answer: C.60%
Explanation: C
60%
In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.
In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.
Therefore, P(Second/First) = P (First and Second)/ P (First)
= 0.25/0.42
=0.60
=60 %
Question: Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?
A.The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 – 2m + 1
B.The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 – 2m + 1.
C.The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
D.The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
Answer: C.The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
Explanation: Explanation :
Given,
=> a + b + c + d = 4m + 1. now squaring this equation:
=> (a+b+c+d)2 = 16m2 + 8m + 1.
=> a2 + b2 + c2 + d2 + 2*( ab + ac + ad + bc + bd + cd ) = 16m2 + 8m + 1.
using the fact that product of two numbers is maximum when they are equal / nearly equal,
expression ab + ac + ad + bc + bd + cd will be maximum when ab , ac , ad, bc , bd , cd will be maximum and this is possible when a, b, c, d are nearly equal to each other. i.e. m , m , m , m+1.
when ab + ac + ad + bc + bd + cd is maximum , obviuosly , a2 + b2 + c2 + d2 will be minimum.
Put values in the above equation we get that the minimum value of a2 + b2 + c2 + d2 comes out to be 4m2 + 2m + 1.
Answer : C
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 1 and 50?
A.500
B.625
C.750
D.550
Answer: B.625
Explanation: numbers are 1,3,5-------,47,49
Average of the set: (largest+smallest)/2=(49+1)/2=25;
# of terms: (largest-smallest)/2+1=(49-1)/2+1=25
The sum = 25*25= 625
Answer: B
Question: Find the area of a cuboid of length 8cm , breadth 6 cm . and height 9cm.
A.400 cm cube
B.410 cm cube
C.420 cm cube
D.432 cm cube
Answer: D.432 cm cube
Explanation: Area of a cuboid = lxbxh =8cm x 6cm x 9cm = 432 cm cube
answer :D
Question: If 10a = 6b = 20, then 120ab =
A.800
B.1000
C.1200
D.1400
Answer: A.800
Explanation: 10a * 6b = 20 * 20 = 400
60 ab = 400
i.e. 120 ab = 800
Answer: Option A
Question: Positive integer x has n factors; 3x has 3 factors; Which of the following values can n take?
I. 1
II. 2
III. 3
A.I only
B.II only
C.I or II
D.II or III
Answer: B.II only
Explanation: Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer B
Question: In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
A.720
B.420
C.320
D.520
Answer: A.720
Explanation: The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).
Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters
=5!=5×4×3×2×1=120
In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves
=3!=3×2×1=6
Hence, required number of ways=120×6=720
Answer : A
Question: If P(A) = 2/15, P(B) = 7/15, and P(A âˆª B) = 16/15 Find P(A|B)
A.1/2
B.16/7
C.3/2
D.4/5
Answer: B.16/7
Explanation: P(A|B) = P(A âˆª B)/P(B)
P(A|B) = (16/15)/(7/15) = 16/7.
B
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 6 times the amount of the second solution?
A.62
B.65
C.68
D.70
Answer: D.70
Explanation: SOL:
Lets assume that 60L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 60*3/4 = 45L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 70L = 45 + 4 = 49L
Alcohol concentration in the new sol: (49/70)*100 = 70%
ANSWER:D
Question: A train covers a distance of 12 km in 16 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.80
B.90
C.60
D.75
Answer: D.75
Explanation: Speed = (12/16 * 60) km/hr = (45 * 5/18) m/sec = 12.5 m/sec.
Length of the train = 12.5 * 6 = 75 m.Answer:D
Question: A machine puts c caps on bottles in m minutes. How many E hours will it take to put caps on b bottles?
A.60bm/c
B.E=bm/60c
C.bc/60m
D.60b/cm
Answer: B.E=bm/60c
Explanation: The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine will take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
Question: What least number should be added to 1056, so that the sum is completely divisible by 23?
A. B. 3
C. 2	D. 1
A.4
B.3
C.2
D.0
Answer: C.2
Explanation: 1056 ÷ 23 = 45 with remainder = 21
21 + 2 = 23.
Hence 2 should be added to 1056 so that the sum will be divisible by 23
Answer: Option C
Question: What is the ratio between the volumes of a cylinder and cone of the same height and of the same diameter
A.2:1
B.3:1
C.4:1
D.5:1
Answer: B.3:1
Explanation: Explanation:
Volume of cylinder/Volume of cone=3/1
Answer: B
Question: What is the probability of getting a King and a Queen in a single draw of two cards from a pack of well-shuffled cards?
A.1/16
B.(4C1 * 4C1) / 52C2
C.4/52 * 4/51
D.8C2 / 52 C 2
Answer: B.(4C1 * 4C1) / 52C2
Explanation: there are 4 kings, so we can choose a king in 4C1 way..
there are 4 Queens, so we can choose a Queen in 4C1 way..
total possible way = 4C1∗4C152C24C1∗4C152C2
B
Question: If a boy lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
A.6
B.8
C.9
D.10
Answer: B.8
Explanation: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
B
Question: On four consecutive flips of a coin, what is the probability that all four produce the same result?
A.1/16
B.1/8
C.1/4
D.3/8
Answer: B.1/8
Explanation: TTTT case --> P = (1/2)^4 = 1/16
HHHH case --> P = (1/2)^4 = 1/16
P(TTTT or HHHH) = 1/16 + 1/16 = 2/16=1/8
Answer: B
Question: The average of 6 no.'s is 6.40. The average of 2 of them is 6.2, while the average of the other 2 is 6.1. What is the average of the remaining 2 no's?
A.2.3
B.2.6
C.6.9
D.4.5
Answer: C.6.9
Explanation: Sum of the remaining two numbers = (6.4 * 6) - [(6.2 * 2) + (6.1 * 2)]
= 38.40 - (12.4 + 12.2) = 38.40 - 24.6 = 13.80
Required average = (13.8 / 2) = 6.9
Answer : C
Question: 3889 + 12.952 - ? = 3854.002
A.47.95
B.49.75
C.45.97
D.47.59
Answer: A.47.95
Explanation: Let 3889 + 12.952 - x = 3854.002.
Then x = (3889 + 12.952) - 3854.002
= 3901.952 - 3854.002
= 47.95.
Answer is A
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
A.1:2
B.1:0
C.1:87
D.1:6
Answer: A.1:2
Explanation: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Question: The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?
A.2000
B.3000
C.4000
D.5000
Answer: C.4000
Explanation: Explanation:
Let monthly income of A = a
monthly income of B = b
monthly income of C = c
a + b = 2 × 5050 .... (Equation 1)
b + c = 2 × 6250 .... (Equation 2)
a + c = 2 × 5200 .... (Equation 3)
(Equation 1) + (Equation 3) - (Equation 2)
=> a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)
=> 2a = 2(5050 + 5200 - 6250)
=> a = 4000
i.e., Monthly income of A = 4000
ANSWER IS C
Question: If W is the set of all the integers between 10 and 332, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
A.111
B.28
C.160
D.213
Answer: D.213
Explanation: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318
Step 2. Divide by 3: 318 / 3 = 106
Step 3. Add 1: 106 + 1 = 107.
So there are 107 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318
Step 2. Divide by 2: 318 / 2 = 159
Step 3. Add 1: 159 + 1 = 160.
So there are 160 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 107 multiples of 3 and the 160 multiples of 2: 107+160=267.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 107+160=267. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 330 - 12 = 318
Step 2. Divide by 6: 318 / 6 = 53
Step 3. Add 1: 53 + 1 =54.
So there are 54 multiples of 6 within the range: we counted 54 numbers twice.
Subtract the 54 multiples of 6 from the sum of the multiples of 2 and 3:
= 107+160 - 54
= 267 - 54
= 213
Therefore, the final number of multiples of 2, 3 or 6 is 213.
Hence, this is the correct answer. (D)
Question: For any positive integer N, the sum of the first N positive integers equals N(N+1)/2 . If M and N are positive integers and M > N, what is the sum of all the integers between M and N, inclusive?
A. M(M+1)/2 + N(N+1)/2
B. M(M+1)/2 - N(N-1)/2
C. M(M+1)/2 - N(N+1)/2
D. M(M+1)/2 + N(N-1)/2
Answer: B. M(M+1)/2 - N(N-1)/2
Explanation: The sum of all the integers between M and N,inclusiveis the sum of the first M positive integersminusthe sum of the first N-1 positive integers.
The sum of the first M positive integers is M(M+1)/2;
The sum of the first N-1 positive integers is (N-1)N/2;
Therefore the answer is M(M+1)/2 - (N-1)N/2.
Answer: B.
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.155. Find the unknown rate of two towels?
A.A)400
B.B)450
C.C)500
D.D)550
Answer: C.C)500
Explanation: 10 * 155 = 1550
3 * 100 + 5 * 150 = 1050
1550 – 1050 = 500
C
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
A.5
B.6
C.8
D.7
Answer: D.7
Explanation: 7 * 8 : 9 * x
= 8:9 => x= 7
Answer:D
Question: Which of the following describes all values of x for which 1–x^2 = 0?
A. x >= 1
B. x <= –1
C. x=1; x=–1
D. x =2
Answer: C. x=1; x=–1
Explanation: Which of the following describes all values of x for which 1–x^2 = 0?
(A) x >= 1
Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong
(B) x <= –1
Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong
(C) x=1; x=–1
Plugged in 1. 1–1^2 = 0. Also -1. 1–(-1)^2 = 0. Since both are correct, answer is c.
(D) x =2
1–(2)^2 = -3. Wrong.
(E) –1 <= x <= 1
1–(-2)^2 = -3. Wrong
Answer is C.
Question: 5005 - 5000 ÷ 10.00 = ?
A.0.5
B.50
C.5000
D.4505
Answer: D.4505
Explanation: Answer
Given expression = 5005 - 5000 ÷ 10.00
= 5005 - 500
= 4505
Correct Option: D
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
A.1:6
B.1:0
C.1:9
D.1:2
Answer: C.1:9
Explanation: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1:9
Answer:C
Question: Find the fraction which has the same ratio to 2/3 that 3/5 has to 6/7
A.1/5
B.2/22
C.3/4
D.7/15
Answer: D.7/15
Explanation: P : 2/3 = 3/5 : 6/7
As the product of the means is equal to the product of the extremes.
P*6/7 = 2/3 * 3/5
P*6/7 = 6/15
P = 7/15 => P = 7/15
ANSWER:D
Question: An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
A.3728
B.3726
C.3720
D.3722
Answer: C.3720
Explanation: A = P(1 + TR/100)
=> 3600 = 3000[1 + (4 * R)/100] => R = 5%
Now R = 6%
=> A = 3000[1 + (4 * 6)/100] = Rs. 3720.
Answer: C
Question: If a quarter Kg of potato costs 60 paise, How many paise will 200 gm cost?
A.48 Paise
B.26 Paise
C.28 Paise
D.11 Paise
Answer: A.48 Paise
Explanation: Explanation:
Let the Required cost be X paise. Less Weight , Less cost (Direct Proportion)
\inline \fn_jvn \therefore \inline \fn_jvn 250:200:: 60:x \inline \fn_jvn \Leftrightarrow \inline \fn_jvn 250\times X =(200\times 60) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{(200\times 60)}{250} \inline \fn_jvn \Leftrightarrow x= 48
Answer: A
Question: In the set of positive integers from 1 to 80, what is the sum of all the odd multiples of 5?
A.180
B.245
C.320
D.260
Answer: C.320
Explanation: reduce to 1 - 80
5 - 15 - 25 - 35 - 45--55--65--75 are valid multiples. Add them --> 320
C
Question: The difference between the two numbers is 1/3 of the larger number. If the smaller one is 48 the larger one is
A.72
B.60
C.32
D.96
Answer: A.72
Explanation: Explanation:
Let the larger number be x. Then,
x - 48 = 1/3 x
x - x/3 = 48
=> 2x/3 = 48 => x = 72
Answer: Option A
Question: Jerry and john play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. john plays first, giving Jerry a third of her cards. Jerry plays next, and john follows. Then the game ends. jerry ended up with 14 more cards than Michelle. How many cards did each player have originally?
A.28
B.27
C.29
D.30
Answer: B.27
Explanation: Game john jerry
Initially2727
After game 1 1836
After game 2 3024
After game 3 2034
Now Merry has 14 cards more than Michelle. This option gives us exactly what number of cards they had initially.
So the answer is B
Question: The ratio of two numbers is 5 to 1. The sum is 18. What are the two numbers?
A.17
B.18
C.19
D.20
Answer: B.18
Explanation: Solution
Let x be the first number. Let y be the second number
x / y = 5 / 1
x + y = 18
Using x / y = 5 / 1, we get x = 5y after doing cross multiplication
Replacing x = 5y into x + y = 18, we get 5y + y = 18
6y = 18
y = 3
x = 5y = 5 × 3 = 15
As you can see, 15/3 = 5, so ratio is correct and 3 + 15 = 18, so the sum is correct.
Answer B
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 5 hats randomly out of the drawer and returning each hat before taking out the next one?
A.1/8
B.1/4
C.1/2
D.5/8
Answer: D.5/8
Explanation: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2 = 1/32
There are 5C3 = 10 such cases so we need to multiply this by 10.
P(exactly 3 red hats) = 10*1/32 = 5/16
Clearly the probability of getting exactly 3 blue hats will also be 5/16.
The sum of the probabilities is 5/16+5/16 = 5/8
The answer is D.
Question: From group of 15 cricket players a team of 11 players is to be chosen. How many ways this can be done?
A.3252
B.1365
C.5325
D.1432
Answer: B.1365
Explanation: 11 players are to be chosen from 15 players. This can be done in 15C11 ways. ie) 15!/11!x4! = 1365 ways. Ans: B
Question: The diagonals of a rhombus are 22 cm and 30 cm. Find its area?
A.358
B.329
C.350
D.330
Answer: D.330
Explanation: 1/2 * 22 * 30 = 330
Answer:D
Question: Two women can do a work in 4 days. Six men can complete the same work in 3 days. What is the ratio between the capacity of a man and a woman?
A.1:2
B.2:1
C.4:9
D.3:2
Answer: C.4:9
Explanation: Explanation:
(2 Ã— 4 ) women can complete the work in 1 day.
âˆ´ 1 woman's 1 day's work = 1/8
(6 Ã— 3) men can complete the work in 1 day.
âˆ´ 1 man's 1 day's work = 1/18
so, required ratio =1/8 : 1/18= 4:9
Answer: C
Question: 85% of a number is added to 24, the result is the same number. Find the number?
A.13√5
B.13√2
C.13√9
D.12√9
Answer: B.13√2
Explanation: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer:B
Question: Kamal obtained 96, 65, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
A.65
B.69
C.72
D.79
Answer: D.79
Explanation: Sol.
Average
= 96 + 65 + 82 + 67 + 85 / 5)
= (395 / 5)
= 79.
Answer D
Question: The sum of two numbers is 25 and their difference is 13. Find their product.
A.104
B.108
C.114
D.325
Answer: C.114
Explanation: Sol.
Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x+y)2 - (x-y)2
= (25)2 - (13)2 = 625 - 169 = 456
⇒ xy = 114.
Answer C
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 35 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
A.22%
B.24%
C.25%
D.26%
Answer: D.26%
Explanation: Total sales =800
Comission = (20/100)*500+ (35/100)*300
=100 + 105
=205
%Comission =(205/800)*100=25.6~ 26%
Answer is D
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 50 years now, the son's age five years back was?
A.18years
B.19years
C.20years
D.21years
Answer: C.20years
Explanation: Let the son's present age be x years. Then, (50 - x) = x
2x = 50.
x = 25.
Son's age 5 years back (25 - 5) = 20 years.
C)
Question: 1, 8, 27, 64, 125, 216, (....)
A.354
B.343
C.245
D.392
Answer: B.343
Explanation: The pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, etc
Hence, next number is 7^3 = 343
Answer is B
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 12% less than the price each head sold for the day before.what was the gross profit on this shipment?
A.$100
B.$115
C.$120
D.$130
Answer: C.$120
Explanation: Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 88% of the previous price: 88/100 * 1/2 = $(11/25)
Total revenue by selling 500 heads = 11/25 * 500 = 220
Total revenue after selling 1500 cabbage heads - 220+500 = $720
Money spent on the purchase: $600
Profit = 720-600 = $120
Ans: "C
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
A.250
B.279
C.277
D.272
Answer: A.250
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15
= 250 m
Answer: A
Question: An escalator moves towards the top level at the rate of 10 ft.sec and its length is 112 feet. If a person walks on the moving escalator at the rate of 4 feet per second towards the top level, how much time does he take to cover the entire length.
A.14 sec
B.10 sec
C.12 sec
D.8 sec
Answer: D.8 sec
Explanation: Time taken to cover the entire length = tot.dist/resultant speed
= 112/ (10+4)
= 8 sec
ANSWER:D
Question: If FRIEND is coded as HUMJTK, how is CANDLE written in that code ?
A.EDRIRL
B.FFIIIUU
C.WDFDD
D.DRFED
Answer: A.EDRIRL
Explanation: Explanation:
The first, second, third, fourth, fifth and sixth letters of th word are respectively moved two, three, four, five, six and seven steps forward to obtain the corresponding letters of the code.
Answer: A
Question: The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 35 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
A.16
B.17
C.19
D.22
Answer: B.17
Explanation: The total sum of the numbers should be increased by 10.
Then the average will increase by 10/10 = 1.
The correct average is 17.
The answer is B.
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5265. What was the number of original inhabitants?
A.7500
B.7800
C.8100
D.8400
Answer: B.7800
Explanation: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 5265
(27/40) * x = 5265
x = 5265 * 40 / 27 = 7800
The answer is B.
Question: A BAG CONTAINS 6 WHITE AND 4 BLACK BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
A.8/9
B.75/4
C.7/15
D.3/7
Answer: C.7/15
Explanation: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Ans: C
Question: A certain company had a total annual expenditure of 1.47∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
A.$20,000
B.$25,000
C.$35,000
D.$40,000
Answer: C.$35,000
Explanation: Given: Total annual expenditure of 1.47∗10^7 on employee salaries
Total employees = 420
Observe that 420*3.5 = 1470
Therefore try to bring the numerator in terms of 1470
Average salary = (1470*10^4) /420 = 3.5*10^4 = 35,000
Option C
Question: A rectangular with dimensions 16 inches by 20 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
A.a) 4 inches
B.b) 6 inches
C.c) 7 inches
D.d) 8 inches
Answer: A.a) 4 inches
Explanation: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
16=2*2*2*2
20=2*2*5
GCF = 2*2= 4
P.S you can make squares with side of 2,4 and we choose 4 because 2 is not in the answers
Answer : A
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%?
A.$500
B.$600
C.$700
D.$900
Answer: B.$600
Explanation: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1054/1000)-1 = 0.054 = 5.4%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.054
(0.05)x +0.06 - (0.06)x = 0.054
-0.01x = -0.006
x= -0.006/-0.01 = 6/10 = 60%
So X = 60% of the 1000 which is 600
ANSWER:B
Question: CX, EV, GT, IR, ?
A.JH
B.UU
C.KP
D.UY
Answer: C.KP
Explanation: ANSWER:C
Question: The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x?
A.D
B.H
C.J
D.H
Answer: A.D
Explanation: Explanation: If you fold the above picture at the dotted lines, X and C are opposite to each other.
Answer:A