RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 22 square meters. What is the area that is covered with three layers of rug ?
A.18 square meters
B.20 square meters
C.24 square meters
D.19 square meters
Answer: D.19 square meters
Explanation: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}
140 = 200 - 22 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 19.
Answer: D.
Question: How many bricks, each measuring 80 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
A.6400
B.2000
C.5500
D.7400
Answer: B.2000
Explanation: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (80 x 11.25 x 6) = 2000
ANSWER:B
Question: A scale 6 ft. 8 inches long is divided into 4 equal parts. Find the length of each part.
A.20 inches
B.77 inches
C.66 inches
D.97 inches
Answer: A.20 inches
Explanation: Explanation:
Total length of scale in inches = (6*12) + 8 = 80 inches
Length of each of the 4 parts = 80/4 = 20 inches
ANSWER:A
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 14 multiples of 14, how many multiples of 7 are there in Q?
A.26
B.27
C.28
D.29
Answer: B.27
Explanation: Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 14+13 = 27.
The answer is B.
Question: What will be the difference in simple and compound interest on 4000 after three years at the rate of 10 percent per annum?
A.160
B.42
C.62
D.124
Answer: D.124
Explanation: For 3 years:
Diff.=Sum×(rate)2(300+rate)/(100)3
= 4000×10×10×310/100×100×100 = 124
Answer D
Question: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 16 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
A.6 2/3
B.15
C.20
D.25
Answer: B.15
Explanation: Here is how I did it:
The cyclist travels 16 miles in 60 mins, so in 5 mins he will travel [(16*5)/60] miles, which equals 4/3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 4/3 miles, he will take [(60*4/3)/4] = 20 mins.
hence 20-5=15 mins
B
Question: The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is?
A.551 cm
B.151 cm
C.156 cm
D.165 cm
Answer: B.151 cm
Explanation: Total height
= 150 * 50 = 7500 cm.
New average
= [7500 - 5 * 146 + 5 * 156 ] / 50
= 151 cm.
Answer: B
Question: A man can do a piece of work in 10days, but with the help of his son, he can finish it in 5days. In what time can the son do it alone?
A.5
B.8
C.7
D.10
Answer: D.10
Explanation: Son's 1day work = 1/5 - 1/10 = 1/10
Son alone can do the work in 10days
Answer is D
Question: Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length Q of time will elapse before they chime together again?
A.2 hr. and 24 min.
B.4 hr. and 48 min.
C.1 hr. and 36 min.
D.5 hr.
Answer: B.4 hr. and 48 min.
Explanation: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) Q= 288 => 4 hours 48 mins.B
Question: Marks of a student were wrongly entered in computer as 83, actual marks of that student were 63. Due to this mistake average marks of whole class got increased by half (1/2). Find the total number of students in that class.
A.25
B.30
C.35
D.40
Answer: D.40
Explanation: Explanation:
Suppose total number of students are = X
Totalincrease=x∗1/2=x/2
=>x/2=83−63=20
=>x=40
Answer: Option D
Question: A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 62. If the marks secured by Reema was written as 50 instead of 85 then find the correct average marks up to two decimal places.
A.63
B.74.31
C.72.43
D.73.43
Answer: A.63
Explanation: Total marks = 35 x 62 =2170
Corrected total marks = 2170 - 50 + 85 =2205
Correct Average = 2205/35 = 63
Answer : A
Question: Find the largest number that will divide 43,91,183 so as to leave the same reminder in each case.
A.5
B.4
C.26
D.35
Answer: B.4
Explanation: Explanation:
Required Number=H.C.F of(91-43),(183-91) and (183-43)
H.C.F of 48,92 and 140=4
Answer:B
Question: Marla is hanging a banner diagonally across a rectangular room. The length of the room is 2 feet shorter than its width. If the total area of the room is 120 square feet, what is the length of the banner (in feet)?
A.Between 13 and 14
B.Between 14 and 15
C.Between 15 and 16
D.Between 16 and 17
Answer: C.Between 15 and 16
Explanation: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have
x(x - 2) = 120. By putting the equation in standard form, we get x^2-2x-120=0. By using the quadratic formula, we get roots of -10 and 12. We know that x is the width, and x-2 is the length, so by using the roots, we get 12 as the width (x), and 10 as the length (x-2).
Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=12^2+10^2
=144+100
=244
The square root of 244 is less than 16, since 16^2 = 256. Going down a number, we can compute 15^2 = 225 < 224. Therefore, the length of the diagonal must be between 15 and 16.
The correct answer is C.
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 10 km per hour and the level part at the rate of 15 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 15 km per hour for the entire route?
A.20
B.25
C.30
D.35
Answer: C.30
Explanation: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 15 km/hour
3D / (D/10 + D/15 + D/V) = 15
1/5 = 1/10 + 1/15 + 1/V
1/V = 1/30 and so V = 30 km/h
The answer is C.
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 9),
what is the maximum possible area of C?
A. 6
B. 9
C. 24
D. 32
Answer: C. 24
Explanation: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
C
Question: A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 25 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
A.5:00
B.5:34
C.5:42
D.6:00
Answer: C.5:42
Explanation: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15 = 45 minutes have passed.
C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60 = 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.
C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.
C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.
C4 loses 10 minutes every hour.
In 6 hours, C4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 5:42pm.
The correct answer is C.
Question: If HCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number?
A.33
B.36
C.38
D.42
Answer: A.33
Explanation: Let the numbers be 11a and 11b
11a × 11b = 363
=> ab = 3
co-primes with product 3 are (1, 3)
Hence the numbers with HCF 11 and product 363
= (11 × 1, 11 × 3)
= (11, 33)
Hence, numbers are 11 and 33
The greater number =
A)
Question: A man can row with a speed of 10 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is?
A.10 kmph
B.5 kmph
C.40 kmph
D.22 kmph
Answer: C.40 kmph
Explanation: M = 10
S = 30
DS = 10 + 30 = 40
ANSWER:C
Question: Find the ones digit of 73^356
A.1
B.5
C.6
D.7
Answer: A.1
Explanation: The units digit of 73^356 will be the same as the units digit of 3^356.
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 356=356+0=(multiple of 4)+0, then the units digit of 3^356 will be thus 1.
Answer: A.
Question: 10^25 - 250 is divisible by all of the following except:
A.A.11
B.B.15
C.C.5
D.D.6
Answer: A.A.11
Explanation: The last three digits ( 1000 - 250 ) 750
750 is divisible by 15,3,6,5
750 is not evenly divisible by 11 so the answer is A) 11
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
A.600 m
B.300 m
C.400 m
D.700 m
Answer: A.600 m
Explanation: A
600 m
Distance covered by Amar = 18/4.8 (1.6km) = 3/8(1600) = 600 m
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years?
A.Rs.3129
B.Rs.3120
C.Rs.3108
D.Rs.3106
Answer: B.Rs.3120
Explanation: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 =
Rs.3120
Answer:B
Question: A person travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the total distane
A.3 km
B.4 km
C.6 km
D.9 km
Answer: A.3 km
Explanation: Explanation:
Let the distance be 3x km,
then,
x/3+x/4+x/5=47/60
47x /60= 47 /60
x=1
So total distance = 3*1 = 3 Km
Option A
Question: A can run 4 times as fast as B and gives B a start of 66 m. How long should the race course be so that A and B might reach in the same time?
A.88 m
B.60 m
C.80 m
D.65 m
Answer: A.88 m
Explanation: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 66m he gains 66*(4/3)
I.e 88m
ANSWER:A
Question: The length of a side of a hexagon is 8 inches. What is the perimeter?
A.40
B.44
C.48
D.50
Answer: C.48
Explanation: Hexagon. It means 6 equal sides.
p = 6(8) = 48 inches
Answer C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 12 sec, then the speed of each train is?
A.22
B.77
C.36
D.90
Answer: D.90
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/12 => x = 25
Speed of each train = 10 m/sec.
= 25 * 18/5 =- 90 km/hr.
Answer: D
Question: Ms. Lopez deposits $ 150 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
A.$118.00
B.$120.00
C.$181.15
D.$122.00
Answer: C.$181.15
Explanation: Using Formula - A = P(1+r/n)^nt
Given
P=150
n=2
t=1
r=0.2
Substituting value in formula
A = 150(1+0.2/2)^2
A= 181.15$=C
Question: How many four digit numbers divisible by 4 can be made with digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: A number is divisible by 4 if the last 2 numbers are divisible by 4 (divisible by 2 twice)
Ending can be
12
24
32
42
52
Case: Ending with 12,24,32,42,54
First digit - 3 choices
Second digit - 2 choices
Third digit - 1 choice
Fourth digit - 1 choice
6 possible choices for each ending (e.g. 3412,3512, 3212 ,4512 ,5312 ,5412)
Total number of 4 digit numbers divisible by 4 = 6 * 5 = 30
ANSWER:C
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
A.10 kmph
B.67 kmph
C.15 kmph
D.88 kmph
Answer: C.15 kmph
Explanation: Speed of the boat in still water
= (60+90)/2
= 75 kmph. Speed of the stream
= (90-60)/2
= 15 kmph.
Answer:C
Question: If 100!/30^n is an integer, which of the following is the greatest possible value of n?
A.28
B.24
C.20
D.15
Answer: B.24
Explanation: 30^n = 2^n * 3^n * 5^n
100! has 97 2's, 48 3's and 24 5's
Since each of 2, 3 and 5 is required to form 30 and there are only 24 5's there can only be 24 30's in 100!
Answer: B
Question: Find the average of all numbers between 6 and 36 which are divisible by 7
A.20
B.15
C.25
D.30
Answer: B.15
Explanation: Explanation:
Average=(7+14+21+28+35)/7=105 / 7=15
Option B
Question: A batch of widgets costs p + 8 dollars for a company to produce and each batch sells for p(7 – p) dollars. For which of the following values of p does the company make a profit?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: to make profit, selling price should be greater than cost price
p(7-p) - p-8 >0
=> p^2-6*p+8<0
hence p=3
A
Question: Find large number from below question The difference of two numbers is 2500. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
A.3345
B.1250
C.1540
D.2997
Answer: D.2997
Explanation: Let the smaller number be x. Then larger number = (x + 1365).
x + 2500= 6x + 15
5x = 2485
x = 497
Large number = 497+1365 = 2997
D
Question: The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres?
A.11
B.12
C.13
D.14
Answer: A.11
Explanation: Speed of the boat downstream = 90 + 18 = 108 kmph
= 108 * 5/18 = 30 m/s
Hence time taken to cover 330 m = 330/30 = 11 seconds.
Answer: A
Question: If p/q =4/5, then the value of 11/7 + {(2q - p) / (2q + p)} is ?
A.3 / 7
B.34
C.1
D.2
Answer: D.2
Explanation: Answer
Given Exp. = 11 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 11/7 + {2-p/q) / (2 + p/q)}
= 11/7 + {(2 - 4/5) / (2 + 4/5)}
= 11/7 + 6/14
= 11/7 + 3/7
=14/7
=2
Correct Option: D
Question: Two cubes of their volumes in the ratio 27 : 125. The ratio of their surface area is:
A.1.5:5
B.2:5
C.3:5
D.1:5
Answer: C.3:5
Explanation: The ratio of their surface area is
27 : 125
3 : 5
Answer is C.
Question: At a certain supplier, a machine of type A costs $21,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
A.$10,560
B.$11,200
C.$12,000
D.$12,800
Answer: A.$10,560
Explanation: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 42000 + (42000 - 20% of 42000) + 40% of (42000 - 20% of 42000)
= 55440
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 55440 = 10560
Hence, A.
Question: A lends Rs. 1500 to B and a certain sum to C at the same time at 8% per annum simple interest. If after 4 years, A altogether receives Rs. 1400 as interest from B and C, then the sum lent to C is
A.Rs.2875
B.Rs.1885
C.Rs.2245
D.Rs.2445
Answer: A.Rs.2875
Explanation: Explanation :
Let the sum lent to C be Rs. x
Simple Interest for Rs.1500 at 8% per annum for 4 years
+ Simple Interest for Rs.x at 8% per annum for 4 years = Rs.1400
⇒1500×8×4/100+ x × 8×4/100=1400
⇒480+32x/100=1400
⇒32x/100=920
⇒x=920×100/32=2875
Answer : Option A
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 22,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
A.1 million
B.1.25 million
C.10 million
D.12.9 million
Answer: D.12.9 million
Explanation: If you type that into the calculator, it results in 13.0 mil
[D], 12.9 mil, is the correct answer... see 2 posts above for quick approx method
Question: If x is an odd integer, which of the following must also be odd?
A.2x + 4
B.x + x
C.3x + 3
D.2x + x
Answer: D.2x + x
Explanation: Odd + odd = even
Odd + even = odd
Odd*odd = odd
Odd*even = even
On checking each option
A. 2x + 4
2x = even, 2 x + 4 = even + even = even.
B. x + x
Odd + odd = even. This will be even
C. 3x + 3
3x = odd, 3x + 3 = odd + odd = even
D. 2x + x
2x = even, 2x + x = even + odd = odd
E. x^2 + 1
x^2 = odd, x^2 + 1 = odd + odd = even
Correct option: D
Question: If x = (y)(y + 1) and y is a prime number less than 11, which of the following could not be the product of 2 consecutive integers?
A.5x
B.11x
C.13x
D.23x
Answer: D.23x
Explanation: Given y is a prime number less than 7
so y can be 2 3 5 7
x=y*(y+1)
so x can be 6 12 30 56
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 23x cannot be
E. 57x can be (56*57)
So answer option D.
Question: What is the remainder when 1003 * 1005 * 1007 is divided by 15
A.3
B.17
C.14
D.0
Answer: D.0
Explanation: 1003/15==> Remainder=13
1005/15==> Remainder=0
1007/15==> Remainder=2
13*0*2=0/15==> Remainder=0
Answer:D
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
A.250
B.203
C.200
D.195
Answer: D.195
Explanation: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER D
Question: A thief is noticed by a policeman from a distance of 500 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 12 km per hour respectively. What is the distance between them after 6 minutes?
A.150 m
B.200 m
C.300 m
D.100 m
Answer: C.300 m
Explanation: Relative speed of the thief and policeman = 12 - 10 = 2 km/hr.
Distance covered in 6 minutes = 2/60 * 6 = 1/5 km = 200 m.
Distance between the thief and policeman = 500 - 200 = 300 m
C
Question: Sum of even numbers between 15 and 25 is
A.70
B.80
C.130
D.100
Answer: D.100
Explanation: Explanation: 16 + 18 + .......24.
Taking 2 common we get = 2 ( 8 + 9 + 10 +.....+ 12)
Sum of n natural numbers upto 12
8 + 9 + 10 +.....+ 12 = (1 + 2 + 3 + ......+ 12) - ( 1 + 2 + 3 + ....+ 7)
By applying the formula for the first n natural numbers sum n(n+1)/2 we get, 12(12+1)/2−7(7+1)/2=50
So 16 + 18 + .......24 = 2 × 50 = 100
Correct Option: D
Question: If 25% of x is 5 less than 10% of 500, then x is?
A.188
B.180
C.156
D.840
Answer: B.180
Explanation: 25% of x = x/4 ; 10% of 500 = 10/100 * 500 = 50
Given that, x/4 = 50 - 5 => x/4 = 45 => x = 180.
Answer: B
Question: A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 30% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow
A.a) 2
B.b) 4.5
C.c) 0.69
D.d) 5.5
Answer: C.c) 0.69
Explanation: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).
Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.
Therefore 6k = 0.3 (11 + 4k)
=> k = 0.69
Therefore the plant grows by 0.69 feet every day.
Option (C)
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 8 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
A.26
B.32
C.43
D.60
Answer: B.32
Explanation: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 8.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 9, 26, 43, 60, 77,...
The answer is B.
Question: Presently the ratio between the ages of David and James is 3:2. after 8 years David will be 29. What is the present age of James?
A.24
B.23
C.14
D.21
Answer: C.14
Explanation: Let the present ages of David and James be 3x years and 2x years respectively
3x+8 = 29
3x = 21
x = 7
James's age = 2x =14 years
Answer is C
Question: A bookseller has two display windows. She plans to display 3 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
A.24
B.72
C.144
D.36
Answer: D.36
Explanation: The left window will have permutations of the 3 fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 6*6 = 36
Answer: D.
Question: Jim wishes to buy 3 gifts that cost 27 dollars, 9 dollars, and 12 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?
A.$57
B.$36
C.$7
D.$17
Answer: B.$36
Explanation: $27 + $9 + $12 = $48 needed
1/4 x $48 = $12 on hand
$48 - $12 = $36 to earn
correct answer B
Question: John goes to his office by car at a speed of 40kmph and reaches 8 minutes earlier. If he goes at a speed of 30kmph , he reaches 4mins late. What is the distance from his house to office?
A.18 km
B.20 km
C.22 km
D.24 km
Answer: D.24 km
Explanation: Let his office time be 10 a.m. He reaches office at 8 minutes earlier when he travels at 40 kmph => He reaches at 9:52 a.m
He reaches his office 4 minutes late when travels at 30 kmph speed=> He reaches at 10.04 a.m
The time difference is (10.04 – 9.52) = 12 minutes
Let the distance be D and time=
Distance
Speed
T1 – T2 = 12 minutes = 12/60
hours = 1/5hours
D/30– D/40= 1/5
(4D-3D)/120= 1/5
D= 24 km
Question: In how many ways can seven members be selected from a group of fifteen members?
A.10C6
B.15C7
C.10C4
D.10C3
Answer: B.15C7
Explanation: seven members can be selected from fifteen members in
15C7
= 15c7 ways.
Answer: B