divelab/Sys2Bench huggingface dataset:
Question: How many multiples of 5 are there between 50 and 500 ?
Options:
A)128
B)91
C)89
D)61
E)60
Rationale: It should be mentioned whether 50 and 500 are inclusive.
If 50 and 500 are inclusive, then the answer is (500-50)/5+1=91.
If 50 and 500 are NOT inclusive, then the answer is (495-55)/5+1=89.
Since OA is C, then we have NOT inclusive case.
Answer: C
Question: What is the remainder when 14,451 × 15,651 × 16,788 is divided by 5?
Options:
A)1
B)2
C)4
D)3
E)5
Rationale: Only the unit's digit of the product will decide the remainder when divided by 5.
Hence, 1*1*8= will give units digit as 8
So, whatever be the number, if it ends in 8, the remainder after dividing with 5 will be 3.
OptionD
Answer: D
Question: If P represents the product of the first 14 positive integers, then P is NOT a multiple of
Options:
A)99
B)84
C)72
D)65
E)85
Rationale: Answer is E.
Since prime factor of 85 is 5x17. 17 is a prime number and not part of the first 14 positive integers.
A) 9 x 11
B) 12 x 7
C) 12 x 6
D) 13 x 5
E) 5 x 17
Answer: E
Question: Six persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with them. Hence the current average age has become 45. Find the age of the 7th person.
Options:
A)69
B)70
C)71
D)72
E)73
Rationale: Let ‘x’ be the average of 6 persons
Since there are 6 after 2 years the age will be increased by 2 for each. So 6*2=12
After two years age will be =x+12
Average age is 43
That is (x+12)/6=43
=>x=246
Let ‘y’ be the 7th person age
(x+y)/7 =45
(246+y)/7=45
y=(45*7)-246
y=69
Answer A
Answer: A
Question: 15 men and 12 boys finish a job in 11 days, 13 men and 13 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
Options:
A)18
B)17
C)12
D)11
E)12
Rationale: 13 M + 4 B ----- 11 days
9 M + 9 B ------- 10 days
12 M +12 B -------?
117 M + 36 B = 108 M +108 B
72 B =9 M => 1 M = 8 B
104 B + 4 B = 108 B ---- 11 days
96 B + 12 B = 108 B -----? => 11 days
Answer: D
Answer: D
Question: A grocer is storing soap boxes in cartons that measure 30 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?
Options:
A)360
B)252
C)280
D)300
E)420
Rationale: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers
Dimensions of the box =30*42*60
Dimensions of the soap = 5*6*7
we get = 6x6x10 = 360
so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number
the answer is (A)
Answer: A
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 210, then how much amount should C pay as his share of rent?
Options:
A)54
B)45
C)25
D)15
E)55
Rationale: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=210×9/35=6×9=54
Answer is A
Answer: A
Question: What should come in place of the question mark (?) in the following number series?
15 19 ? 27 31
Options:
A)21
B)23
C)20
D)25
E)None of these
Rationale: Explanation:
It increases by 4.
Answer:B
Answer: B
Question: In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 65π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
Options:
A)105π
B)130π
C)200π
D)260π
E)320π
Rationale: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.
4(65π) = 260π
The answer is D.
Answer: D
Question: A basketball is dropped from a height of 20 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 2 full bounces.
Options:
A)50
B)55
C)60
D)75
E)100
Rationale: Initial distance = 40 feet
first bounce = 20 feet up + 20 feet down = 40 feet
second bouche = 10 feet up + 10 feet down = 20 feet
total distance covered = 40+40+20= 100
ANSWER IS E
Answer: E
Question: At a certain zoo, the ratio of sea horse to penguins is 5 to 11. If there are 85 more penguins than sea horses at the zoo, how many sea horses are there?
Options:
A)24
B)36
C)48
D)70
E)132
Rationale: 5/11 = x / x+85
5*85 = 6x
x=70
D. 70
Answer: D
Question: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 10-percent solution?
Options:
A)35
B)33 1/3
C)27
D)16 2/3
E)15
Rationale: 3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 10% of the solution. Set up an inequality and solve for x:
1.5/x = 1/10
x = 15
Since you need a 15L solution, you must evaporate 35 of the original 50L solution to get a 10% solution.
Answer is A.
Answer: A
Question: Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 50 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
Options:
A)20
B)34
C)38
D)40
E)46
Rationale: Nice question +1
We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 46
Hence answer is E
Answer: E
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . How many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference?
Options:
A)10 feet
B)12 feet
C)27 feet
D)15 feet
E)18 feet
Rationale: total circuit=27/3=9
total feet squirrel travels=9*3=27 feet
ANSWER:C
Answer: C
Question: 7 people average age is 30. youngest person age is 8. find average of the people when youngest was born.
Options:
A)23
B)24
C)25
D)22
E)27
Rationale: average age of people =30
so have total age =210
before 7 years we have to deduct each person age by seven years 210-56=154
so average age would be 154/7=22
ANSWER:D
Answer: D
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
Options:
A)12
B)14
C)16
D)17
E)19
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
C)
Answer: C
Question: At the time of marriage, a man was 10 years elder to his wife. 16 years after their marriage, his age is 6/5 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
Options:
A)36 years
B)16 years
C)14 years
D)24 years
E)10 years
Rationale: let wifes age= x
husband age = x+10
now after 16 years of mrg x+16 wifes age
x+10+12 husbands age
6/5(x+16)=x+10+12
after solving x=14
ANSWER:C
Answer: C
Question: A man is 22 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:
Options:
A)14 years
B)18 years
C)20 years
D)22 years
E)16 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 22) + 2 = 2(x + 2)
x + 24 = 2x + 4
x = 20.
answer :C
Answer: C
Question: Two pipes P and Q can fill a cistern in 12 and 14 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)11 1/2 min
B)11 1/4 min
C)11 2/4 min
D)11 1/5 min
E)10 1/2 min
Rationale: 3/12 + x/14 = 1
x= 10 1/2
Answer: E
Answer: E
Question: For a race a distance of 224 meters can be covered by P in 16 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
Options:
A)232m
B)238m
C)224m
D)331m
E)236m
Rationale: Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/16 = 14m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 16 seconds
Therefore, Distance covered by P in that time= 14m/s x 16 seconds = 224 metres
ANSWER: C
Answer: C
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 12?
Options:
A)5/6
B)7/36
C)5/36
D)1/36
E)12/36
Rationale: The sum of numbers appeared is 12.
Therefore, the required probability = n(E)/n(S) = 1/36.
ANSWER:D
Answer: D
Question: If P(32, 6) = kC (32, 6), then what is the value of k?
Options:
A)6
B)32
C)120
D)720
E)820
Rationale: Solution
Since 32P6 = k32C6
⇒ 32!/ ( 32-6 )!= k 32!/ ( 32-6 )!
⇒k = 6! = 720. Answer D
Answer: D
Question: On a certain planet where people usually tend to live for more than a century, the ratio of present ages of father and son is 7:4. 10 years later, the ratio of their ages will be 5:3. What is the sum of their present ages?
Options:
A)220
B)200
C)140
D)80
E)60
Rationale: The ratio of present ages of father and son is 7:4, so suppose the present ages are 7x and 4x, respectively.
10 years later, the ages of father and son, respectively, shall be 7x + 10 and 4x + 10.
The ratio of ages 10 years later is given to be 5:3.
This means
(7x + 10)/(4x + 10) = 5/3
Solving we get x = 20.
So present age of father is 7x = 140 and present age of son is 4x = 80.
The sum of present ages is thus 220.
Ans A
Answer: A
Question: Venkat purchased twenty dozens of toys at the rate of 375 per dozen. He sold each one of them at the rate of 33. What was his percentage profit?
Options:
A)6.5
B)5.6
C)3.5
D)4.5
E)None of these
Rationale: Cost price of 20 dozen toys = 20 × 375 = 7,500
Selling price of 20 dozen toys = 20 × 33 × 12 = 7,920
Profit percentage = 7920−7500/7500×100=5.6%
Answer B
Answer: B
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.7. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
Options:
A)(0.7)^5
B)2(0.7)^4
C)3(0.7)^4
D)4(0.7)^4(0.3) + (0.7)^5
E)5(0.7)^4(0.3) + (0.7)^5
Rationale: P(5 heads) = (0.7)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.7)^4(0.3)
The answer is E.
Answer: E
Question: 1/3 of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the avg speed for the whole journey.
Options:
A)25.56 kmph
B)28.675 kmph
C)33.333 kmph
D)40.134 kmph
E)50.254 kmph
Rationale: Average speed = total distance / total time
LCM = 3, 4 = 12
Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)
= 12/ (4/25 + 3/30+ 5/30
= 150*12/54 = 33.333 kmph
C
Answer: C
Question: In a basketball game, Dhoni scored 10 points more than Dravid, but only half as many points as Shewag. If the three players scored a combined total of 130 points, how many points did Dhoni score?
Options:
A)45
B)55
C)35
D)65
E)70
Rationale: Let Dravid scored point = x
Then Dhoni Scored = x+10
Shewag Scored = 2*(x+10) = 2x+20
As given, x+x+10+2x+20 = 130 points
4x+30 = 130
x = 130-30/4 = 25
So Dhoni Scored = x +15 i.e) 25+10 = 35
Answer : C
Answer: C
Question: If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2.
Options:
A)Cannot be determined
B)1
C)2
D)3
E)4
Rationale: take square of any prime number
remainder will be 1
Ans B
Answer: B
Question: In the coordinate plane, a circle centered on point (-3, -3) passes through point (1, 1). What is the area of the circle?
Options:
A)9π
B)32π
C)25π
D)37π
E)41π
Rationale: r^2=(-3-1)^2+(-3-1)^2=16+16=32
Area of circle=πr^2=32π
Answer : B
Answer: B
Question: Rahul can done a work in 5 days and meena can done a work in 10 days.In how many days that both are work together?
Options:
A)3/10
B)10/3
C)1/3
D)5
E)6/3
Rationale: A's one day work=1/5
B's one day work=1/10
A+B=1/5+1/10=10+5/50=10/3 days
Ans:option B
Answer: B
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
Options:
A)1:5
B)1:3
C)1:1
D)1:2
E)1:9
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1
Answer: D
Answer: D
Question: At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 40% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
Options:
A)4/25
B)8/23
C)2/5
D)8/15
E)2/5
Rationale: let there be 100 books in all
Historic fiction books = 40% of total = 40
Other books = 60
New historic fiction = 40% of 40 = 16
Other new books = 40% of 60 = 24
total new books = 24+16 = 40
fraction = 16/40 = 2/5
Ans: E
Answer: E
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?
Options:
A)Rs.7500
B)Rs.7200
C)Rs.6000
D)Rs.5750
E)Rs.6750
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
ANSWER:C
Answer: C
Question: In how much time will a train of length 140 m, moving at 36 kmph cross an electric pole?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 140/10 = 14 sec.
Answer:D
Answer: D
Question: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n41?
Options:
A)100~1,000
B)1,000~10,000
C)10,000~100,000
D)100,000~1,000,000
E)1,000,000,000,000~
Rationale: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n41=2^40=(2^10)^4>(10^3)^4=10^12
Thus, the answer is E.
Answer: E
Question: The ratio between the speeds of two persons is 7:8.If the second main runs 400 km in 4 hours,then find the speed of the another person?
Options:
A)91.6km/hr
B)87.5km/hr
C)80.5 km/hr
D)92 km/hr
E)120.1 km/hr
Rationale: Let the speed of two persons be 7x and 8x km/hr
8x=400/4
x=100/8
x=12.5
Speed of first person=(7*12.5)km/hr
=87.5 km/hr
Answer is option B
Answer: B
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Options:
A)08 a.m.
B)09 a.m.
C)12 a.m.
D)10 a.m.
E)07 a.m.
Rationale: D
10 a.m.
D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: D
Question: In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 4-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
Options:
A)174
B)171
C)186
D)196
E)200
Rationale: Case 1
1french 3either German or Spanish: 4C1 * 6C3 = 80
Case 2
2french 2either German or Spanish: 4C2 * 6C2 = 90
Case 3
4french 4C4 = 1
Answer is B = 171
Answer: B
Question: Rectangular tile each of size 80cm by 40cm must be laid horizontally on a rectangular floor of size 130cm by 230cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
Options:
A)6
B)2
C)8
D)9
E)7
Rationale: Area of tile = 80*40 = 3200
Area of floor = 130*230 = 29900
No of tiles = 29900/3200 = 9.34
So, the no of tile = 9
ANSWER:D
Answer: D
Question: There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Options:
A)5/12
B)5/7
C)5/3
D)5/8
E)5/1
Rationale: Let the two numbers be x and y.
60/100 * x + y = 5/4y
=> 3/5 x = 1/4 y => x/y
= 5/12
Answer: A
Answer: A
Question: At what rate percent per annum will a sum of money double in 9 years.
Options:
A)12.5%
B)13.5%
C)11.5%
D)11.1%
E)21.5%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 9)]% = 11.1% per annum. Answer: D
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?
Options:
A)11
B)25
C)66
D)88
E)11
Rationale: 600 --- 400
100 --- ? => 66%
Answer:C
Answer: C
Question: A certain car dealership offers its newest model in ten exterior and nine interior colors. If the ten interior colors are identical to the nine exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
Options:
A)45
B)81
C)90
D)10!/2!
E)10!
Rationale: I lined up the 10 different colours for Exterion and Interior like this:
E: A B C D E F G H I J
I: A B C D E F G H I J
I calculated the number of combinations: 10*10= 100 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 81.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
B
Answer: B
Question: Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)20
B)22
C)25
D)27
E)29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131
a + b + c = √625 = 25
C
Answer: C
Question: If a is a positive number and 1/4 the square root of a is equal to 2a, then a =
Options:
A)1/64
B)1/16
C)1/2
D)4
E)16
Rationale: 1/4 of sqrt(a) = 2a, which means that sqrt(a) = 8a
or a = 64a^2 -> divide by a
1=64a
a=1/64
A.
Answer: A
Question: In March, Bill ran an average of 1 mile an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Bill to complete one mile in June?
Options:
A)3590/60^2
B)2410/60^2
C)2390/60^2
D)3586/60
E)60^2/3590
Rationale: Bill ran at an average of 1 mile/hour in march. So to run 1 mile he would take 1 hour = (60 * 60) seconds = 3600 seconds.
If he increases his speed by 10 seconds, he will complete a mile in 3590 seconds. Converting in hours = 3590/(60 * 60) = 3590/(60^2)
ANSWER: A
Answer: A
Question: If positive integers x is even and y is odd, which of the following must be odd?
Options:
A)2xy
B)3x+y-1
C)x+y
D)x + y -1
E)3(x + y) - 3
Rationale: Let x = 2 and y = 1
2xy = 2*2*1 = 4
3x+y-1 = 3*2 + 1 -1 = 6
x+y = 2+1 = 3
x+y-1 = 2+1-1 = 2
3(x+y) - 3 = 6+3-3 = 6
Answer: C
Answer: C
Question: A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
Options:
A)7 km/hr
B)7.2 km/hr
C)8 km/hr
D)8.2 km/hr
E)8.3 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: B
Question: Last year the price range (per kg) for 100 varieties of apples in wholesale market was $1,00. If the prices of each of the 100 varieties increased by 10 percent this year over what it was last year, what is the range of the wholesale prices of the 1000 varieties of apples this year?
Options:
A) $ 50
B) $ 100
C) $ 110
D) $600
E) $300
Rationale: let the lowest price be x.
Therefore, highest price is x +100.
Now price of each variety is increased by 10%.
Therefore the price will remain arranged in the same order as before.
or Lowest price = 1.1x and Highest = 1.1 * (x+100)
or Range = highest - lowest = 1.1 * (x+100) - 1.1x
= 110, Hence, C
Answer: C
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $3,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
Options:
A)$18,400
B)$19,500
C)$22,200
D)$20,400
E)$21,100
Rationale: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 3500
Net price of the car in 02 = 18700 + 3500 = $22200
Correct Option: C
Answer: C
Question: A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0019)?
Options:
A)25
B)20
C)21
D)18.81
E)22
Rationale: You get 10^2 (100-1) (.0019)
we know 19/10000 = .0019
10^2 (99) * (19/10000)
10^2 = 100 and 100^2 = 10000
Cancel out the 100 with the 10^2
Left with 99(19/100).
0.99*19 = 18.81
Answer : D
Answer: D
Question: Two assembly line inspectors, smithy and glen, inspect widgets as they come off the assembly line. If smithy inspects every fifth widget, starting with the fifth, and glen inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?
Options:
A)50
B)53
C)55
D)60
E)65
Rationale: Widgets inspected by smithy: ((95-5)/5)+1=18+1=19
Widgets inspected by glen: ((96-3)/3)+1 =31+1 =32
Widgets inspected by both: ((90-15)+1 =6
Total : 19+32 -6=45
hence, widgets not inspected: 98-45=53
Option B
Answer: B
Question: A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 . The emptying capacity of the tank is 10 per minute heigher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?
Options:
A)50 m^3/min
B)90 m^3/min
C)50 m^9/min
D)59 m^3/min
E)50 m^4/min
Rationale: Explanation:
Let the filling capacity of the pump be x /min.
Then, emptying capacity of the pump=(x+10) /min.
so,
Answer: A) 50 m^3/min
Answer: A
Question: The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 20 percent of the budget?
Options:
A) 15 °
B) 36 °
C) 54 °
D) 72 °
E) 150 °
Rationale: 100 percent = 360 degrees
20 percent = 360*20/100 = 72 degrees
Answer is D.
Answer: D
Question: Marts income is 50 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income
Options:
A)124%
B)b) 120 %
C)c) 96 %
D)d) 90 %
E)e) 64 %
Rationale: M = (150/100)T
T = (60/100)J
=> M = (90/100)J
Answer D.
Answer: D
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 60. He was allowed to drop his lowest score. After doing so, his average test score improved to 65. What is the lowest test score that was dropped?
Options:
A)20
B)45
C)55
D)65
E)80
Rationale: The arithmetic mean of 4 equally weighted tests was 60. So what we can assume is that we have 4 test scores, each 60.
He dropped his lowest score and the avg went to 65. This means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 60.
So the lowest score = 60 - 15 = 45
Answer (B)
Answer: B