RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: An Air Cooler is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
A.18%
B.19%
C.21.2%
D.21.81%
Answer: D.21.81%
Explanation: Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it: Air Cooler on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Question: The average age of a committee of 12 members is 40 years. A member aged 55 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
A.38.7 years
B.38 years
C.36 years
D.35 years
Answer: A.38.7 years
Explanation: Exp. Total age of the committee = 40*12 = 480,
Total age when a member is retired
and a new one was joined = 480-55 +39, =464
Average age of present committee = 464/12 = 38.7.
Answer: A
Question: What is the probability of flipping a fair coin eight times and the coin landing on heads on at least two flips?
A.61/64
B.117/128
C.123/128
D.247/256
Answer: D.247/256
Explanation: The number of possible outcomes is 2^8=256.
0 heads: There is 1 way to have all tails.
1 head: There are 8 ways to have one head.
P(0 or 1 head)=9/256
P(at least 2 heads)=1 - 9/256 = 247/256
The answer is D.
Question: A radio station has to choose five days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any five of the seven weekdays can be chosen. How many different five-day combinations of the seven weekdays can be constructed?
A.9
B.15
C.21
D.56
Answer: C.21
Explanation: Pick 5 days out of 7.. 7C5 = = 21
Answer : C
Question: 14 men can complete a piece of work in 22 days. In how many days can 18 men complete that piece of work?
A.23 days
B.26 days
C.17 days
D.29 days
Answer: C.17 days
Explanation: C
17 days
14 * 22 = 18 * x => x = 17 days
Question: If the complement of a certain angle is four times the measure of that certain angle, then what is the measure of that certain angle?
A.45°
B.30°
C.22.5°
D.18°
Answer: D.18°
Explanation: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 4x, and together, these add up to 90 degrees.
x + 4x = 90
5x = 90
x = 18°
Answer = (D)
Question: Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 1.5. Which of the following operations would decrease the standard deviation of Set J?
A.Multiply each term by e/d
B.Divide each term by b/c
C.Multiply each term by −1
D.Divide each term by a/e
Answer: D.Divide each term by a/e
Explanation: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
D
Question: The measurement of a rectangular box with lid is 25cmx6cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
A.288
B.48
C.36
D.864
Answer: C.36
Explanation: d=6, r=2;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*3*3*3= 36πcm3 ANSWER:C
Question: A river 2m deep and 45 m wide is flowing at the rate of 5 kmph the amount of water that runs into the sea per minute is?
A.4500 M3
B.4580 M3
C.7500 M3
D.4900 M3
Answer: C.7500 M3
Explanation: Explanation:
(5000 * 2 * 45)/60 = 7500 M3
Answer: Option C
Question: A train passes a train coming from opposite direction, speed 32 kmph in 25 sec. If the speed of the train is 40 km/hr. What is the length of train?
A.300
B.400
C.500
D.350
Answer: C.500
Explanation: Speed = (40+32) * 5/18 = 72 * 5/18 = 20 m/sec.
Length of the train = 25 * 20 = 500 m.
Answer: C
Question: A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 104 pounds?
A.8
B.7
C.16
D.10
Answer: D.10
Explanation: Ans is D:
39 pounds --> 6 days
104 pounds --> x days
x = 104*6/39 = 16
the animal has already consumed food in 6 days so the the number of days
for it's total consumption be 104 pounds is 16-6 = 10
Question: A motorcyclist goes from Nagpur to Pune, a distance of 500 kms at an average of 100 kmph speed. Another man starts from Nagpur by car 3 Â½ hours after the first, and reaches Pune Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
A.1:2
B.1:7
C.3:5
D.1:5
Answer: C.3:5
Explanation: T = 500/100 = 10 h
T = 10 - 4 = 6
Time Ratio = 10:6 = 5:3
Speed Ratio = 3:5
Answer: C
Question: A and B starts a business with Rs.8000 each, and after 6 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
A.18:11
B.2:3
C.3:2
D.11:9
Answer: C.3:2
Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 6 months and then withdraws Rs.4000. So, the investment of B for remaining 12 months is Rs.4000 only.
A : B
8000*18 : (8000*6) + (4000*12)
144000 : 96000
A:B = 3:2
ANSWER:C
Question: If 4XZ + YW = 10 and XW + YZ = 20, what is the value of the expression (2X + Y)(2Z + W)?
A.9.
B.12.
C.15.
D.50.
Answer: D.50.
Explanation: (2x+y)*(2z+w) = 10+2(20) =50
Answer : D
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.86. How much was lent at 5%?
A.228
B.299
C.400
D.500
Answer: C.400
Explanation: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 â€“ 6x/100 = 86
x/100 = 4
=> x = 400
Answer:C
Question: A cistern 4 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
A.28
B.32
C.36
D.40
Answer: C.36
Explanation: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 4 x 1.25) + 4 x 4]
= 36
The answer is C.
Question: Hal bought walnuts at 5 for $1 and apples at 4 for $1.He spent a total of $19.50 . He sells both at 20 for $5 and as a result gains $3 .How many walnuts did Hal buy ?
A.50
B.45
C.60
D.80
Answer: C.60
Explanation: Let's start with the concrete information:
He buys everything for $19.50 and earns $3 after selling so he sells everything for $22.50 (= 2250 cents).
He sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items
Cost of each walnut = 1/5 = $.2 = 20 cents
Cost of each apple = 1/4 = $.25 = 25 cents
Now we have one equation to solve:
20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys)
4w + 5(90 - w) = 390
w = 60
Answer (C)
Question: A cubical tank is filled with water to a level of 1 foot. If the water in the tank occupies 16 cubic feet, to what fraction of its capacity is the tank filled with water?
A.1/2
B.1/3
C.1/4
D.1/5
Answer: C.1/4
Explanation: The volume of water in the tank is H*L*B = 16 cubic feet.
Since H = 1, then L*B = 16 and L = B = 4.
Since the tank is cubical, the capacity of the tank is 4*4*4 = 64.
The ratio of the water in the tank to the capacity is 16/64 = 1/4
The answer is C.
Question: A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 10% below the cost price of the claimed weight.
A.19.81%
B.20%
C.37.5%
D.23.75%
Answer: D.23.75%
Explanation: There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.
But he also sells at 10% less
(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 9/10 = (1 + p%)
profit % = 23.75%
D
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
A.297 cm2
B.384 cm2
C.672 cm2
D.267 cm2
Answer: B.384 cm2
Explanation: Area of a parallelogram
= base * height
= 24 * 16
= 384 cm2
Answer: B
Question: How many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 5 percent sugar solution?
A.20
B.25
C.30
D.32
Answer: C.30
Explanation: Let x be the amount that needs to be evaporated.
0.02(50) = 0.05(50-x)
0.05x = 2.5 - 1
x = 1.5/0.05 = 30 liters
The answer is C.
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.2 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
A.2:5
B.2:3
C.2:4
D.1:1
Answer: D.1:1
Explanation: Let the ratio be k : 1. Then,
k * 16.2 + 1 * 15.4 = (k + 1) * 15.8
= (16.2 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.4 = 1/1
Required ratio = 1/1 : 1 = 1:1.
Answer:D
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
A.16 2/8%
B.11 2/3%
C.16 9/3%
D.16 2/3%
Answer: D.16 2/3%
Explanation: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Question: A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is.
A.200 m
B.150 m
C.148 m
D.140 m
Answer: A.200 m
Explanation: Explanation:
Let the triangle and parallelogram have common base b,
let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then
Area of triangle =1/2∗b∗h1
Area of rectangle =b∗h2
As per question 1/2∗b∗h1=b∗h2
1/2∗b∗h1=b∗100
h1=100∗2=200m
Option A
Question: In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 6,000 have been vaccinated against both, how many have been vaccinated only against rubella?
A.2,5000
B.7,500
C.12,000
D.15,000
Answer: C.12,000
Explanation: Use a single variable as far as possible.
Number vaccinated only against mumps = x
Number vaccinated against both = 2x = 6000 (so x = 3000)
Then, number vaccinated against mumps (including both) = x + 2x = 3x
Number vaccinated against rubella = 2*3x = 6x
Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*3000 = 12,000
Answer (C)
Question: Each of the following equations R has at least one solution EXCEPT
A.R=–2^n = (–2)^-n
B.R=2^-n = (–2)^n
C.2^n = (–2)^-n
D.(–2)^n = –2^n
Answer: A.R=–2^n = (–2)^-n
Explanation: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.
Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.
In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.
If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Question: AT + CD = AAA, where AT and CD are two-digit numbers and AAA is a three digit number; A, T, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
A. 1
B. 3
C. 7
D. 9
Answer: D. 9
Explanation: Since AT and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.
So, A=1 and we have 1T+CD=111
Now, C can not be less than 9, because no two-digit integer with first digit 1 (1T<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1T<111).
Hence C=9.
Answer: D.
Question: The labeled price of a table is Rs. 8,000. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
A.Rs. 5758
B.Rs. 6195
C.Rs. 6608
D.Rs. 7200
Answer: C.Rs. 6608
Explanation: Explanation:
Labeled price = Rs. 8,000
By giving 5% discount on labeled price, the selling price is
= 95 / 100 * 8000 = Rs. 7600
By earning 15% profit on the selling of price Rs. 7600 the cost price is
= 100 / 115 * 7600= Rs. 6608
Therefore, approximate cost is 6608
ANSWER C
Question: An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?
A.Rs. 72
B.Rs. 90
C.Rs. 66
D.Rs. 96
Answer: A.Rs. 72
Explanation: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
ANSWER:A
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.170
B.180
C.190
D.120
Answer: B.180
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: Option B
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 12 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
A.$223
B.$225
C.$224
D.$213
Answer: C.$224
Explanation: Final price = (1+12/100) * Original Price
= 1.12 * Original Price
From options given only 224 is divisible by 1.12 as it is stated OP is whole dollar amount.
Hence C
Question: If the sides of a square are multiplied by 10, the area of the original square is how many times as large as the area of the resultant square?
A.1%
B.10%
C.100%
D.500%
Answer: A.1%
Explanation: Let x be the original length of one side.
Then the original area is x^2.
The new square has sides of length 10x, so the area is 100x^2.
The area of the original square is 1/100 = 1% times the area of the new square.
The answer is A.
Question: Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink?
A.1/49
B.4/7
C.3/7
D.16/49
Answer: B.4/7
Explanation: The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 9/49 = (3/7) * (3/7)
Therefore probability that the next one she draws is pink = 4/7
Option (B)
Question: In a race, the odds in favour of cars P, Q, R, S are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find the probability that one of them wins the race.
A.9/17
B.114/121
C.319/420
D.27/111
Answer: C.319/420
Explanation: P(P) = 1/4, P(Q) = 1/5, P(R) = 1/6 and P(S) = 1/7.
All the events are mutually exclusive and hence,
the required probability:
= P(P) + P(Q) + P(R) + P(S)
= 1/4 + 1/5 + 1/6 + 1/7
= 319/420
ANSWER:C
Question: At a game of billiards, A can give B 15 points in 60 & A can give C 20 points in 60. How many points can B give C in a game of 90?
A.30 points
B.20 points
C.10 points
D.5 points
Answer: C.10 points
Explanation: 10 points
ANSWER:C
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 20 km, if the person completes half of the distance by walking and the other half by running?
A.2.75
B.3.25
C.3.75
D.4.25
Answer: C.3.75
Explanation: time = 10/4 + 10/8 = 30/8 = 3.75 hours
The answer is C.
Question: If a man's rate with the current is 15 km/hr and the rate of the current is 11⁄2 km/hr, then his rate against the current is
A.12 km/hr
B.22 km/hr
C.23 km/hr
D.28 km/hr
Answer: A.12 km/hr
Explanation: Speed downstream = 15 km/hr
Rate of the current= 11⁄2 km/hr
Speed in still water = 15 - 11⁄2 = 131⁄2 km/hr
Rate against the current = 131⁄2 km/hr - 11⁄2 = 12 km/hr
Answer is A
Question: What approximate value should come in place of the question mark (?) in the following equation?47.05 Ã— 8.65 â€“ 25.22 Ã— 6.4 = (28 + ?) Ã— 5
A.28.1149
B.24.1149
C.21.1149
D.22.1149
Answer: C.21.1149
Explanation: Solve using approximation
Answer C
Question: A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
A.10,700
B.10,800
C.10,900
D.11,000
Answer: D.11,000
Explanation: population that is 10% greater than the population of any other district..
11000.. 10% of 11000 = 1100.. so the next population will be 12100..
10*12,100 + 11000 = 132000. D
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.162. Find the unknown rate of two blankets?
A.420
B.550
C.490
D.570
Answer: D.570
Explanation: 10 * 162 = 1620
3 * 100 + 5 * 150 = 1050
1620 – 1050 = 570
Answer:D
Question: If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest?
A.The average (arithmetic mean) of set S
B.The median of set S
C.The mode of set S
D.The range of set S
Answer: A.The average (arithmetic mean) of set S
Explanation: Time consuming question...
A) 99, 100, 100, 105, 106, 116, 123 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 123 -99 = 24.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n
=> sq root (64+49+49+4+1+676)/7
= sq rt ( 893/7)
= sq rt ( 127) < 100
Answer: option A is correct answer..
Question: On thrusday mabel handled 90 transactions. anthony handled 10 % more transaction than mabel, cal handled 2/3rds of the transactions that anthony handled and jade handled 16 more transaction than cal. how much transaction did jade handled?
A.92
B.80
C.72
D.82
Answer: D.82
Explanation: Mabel handled 90 transaction, anthony 10 % more transaction the mabel. anthony = 90+90 * 10%, = 90 + 90 * 0.10 , = 90 + 9, =99, cal handled 2/3rds than anthony handled, cal = 2/3 * 99=66, jade handled 16 more than cal. jade = 66 + 16= 82, jade handled = 82 tranasactions.
correct answer: (D)
Question: Which of the following statements is equivalent to 8+2X<18−6X<23+2X8+2X<18−6X<23+2X?
A.4/5 < X < 2.5.
B.4/5 < X < 8/5.
C.-5/8 < X < 5/4.
D.2.5 < X < 3.5.
Answer: C.-5/8 < X < 5/4.
Explanation: 8+2X<18−6X<23+2X
8<18-8x<23 (add -2x on all sides)
-10<-8x<5
10>8x>-5 (multiply by -1 on all sides)
5/4>x>-5/8
C is the answer
Question: Two numbers are in ratio 4:5 and their LCM is 180. The smaller number is
A.9
B.15
C.36
D.45
Answer: C.36
Explanation: Solution: Let two numbers be 4x and 5x;
their LCM = 180 and HCF = x; Now,
1st number * 2nd number = LCM*HCF
Or, 4x*5x = 180*x;
Or, 20x = 180;
Or, x = 9;
then, the smaller number = 4*9 = 36.
Answer: Option C
Question: A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?
A.700
B.300
C.200
D.500
Answer: A.700
Explanation: sell 40% oranges and 420 oranges remaining
=>60% of oranges = 420
total oranges * 60/100 = 420
total oranges = 420*100/60 = 700
ANSWER A
Question: A can do a piece of work in 4 hours. B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A.10 hr
B.12 hr
C.15 hr
D.13 hr
Answer: B.12 hr
Explanation: A's 1 hour work = 1/4
B+C 1 hour work = 1/3
A+C 1 hour work = 1/2
A+B+C 1 hour work = 1/4 + 1/3 = 7/12
B's 1 hour work = 7/12 - 1/2 = 1/12
B alone will take 12 hours to do the work
Answer is B
Question: x+(1/x) = 2 find x^2 + (1/x^2)
A.2
B.3.25
C.4.25
D.5.25
Answer: A.2
Explanation: squaring on both sides (x+1/x)^2=2^2
x^2+1/X^2=4-2
x^2+1/X^2=2
ANSWER:A
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 70/kg. how much did a kg of coffee cost in june ?
A.70
B.60
C.80
D.100
Answer: A.70
Explanation: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (700gm) of tea and 1/2 kg (700gm) of coffee (equal quantities) = 70
1.2x(1/2) + 0.8x(1/2) = 70
=> x =70
Thus proved...option A.
Question: A man's age is 125% of what it was 10 years ago, but 83 1/3%
of what it will be after 10 years. What is his present age?
A.50
B.70
C.80
D.55
Answer: A.50
Explanation: 125x/100 = x + 10
x = 40
present age = x + 10 =40+10 = 50
ANSWER A
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 80 inches. Find b.
A.8
B.16
C.24
D.32
Answer: B.16
Explanation: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 80 (2^4*5), sob=2^4 or 2^4*5 (16 or 80).
Combining 2 premises shows the answer is B(16).
Question: For an upcoming charity event, a male vocalist has agreed to sing 3 out of 8 “old songs” and 4 out of 7 “new songs.” How many ways can the singer make his selection?
A.25
B.50
C.150
D.147
Answer: D.147
Explanation: =8C6*7C4
=8*7/4*7*6/4
=7*7*3
=147
Ans = D
Question: Kim bought a total of $4.65 worth of postage stamps in four denominations. If she bought an equal number of 10-cent and 25-cent stamps and twice as many 20-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?
A.5
B.10
C.75
D.90
Answer: D.90
Explanation: Let:
# of 10 and 25 cents stamps = n
# of 20 cent stamps = 2n
# of 1 cent stamps = m
Therefore:
10n + 25n + 20(2n) + m = 465 cents
75n + m = 465
Forleastnumber of 1 cents stamps, maximize 50n. Hence,
75*5 + m = 465
m = 90 i.e. 90 stamps 1 cents each
Answer: D
Question: The average earning of a person for the first four days of a week is Rs 18 and for the last four days is Rs 22. If he earns Rs 20 on the fourth day, his average earning for the whole week is?
A.Rs 18.95
B.Rs 16
C.Rs 20
D.Rs 25.71
Answer: C.Rs 20
Explanation: Total earning for the week
= Rs (4 × 18 + 4 × 22 - 20) = Rs 140
Average earning = Rs 140/7 = Rs 20.
ANSWER:C