RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Find the area, diameter = 10m.
A.78.24 square meter
B.78.57 square meter
C.78.26 square meter
D.24.24 square meter
Answer: B.78.57 square meter
Explanation: Diameter = 10 meter.
Radius = diameter/2.
= 10/2.
= 5 meter.
Area of a circle = Ï€r2.
Here, pi (Ï€) = 3.14 meter, radius (r) = 5.
Area of a circle = 3.14 Ã— 5 Ã— 5..
= 3.14 Ã— 25.
= 78.57 square meter ANSWER : B
Question: The sides of a rectangular region measured to the nearest centimeter are 10 cm and 6 cm. Out of the following which is the largest possible value of actual area of rectangle ?
A.48
B.65.25
C.52.29
D.44
Answer: B.65.25
Explanation: acan be anywhere between 9.5 and 10.4 andbcan be anywhere between 5.5 and 6.4.
Hence max area can be 10.4*6.4 eq 66.56.
largest value which is near to 66.56 is 65.25.
Hence B.
Question: How many different three-digit multiples of 5 can be composed of digits 2, 3, 6, and 5 if none of the digits is repeated?
A.3
B.6
C.10
D.12
Answer: B.6
Explanation: = 3c2 x 2 = 6
can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 3 possible choices.
X can be any of the 2 possible choices.
2+3+1= 6
B
Question: A block of wood has dimensions 10cm x 10cm x 40cm. The block is painted red and then cut evenly at the 20 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?
A.5%
B.10%
C.15%
D.20%
Answer: B.10%
Explanation: The area of each half is 100+4(200)+100 = 1000
The area that is not painted is 100.
The fraction that is not painted is 100/1000 = 1/10 = 10%
The answer is B.
Question: From a circular sheet of paper with a radius of 20cm,four circles of radius 5cm each are cut out.what is the ratio of the uncut to the cut portion?
A.1:3
B.4:1
C.3:1
D.4:3
Answer: C.3:1
Explanation: area of uncut=(400-100)3.14
area of cut=4*25*3.14=(100)3.14
ratio=3:1
ANSWER:C
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 46?
A.11
B.12
C.13
D.14
Answer: A.11
Explanation: four wheeler=11*4=44(max)
2 wheel=1
so no of 4 wheeler=11
ANSWER:A
Question: The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
A.2.3 m
B.4.6 m
C.7.8 m
D.9.2 m
Answer: D.9.2 m
Explanation: Solution
Let AB be the wall and BC be the ladder.
Then, < ABC	= 60°
AC	= 4.6 m.;
AC/BC	= cos 60°
= 1 /2
‹=›BC=2×AC
=(2× 4.6) m
= 9.2 m
Answer D
Question: A two digit number is 18 less than the square of the sum of its digits. How many such numbers are there?
A.22,33
B.22,22
C.221,1
D.63,82
Answer: D.63,82
Explanation: Option 2
Take N = 10a+b.
Given that, (10a+b)+18 = K2 = (a+b)2
Given number = K2 - 18 = (10a+b)
That means, when we add 18 to the given number it should be a perfect square. So K2 takes the following values. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ....
1 to 16 are ruled out as if we subtract 18 from them, the resulting number is a single digit number.
Now 25 - 18 = 7
36 - 18 = 18
49 - 18 = 31
64 - 18 = 46
81 - 18 = 63
100 - 18 = 82
121 - 18 = 103
Now 63, 82 satisfies.
Answer:D
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 63 kmph, find the speed of the stream?
A.15
B.19
C.14
D.21
Answer: D.21
Explanation: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 63/3 = 21 kmph.
Answer:D
Question: How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits A equal to 28?
A.14
B.24
C.28
D.48
Answer: D.48
Explanation: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So A=24+24=48.D
Question: The average marks obtained by 120 candidates in a certain examinationis 35.if the average marks of passed candidate is 39 and that of the failed candidates is 15,what is the no. of candidates who passed the examination?
A.80
B.100
C.120
D.140
Answer: B.100
Explanation: Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
B
Question: A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?
A.35
B.30
C.25
D.20
Answer: A.35
Explanation: Let the truth spoken by A and B be pl and p2
respectively, i.e., pl = 3⁄4 and p2 = 4⁄5
They will contradict each other only when one speaks truth and the other is lying.
i.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35%
Answer A
Question: The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
A.1008
B.1015
C.1022
D.1032
Answer: B.1015
Explanation: Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015
Answer: B
Question: The distance between West-Town to East-Town is 14 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 5 kilometers per minute and the second bird, leaving from East-Town, at a speed of 2 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
A.3.
B.7.
C.10.
D.12.
Answer: C.10.
Explanation: Time taken by the birds to meet = 14/(5+ 2) = 2 mins
Distance traveled by the bird traveling from West-Town = 5 * 2 = 10
Answer: C
Question: If a boat is rowed downstream for 96 km in 3 hours and upstream for 88 km in 11 hours, what is the speed of the boat and the river?
A.12 , 20
B.20 , 20
C.20 , 11
D.20 , 12
Answer: D.20 , 12
Explanation: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x â€“ y
x = (Ds + Us) / 2
y = (Ds â€“ Us) / 2
In the above problem Ds = 32 ; Us = 8
x = (32 + 8) / 2 = 40/2 = 20 km/hr
y = (32 - 8)/2 = 24/2 = 12 km/hr
ANSWER: D
Question: A bag marked at $250 is sold for $120. The rate of discount is?
A.10%
B.25%
C.20%
D.52%
Answer: D.52%
Explanation: Rate of discount = 130/250 * 100 = 52%
Answer is D
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
A.1276
B.1200
C.2832
D.1299
Answer: B.1200
Explanation: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: Option B
Question: The radius of a semi circle is 2.1 cm then its perimeter is?
A.32.5
B.11.12
C.32.1
D.10.8
Answer: D.10.8
Explanation: 36/7 r = 2.1 = 10.80
Answer:D
Question: Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
A.2%
B.2.15%
C.2.25%
D.2.50%
Answer: C.2.25%
Explanation: Generally in such cases, there is always loss.
So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.
Loss% = Common loss and gain% 2 = x 2
10 10
Therefore, here common loss and gain % = 15%
Hence,
Loss% = 15 2 = 2.25%
C
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
A.1:2
B.3:4
C.4:5
D.5:7
Answer: B.3:4
Explanation: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?
A.A)5
B.B)8
C.C)10
D.D)15
Answer: A.A)5
Explanation: Total number of ways to choose 6 chairs from 5= 6C2=15
Total number of combination=150
That means we need get 10 combinations from the selection of tables....
Screening through the answers.... 5C3=10..... 10*15=150
Answer is 5... A
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 his son is
A.20 years
B.21 years
C.22 years
D.24 years
Answer: C.22 years
Explanation: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22
Answer: Option C
Question: The difference between two angles of a triangle is 24o. The average of the same two angles is 54o. Which one of the following is the value of the greatest angle of the triangle
A.45o
B.45o
C.66o
D.72 degree
Answer: D.72 degree
Explanation: Solution:
Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24o.
=> a – b = 24.
Since the average of the two angles is 54o, we have (a+b)/2 =54.
Solving for b in the first equation yields b=a–24, and substituting this into the second equation yields,
[{a+(a−24)}/2] =54
2a−24 = 54*2
2a−24 = 108
2a = 108 +24
2a =132
a =66
Also,
b=a−24=66−24=42.
Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is
180o, a+b+c =180.
Putting the previous results into the equation yields 66+42+c =180.
Solving for c yields c =72
Hence, the greatest of the three angles a, b and c is c, which equ
Answer: Option D
Question: (0.66)(power 3) - (0.1)(power 3)/ (0.66)(power 2) + 0.066 + (0.1)(power 2) is:
A.0.86
B.0.56
C.0.96
D.0.69
Answer: B.0.56
Explanation: Given expression
= (0.66) (power 3) - (0.1)(power 3) / (0.66)(power 2) + (0.66 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.66 - 0.1)
= 0.56
Answer is B
Question: 144 choclates are distributed to children with the same number. What can’t be the range including the number of children?
A.1~10
B.50~60
C.20~30
D.10~20
Answer: B.50~60
Explanation: -> In 144=1*144=2*72=4*36=6*24=8*18=9*16, you can come up with 4 cases.
Amongst these cases, what is not included is B. 50~60. Therefore, the answer is B.
Question: On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.25 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
A.0.027
B.0.09
C.0.417
D.0.578
Answer: D.0.578
Explanation: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.25
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.75 * 0.25 = 0.1875
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.75^2 * 0.25 = 0.1406
Total = 0.578
Ans D
Question: The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is :
A.15
B.16
C.18
D.20
Answer: A.15
Explanation: Let the larger number be x.
Then, x -12 = 20% of x<>x-(x/5)=12
4x/5=12<=> x=(12∗5)/5=15.
Answer :A
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 33 years, then find the age of the person sitting in the middle of the row?
A.9 years
B.22 years
C.18 years
D.19 years
Answer: B.22 years
Explanation: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (33 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 33 * 3 = 196 - 75 - 99 = 22 years.
ANSWER:B
Question: One type of liquid contains 20% of water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of 1st liquid and 4 parts of 2nd liquid. The percentage of water in the new mixture in the glass is?
A.22.15%
B.23.5%
C.24.3%
D.25%
Answer: C.24.3%
Explanation: Required percentage = (20% of 10 + 35% of 4)/10+4 *100
= 3.4/14 * 100 = 24.3%
Answer is C
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.3100
B.210
C.21300
D.25200
Answer: D.25200
Explanation: Number of ways of selecting 3 consonants from 7 =7C3
Number of ways of selecting 2 vowels from 4 = 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
= 210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
=5! = 5*4*3*2*1 = 120
Hence, required number of ways=210×120=25200
option - D
Question: In a box, there are 9 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
A.2/3
B.8/21
C.3/7
D.9/22
Answer: D.9/22
Explanation: Explanation:
Total number of balls = (9 + 7 + 6) = 22
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 9/22.
Answer: Option D
Question: Two sides of a triangle have length 5 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24
A.I, II, and III
B.I and II only
C.II and III only
D.I and III only
Answer: A.I, II, and III
Explanation: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Question: The sum of first five prime numbers is:
A.11
B.18
C.26
D.28
Answer: D.28
Explanation: Explanation:
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
ANSWER IS D
Question: Mixture S is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture S, how many kilograms of mixture S must be added to make a 70% material B in the new mixture?
A.A)6
B.B)7
C.C)8
D.D)9
Answer: A.A)6
Explanation: Can be done with weighted avg method.
if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil .
S1=20(initial mix.)
Avg. is what we need..ie 70% of material B means 30% of oil
S2=36(36% of 10 kg mix)
w1/w2=(S2-Avg)/(Avg-S1)
(36-30)/(30-20)
6/10
means for every 10 kg of new mix. we need 6 kg of mix S
Ans A
Question: Randy'sbar serves customers every weeknight from 4 pm to 1 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?
A.Monday, 7:30 pm
B.Monday, 9 pm
C.Monday, 7 pm
D.Monday, 6:45 pm
Answer: C.Monday, 7 pm
Explanation: Let the keg be a 150 Litre keg
At 5 pm.. There are 75 litres
At 6:30 pm there are 50 litres.
So, consumption rate is 25 litres per 1.5 hours.
So it will take 3 hours to finish 50 litres at this rate.
During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.
So, keg becomes empty at 6:30 + 1 hour = 7 pm
Answer is C
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 55 meters. How many times did the ball bounce?
A.5
B.6
C.3
D.8
Answer: C.3
Explanation: Going down = 20 m
Going Up = 10 --> Total = 30
Going down = 10 --> Total = 40
Going Up = 5 --> Total = 45
Going down = 5 --> Total = 50
Going up = 2.5 --> Total = 52.5
Going down = 2.5 --> Total =55(Caught)
No of bouncing = 3
Answer : C
Question: The difference between the compound interest and simple interest accrued on an amount at the end of three years at the rate of 12% is Rs.381.888. What is the amount?
A.Rs. 9500
B.Rs. 8400
C.Rs.8500
D.Rs.8200
Answer: C.Rs.8500
Explanation: Explanation:
C.I = P[(1+R/100)T - 1]
= P[(1+12/100)3 - 1] = P[(28/25)3 - 1]
= P[(21952/15625) - 1]
= 6327P/15625
S.I = (P x 3 x 12)/100 = Rs. 9P/25
6327P/15625 - 9P/25 = 381.888
=> 702P/15625 = 381.888
=> P = (381.888 x 15625)/702
= Rs. 8500
Answer: Option C
Question: 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term Y of the sequence?
A.360
B.365
C.369
D.374
Answer: D.374
Explanation: First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term Y, t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Question: For all integers a and b, a%b = (a + b)(a - b). If 4%x = 7, then which of the following could be a value of x?
A.-4
B.-3
C.2
D.4
Answer: B.-3
Explanation: 4%x = (4+x)(4-x)
16-x^2 = 7
x^2 = 9
x=-3,3
Ans: B
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
A.480
B.487
C.481
D.729
Answer: A.480
Explanation: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer:A
Question: A full-time employee’s hourly wage was increased by 10%. He decided to decrease the number of hours worked per week so that his total income did not change. By approximately what percent should the number of hours worked be decreased?
A.7%
B.9%
C.25%
D.50%
Answer: B.9%
Explanation: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 10% wage increase, the employee makes $1.10/hour
We want the employee's income to remain at $100/week.
So, we want ($1.10/hour)(new # of hours) = $100
Divide both sides by 1.10 to get:
new # of hours = 100/1.10
≈ 90 hours
So, the number of hours decreases from 100 hours to (approximately) 90 hours.
This represents a 10% decrease (approximately) .
Answer choice B is the closest answer.
Question: A train passes a station platform in 37 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.248 m
B.240 m
C.277 m
D.255 m
Answer: D.255 m
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/37 = 15 ==> x + 300 = 555 ==> x
= 255 m.
Answer: D
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
A.55 kmph
B.45 kmph
C.54 kmph
D.35 kmph
Answer: B.45 kmph
Explanation: B
45 kmph
Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
Question: Double of Quarter of 2 percent written as a decimal is :
A.0.01
B.0.0005
C.0.25
D.0.005
Answer: A.0.01
Explanation: Explanation :
Solution: (2)*(1/4)*2% = 2*(1/4 * 2/100) = 0.01.
Answer : A
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
A.635.5
B.635.59
C.635.51
D.635.56
Answer: A.635.5
Explanation: Explanation:
4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer:A
Question: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 60 km more than the other. What is the distance between the two stations?
A.540 km
B.767 km
C.276 km
D.178 km
Answer: A.540 km
Explanation: Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 60 km more than the other,
25x – 20x = 60
5x = 60
x = 12 hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*12 = 540 km.
ANSWER: A
Question: John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount Q of dollars he could have spent for the $12 tickets?
A.$48
B.$60
C.$84
D.$96
Answer: B.$60
Explanation: 60 ..... 12 *5 Q= 60. (min). Thus answer .B
Question: If p^2 – 13p + 40 = s, and p is a positive integer between 1 and 10, inclusive, what is the probability that s < 0?
A.1/10
B.1/5
C.2/5
D.3/5
Answer: B.1/5
Explanation: p2 – 13p + 40 = s
so (p – 8)(p – 5) = s
For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
Question: Dacid obtained 61, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
A.29
B.72
C.39
D.37
Answer: B.72
Explanation: Average = (61 + 65 + 82 + 67 + 85)/5
= 72
Answer: B
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62 percent of those who attended the meeting were stockholders and 42 percent were employees, what percent were stockholders who were not employees?
A. 34%
B. 58%
C. 45%
D. 53%
Answer: B. 58%
Explanation: Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M
were stockholders and 42% of M or 0.42M were employees, it follows that 0.62M +
0.42M = 1.04M were either stockholders, employees, or both. Since 1.04M exceeds
M, the excess 1.04M − M = 0.04M must be the number of attendees who were both
stockholders and employees, leaving the rest 0.62M − 0.04M = 0.58M, or 58%, of
the meeting attendees to be stockholders but not employees.
The correct answer is B.
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is?
A.70 km/hr
B.75 km/hr
C.84 km/hr
D.87.5 km/hr
Answer: D.87.5 km/hr
Explanation: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = [ 400/4] = 100
x = [100/8] = 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Answer is D