RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If n = 3p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
A. Two
B. Three
C. Four
D. Six
Answer: B. Three
Explanation: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is B.
Question: If P= {multiplies of 3 between 1 and 20}, Q = {even natural number upto 15} , find the intersection of the two given set P and Q.
A.P∪Q= {6,12}
B.P∩Q= {6,12}
C.P∩Q= {10,12}
D.P∪Q= {10,12}
Answer: B.P∩Q= {6,12}
Explanation: P= {3,6,9,12,15,18}, Q= {2,4,6,8,10,12,14}
Intersection of P and Q is the largest set containing only those elements which are common to both the given sets P and Q. correct answer : (B) P∩Q= {6,12}
Question: 46080, 3840, 384, 48, 8, 2, ?
A.1
B.1⁄64
C.1⁄8
D.None of these
Answer: A.1
Explanation: Explanation :
46080 ÷ 12 = 3840
3840 ÷ 10 = 384
384 ÷ 8 = 48
48 ÷ 6 = 8
8 ÷ 4 = 2
2 ÷ 2 = 1
Answer : Option A
Question: A, B and C rents a pasture for Rs.950. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
A.295
B.199
C.676
D.156
Answer: A.295
Explanation: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 950= 295
Answer: A
Question: In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows.
A.12
B.14
C.16
D.18
Answer: B.14
Explanation: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 28 + 2(c + d)
=> d + 2c = 14 + c + d
=> 2c = 14 + c
=> c = 14
i.e., total number of cows = 14
Answer is B.
Question: A box contains 2 white balls and 4 red ball. in how many ways can 3 balls be drawn from the box , if at least one black ball is to be included i the draw ?
A.32
B.48
C.64
D.96
Answer: C.64
Explanation: Solution
We have many (1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
So, Required number of ways = (3 C 1 × 6 C 2) + (3 C 2 × 6 C 1) + (3 C 3)
= ( 3x 6x 5/2x1) + ( 3x 2/2x1x 6) + 1 = (45 + 18 + 1) = 64.
Answer C
Question: An egg seller sells his eggs only in the packs of 3 eggs, 6 eggs, 9 eggs, 12 eggs etc., but the rate is not necessarily uniform. One day Raju (which is not the same egg seller) purchased at the rate of 3 eggs for a rupee and the next hour he purchased equal number of eggs at the rate of 6 eggs for a rupee. Next day he sold all the eggs at the rate of 9 eggs for Rs. 2. What is his percentage profit or loss?
A.10% loss
B.11.11% loss
C.3% loss
D.2.5 % profit
Answer: B.11.11% loss
Explanation: Solution: CP of one egg in first case = 1/3 = 33.33 paise
CP of one egg in second case = 1/6 = 16.66 paise
Average CP = (33.33 +16.66)/2 = 25 paise
Selling price of 9 eggs = Rs. 2
SP of one egg = 200/9
Profit or loss = [(25 - (200/9))*100]/25
Profit or loss = -11.11. (loss)
Answer: Option B
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.50
B.77
C.55
D.43
Answer: A.50
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Question: A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work?
A.10.9
B.10.5
C.10.8
D.10.1
Answer: B.10.5
Explanation: Ans: Let us assume A can do 2 units of work each day, then B can do only 1 unit a day. If both can complete the work in 7 days, total work done by these two togeter = (2 + 1 ) x 7 = 21 units
If these 21 units to be done by A alone, then he will take 21 / 2 = 10.5 days.
\Answer:B
Question: In a public show 50 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
A.100
B.110
C.120
D.300
Answer: D.300
Explanation: 50 % of 600
= 50/100 × 600
= 300
Therefore, the number of vacant seats = 600 - 300 = 300.
Answer:D
Question: Which of the following numbers is not prime?
A.5-3
B.11+12
C.31-2
D.4+6
Answer: D.4+6
Explanation: 2 can be factored out of both 4 and 6. --> 4+6= 2*(2+3). The correct answer is D.
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
A.230 m
B.245 m
C.260 m
D.275 m
Answer: A.230 m
Explanation: Relative speed = (120 + 80) km/hr
= 200 x 5/18
= 500/9 m/sec
Then, (x+270)/9 = 500/9
--> x + 270 = 500
--> x = 230.
Answer : A.
Question: {130, 280, 250, n}
Which of the following could be the median of the 4 integers listed above?
I. 160
II. 210
III. 250
A.I only
B.II only
C.I and II only
D.II and III only
Answer: D.II and III only
Explanation: If 160 is the median, (n+250) / 2 = 160. Then n = 70. But n < 130, so 160 can not be the median.
If 210 is the median, (n+250) / 2 = 210. Then n = 170. Thus 210 can be the median.
If 250 is the median, (n+250) / 2 = 250. Then n = 250. Thus 250 can be the median.
The answer is D.
Question: What will be the acute angle between hands of a clock at 2 : 30?
A.105°
B.115°
C.95°
D.135°
Answer: A.105°
Explanation: At 2'O Clock, Minute Hand will be 10 × 6 = 60°
behind the Hour Hand.
In 30 minutes, Minute Hand will gain (51⁄2)° × 30
= 150 + 15 = 165°
∴ Angle between Hour Hand and Minute Hand
= 165 – 60 = 105°
Answer A
Question: A box contains SEVEN bulbs out of which 4 are defective. If THREE bulbs are chosen at random, find the probability that atleast one bulb is good
A.5/38
B.4/39
C.4/31
D.4/35
Answer: D.4/35
Explanation: Required probability = 1-4C3/7C3=1 - 4/35 = 31/35.Answer:D
Question: A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
A.8 km/hr, 1 km/hr
B.5 km/hr, 4 km/hr
C.1 km/hr, 6 km/hr
D.2 km/hr, 1 km/hr
Answer: A.8 km/hr, 1 km/hr
Explanation: Downstream speed=72km/8hrs
=9kmph
upstream speed=84km/12hrs
=7kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(9+7)/2kmph
=8kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(9-7)/2kmph
=1kmph
ans is 8km/hr,1km/hr
ANSWER:A
Question: If a^2 = b^2, which of the following must be true?
A.|a| = |b|
B.a = −b
C.a = |b|
D.a = −|b|
Answer: A.|a| = |b|
Explanation: Since a^2=b^2 we have 0=a^2 – b^2 =(a-b)*(a+b). So a=b or a=-b.
So only (E) and only (B) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (D) tells us that k should be less than or equal to 0.
So neither (C) nor (D) cannot be the answer.
The answer is, therefore, (A).
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A
A.Rs.300
B.Rs.56
C.Rs.100
D.Rs. 240
Answer: D.Rs. 240
Explanation: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 =Rs. 240
ANSWER:D
Question: 90 + 5 * 12 / (180/3) = ?
A.23
B.78
C.27
D.91
Answer: D.91
Explanation: Explanation:
90 + 5 * 12 / (180/3) = 90 + 5 * 12 / (60)
= 90 + (5 * 12)/60 = 90 + 1 = 91.
Answer:D
Question: One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
A.4%
B.5%
C.6%
D.11%
Answer: A.4%
Explanation: 1/6 of the switches are defective.
The defective switches that are not rejected are 1/5*1/6 = 1/30 = 4/120 of all switches.
The non defective switches that are sold are 5/6*19/20 = 95/120 of all switches.
The percent of switches sold that are defective is 4/99 which is about 4%.
The answer is A.
Question: Which one the following fractions has the exact division of nine?
A.47776/9
B.37777/9
C.87777/9
D.57777/9
Answer: C.87777/9
Explanation: Numerator for all option is 9. If the numerator value digits are added together and forms the number equal to 9, then it is exact division of 9. So Option (C) 8+7+7+7+7 = 36= 3+6 = 9. Answer (C).
Question: The 5 th term and 21 st term of a series in A.P are 10 and 42 respectively. Find the 31 st term.
A.50
B.55
C.65
D.62
Answer: D.62
Explanation: a + 4d = 10 ………….. (1)
a + 20d = 42 ………….. (2)
Eqn (2) – Eqn (1) gives 16d = 32 , d = 2
Substituting d =2 in either (1) or (2), a = 2.
31 st term = a + 30d = 2 + 30*2 = 62
ANSWER:D
Question: . A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
A.21 years
B.22 years
C.23 years
D.24 years
Answer: B.22 years
Explanation: Explanation:
Let's Son age is x, then Father age is x+24.
=> 2(x+2) = (x+24+2)
=> 2x+4 = x+26
=> x = 22 years
Answer: Option B
Question: (xn - an) is completely divisible by (x - a), when
A.n is any natural number
B.n is an even natural number
C.n is and odd natural number
D.n is prime
Answer: A.n is any natural number
Explanation: For every natural number n, (xn - an) is completely divisible by (x - a).
A)
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution?
A.A)5.8
B.B)1.3
C.C)9.6
D.D)12.5
Answer: A.A)5.8
Explanation: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=15/100
200+20x=300+3x
17x = 100
x = 5.8
Answer is A
Question: If a coin is tossed 6 times what is the probability that it will land either heads 6 times or tails 6 times?
A.1/4
B.1/8
C.1/16
D.1/32
Answer: D.1/32
Explanation: The probability of 6 heads is (1/2)^6 = 1/64
The probability of 6 tails is (1/2)^6 = 1/64
The probability of 6 heads or 6 tails is 1/64 + 1/64 = 1/32
The answer is D.
Question: The ages of two persons differ by 16 years. 7 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
A.15
B.31
C.25
D.30
Answer: B.31
Explanation: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 7) = 3 (x-16-7)
=> x � 7 = 3x � 69
=> 2x = 62
=> x = 62/2 = 31
Answer: Option B
Question: The perimeter of a square is equal to the radius of a circle having area 39424 sq cm, what is the area of square?
A.1225 sq cm
B.441 sq cm
C.784 sq cm
D.Can’t say
Answer: C.784 sq cm
Explanation: Let the side of square =a cm and radius of circle=r cm
Given, 4a= r
Also Area of square= Pi*r^2= 39424, r^2=12544 or r=112
So a= r/4= 112/4=28
Hence Area of square=a^2=28^2=784 cm^2
ANSWER:C
Question: The sum of 11 hours 45 minutes and 2 hours 15 minutes is approximately what percent of a day?
A. approx 54%
B. approx 58%
C. approx 74%
D. 28%
Answer: B. approx 58%
Explanation: Since the question is asking for an approximate percentage
11:45+2:15 ~ 14 hours
% of day = 14*100/24 ~ 58%
Answer is B.
Question: How much time will take for an amount of Rs. 450 to yield Rs. 78 as interest at 4.5% per annum of simple interest?
A.8 years
B.3 years 10 months
C.3 years
D.9 years
Answer: B.3 years 10 months
Explanation: Time = (100 * 78) / (450 * 4.5)
= 3 years 10 months
Answer: B
Question: The average weight of 36 men is 50 kg. It was found later that the figure of 37 kg was misread as 73 kg. What is the correct average?
A.49 kg
B.51 kg
C.50.5 kg
D.51.5 kg
Answer: A.49 kg
Explanation: Correct average = [( 50 x 36) - 73 + 37 )]/36 = 1764/36 = 49 kg.
ANSWER:A
Question: A snooker tournament charges $45.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 300 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
A.212
B.240
C.220
D.230
Answer: C.220
Explanation: let no of sits in vip enclosure is x then x*45 +15( 300-x) =7500 or 30x = 7500 -4500 , x = 3000/30 =100
vip =100 general 220
C
Question: The average of first 10 odd numbers is?
A.11
B.10
C.87
D.26
Answer: B.10
Explanation: Sum of 10 odd no.
= 100
Average = 100/10
= 10
Answer:B
Question: In a village of 100 households, 80 have at least one DVD player, 90 have at least one cell phone, and 65 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:
A.65
B.55
C.45
D.30
Answer: D.30
Explanation: Am I missing something here??? it seems straightforward......
The obvious maximum that have all 3 is 65, because you are limited by the SMALLEST number.
The minimum is simply the sum of the max of each people who DONT have the product, so:
100-90 = 10 don't have Cell
100-80 = 20 don't have DVD
and 100-65 = 35 don't have MP3
SO a total of 10+20+35 = 65 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-65 = 35.
65-35 = 30
D
Question: 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds
A.11:9
B.13:9
C.17:9
D.21:9
Answer: A.11:9
Explanation: Explanation:
We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
So ratio of their speed = 110:90 = 11:9
Option A
Question: If 2 persons can do 2 times of a particular work in 2 days, then, 7 persons can do 7 times of that work in?
A.2 days
B.4 days
C.6 days
D.7 days
Answer: A.2 days
Explanation: That is, 1 person can do one time of the work in 2 days.
Therefore, 7 persons can do 7 times work in the same 2 days itself
A)
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical A required to keep the reaction rate unchanged.
A.100 % decrease
B.50% decrease
C.40% decrease
D.40% increase
Answer: C.40% decrease
Explanation: r = k A^2 / B for some constant k<>0
(Question should also give B<>0)
So we have
r1 = k A1^2 / B1
r2 = k A2^2 / B2
r1 = r2
B2 = (1+100%)B1 = 2B1
k A1^2 / B1 = k A2^2 / B2
A1^2 / B1 = A2^2 / 2B1
2A1^2 = A2^2
(sqrt(2)A1)^2 = A2^2
A1,A2>0
A2 = sqrt(2) * A1
A2 = (1 + 41.4%) * A1
About 40% increase
ANSWER:C
Question: One-fourth of the boys and three-eighth of the girls in a school participated in the sports. What fractional part of the total student population of the school participated in the annual sports ?
A.4/12
B.5/8
C.8/12
D.Data inadequate
Answer: D.Data inadequate
Explanation: Explanation:
Boys and girls ratio was not given.
Correct Option:D
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
A.150
B.330
C.277
D.279
Answer: A.150
Explanation: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer:A
Question: A room 13 m 47 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
A.116636
B.116406
C.116647
D.116291
Answer: D.116291
Explanation: Explanation:
Area of the room = (1347 x 777) cm2.
Size of largest square tile = H.C.F. of 1347 cm and 777 cm = 3 cm.
Area of 1 tile = (3 x 3) cm2.
Number of tiles required =(1347×777)/(3×3)=116291
Answer: Option D
Question: For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”3?
A.5
B.3
C.2
D.1
Answer: A.5
Explanation: 4”3= 9 - 4=5
Answer: A
Question: The ratio of pens to pencils is 5 to 6. There are 8 more pencils than pens. How many pencils are there?
A.30
B.32
C.48
D.55
Answer: C.48
Explanation: Let x equal the number of pens, and y the number of pencils.
Then, x = 5/6y.
We also know that x = y - 8. And so, we can substitute:
y - 8 = 5/6y
So to isolate y, we get:
1/6y = 8
And therefore:
y = 48
Answer: C
Question: Find √? /15= 4 ?
A.76
B.5776
C.304
D.3600
Answer: D.3600
Explanation: Answer
Let √N/15= 4
Then √N = 15 x 4 = 60
∴ N = 60 x 60 = 3600.
Correct Option: D
Question: We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 10, and the difference between the total number of strawberries and the total number of blueberries would increase by 50. Each blue box contains how many blueberries?
A.10
B.15
C.20
D.25
Answer: C.20
Explanation: Let x be the number of blueberries in each blue box.
Then there are x+10 strawberries in each red box.
x+(x+10)=50
x = 20
The answer is C.
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 7?
A. 48 kmph
A.33
B.54
C.28
D.27
Answer: B.54
Explanation: Let the distances between city A to B and B to C be 2x km and 7x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (7x)/60 = (6x + 14x)/120 = 20x/120 = x/6 Average speed = (2x + 7x)/(x/6) = 54 kmph.
Answer: B
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 3/5 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?
A.30
B.45
C.60
D.150
Answer: D.150
Explanation: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 30. These are (3/5) of total igneous rocks.
(3/5)*Total igneous rocks = 30
Total igneous rocks = 30 * (5/3) = 50
Total sedimentary rocks = 2*Total igneous rocks = 2*50 = 100
Total number of rocks = 50 + 100 = 150
Answer (D)
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
A.8876
B.2765
C.6000
D.1298
Answer: C.6000
Explanation: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
Answer:C
Question: If air is called green , green is called blue, blue is called tangerine, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?
A.Blue
B.Sky
C.Water
D.Tangerine
Answer: D.Tangerine
Explanation: Explanation:The colour of clear sky is 'blue' and as given, 'blue' is called 'tangerine'.So, the colour of clear sky is 'tangerine'.Answer: D
Question: Donovan took a math test and got 35 correct and 13 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
A.57.78%
B.67.78%
C.72.92%
D.47.78%
Answer: C.72.92%
Explanation: 35 correct our of 48 total (35+13)
35/48
correct answer C
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
A.11
B.18
C.92
D.27
Answer: B.18
Explanation: Explanation:
=> 2l + 2b = 5b
=> 3b = 2l
b=(2/3)l
Then, Area = 216 cm2
=> l x b = 216
=> l x (2/3)l =216
=> l2 = 324
l = 18 cm.
Answer: B) 18
Question: 14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
A.7
B.9
C.8
D.5
Answer: A.7
Explanation: x + y = 25
xy = 144
(x- y)2 = (x + y)2 â€“ 4xy
(x- y)2 = 625 â€“ 576 => (x â€“ y) = 7
ANSWER: A
Question: How long will it take a train travelling at 98kmph to pass an electric pole if the train is 140 m long
A.6.15
B.5.15
C.3.15
D.1.15
Answer: B.5.15
Explanation: Sol.
Speed = [ 98x5/18] m/sec =27.2 m / sec.
Time taken = (140/27.2)sec =5.15 sec.
Answer B
Question: A third of Arun’s marks in mathematics exceeds a half of his marks in English by 80.if he got 240 marks In two subjects together how many marks did he got in English?
A.180,60
B.150,80
C.140,70
D.120,90
Answer: A.180,60
Explanation: Let Arun’s marks in mathematics and english be x and y
Then 1/3x-1/2y=30
2x-3y=180……>(1)
x+y=240…….>(2)
solving (1) and (2)
x=180
and y=60
Answer is A.
Question: 15 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required?
A.10days
B.11days
C.9days
D.8days
Answer: A.10days
Explanation: That is, 1 work done = 15 × 8 × 10
Then, 12 8 × 10 = ? × 15 × 8
? (i.e. No. of men required) = 15 × 8 × 10/15× 8 = 10 days
A)
Question: How many integers between 4000 and 5000 that have distinct digits and increase from left to right ?
A.10
B.48
C.60
D.20
Answer: D.20
Explanation: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
445_ --> 4
446_ --> 3
447_ --> 2
448_ --> 1
456_ --> 3
457_ --> 2
458_ --> 1
467_ --> 2
468_ --> 1
478_ --> 1
Number of integers =20
D
Question: A certain rectangular window is two times as long as it is wide. If its perimeter is 30 feet, what are its dimensions in terms of length by width?
A.12 by 2
B.11 by 3
C.10.5 by 3.5
D.10 by 5
Answer: D.10 by 5
Explanation: 2x+2y=30
x+y=15
x+2x=15
3x=15
x=5
Answer D
Question: 125 students of a school are about embarking on a trip. What is the least number of vans needed to convey them given that each van will only take 10 students each?
A.12
B.11
C.13
D.18
Answer: B.11
Explanation: To find the number of vans, we divide 125 by 10.
125/10 = 12 and remainder = 5
So 10 vans are needed to transport 125 students, and 1 van is needed to transport the 5 remaining students. A total of 11 vans are needed.
correct answer B
Question: Convert 0.36 in to a vulgar fraction ?
A.18/50
B.16/50
C.17/50
D.9/25
Answer: D.9/25
Explanation: Answer
0.36 = 36/100 = 9/25
Correct Option: D
Question: A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 60. When the number of legs was counted, the number totaled up to 160. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.
A.16
B.20
C.24
D.28
Answer: B.20
Explanation: Let x be the number of chickens.
Then 60-x is the number of pigs.
2x+4(60-x)=160
2x=80
x=40 (chickens)
60-x=20 (pigs)
There are 40-20=20 more chickens on the farm.
The answer is B.
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 30 times, A has killed:
A.60 birds
B.72 birds
C.33 birds
D.80 birds
Answer: C.33 birds
Explanation: Let the total number of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B =(3/8)x
Killing shots by A =(1/3)of	(5/8)x=(5/24)x
Shots missed by B =(1/2) of (3/8)x	=(3/16)x
3x/16= 30 or x =(30 x 16)/3= 160.
Birds killed by A =(5x/24)	=(5/24*160)= 33.
Answer is C.
Question: Each of four different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
A.1/8
B.1/6
C.1/4
D.3/8
Answer: C.1/4
Explanation: Total # of ways to assign the keys to the locks is 4!4!.
C^24 to choose which 2 keys will fit. Other 2 keys can be arranged only one way.
So P=C^24/4!=14
Answer: C.