RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1270. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
A. 2480
B. 3490
C. 6785
D. 8245
Answer: D. 8245
Explanation: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1270, we get the answer of 8245. (ANS D)
Question: Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs 4000, the new ratio becomes 40:57. What is Sumit present salary.
A.32000
B.34000
C.38000
D.40000
Answer: C.38000
Explanation: Explanation:
Let the original Salaries of Ravi and Sumit is 2x and 3x.
So as per question
2x+4000/3x+4000=40/57
=>57(2x+4000)=40(3x+4000)
=>6x=68000
=>3x=34000
Sumit Salary =3x+4000
34000+4000=38000
Option C
Question: A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?
A.$10
B.$16
C.$20
D.$24
Answer: C.$20
Explanation: Let P be the original price paid by the retailer.
1.25*P = 100
P = 80
The profit is $20.
The answer is C.
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rohan’s and Sudhir’s share in the profit?
A.Rs.345
B.Rs.350
C.Rs.352
D.Rs.362
Answer: D.Rs.362
Explanation: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3982 × 1/11 = Rs.362.
D
Question: A card player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many hearts as clubs and twice as many diamonds as hearts. How many spades does he hold?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: Sol.
The player holds 1 club, 2 hearts and 4 diamonds.
As he holds 13 cards (or seven black cards), it follows that there must be 6 spades.
Answer : A
Question: A certain bag contains 100 balls — 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
A.0.9
B.0.75
C.0.6
D.0.8
Answer: A.0.9
Explanation: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 10)/100 = 90/100 = 0.9.
Answer is A
Question: y and z represents 2 gas stations which are 270 km apart. if two cars leave each gas station and drive towards each other, at what time will they meet each other given that the first car left the gas station at 10 a.m. and travels at a speed of 75 kmph while the second car left the station at 11 a.m. and travels at a speed of 55 kmph.
A.12.00 p.m
B.11.30 p.m
C.2.30 p.m
D.12.30 p.m
Answer: D.12.30 p.m
Explanation: Suppose they meet x hours after 10 a.m.
Distance moved by first car in x hours + distance moved by 2nd car in x-1 hrs = 270
75x+55(x-1) = 270
75x+55x-55= 270
130x= 325
x = 2.5
So they meet 2.5 hr after 10 a.m. which is at 12.30 p.m.
Answer is D
Question: What should come in place of question mark (?) in the following equation?
5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = ?
A.7
B.8 1⁄2
C.7 1⁄2
D.6 1⁄2
Answer: A.7
Explanation: ? = 5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = 28⁄5 ÷ 56⁄15 + 11⁄2
= 28⁄5 × 15⁄56 + 11⁄2 = 3⁄2 + 11⁄2 = 14⁄2 = 7
Answer A
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 30 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
A. 16
B. 18
C. 20
D. 24
Answer: B. 18
Explanation: Time taken = Total Distance / Relative Speed
Total Distance = 30 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 30 / 10 = 3 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 3 = 18 kms... Answer - B
Question: If x^2+(1/x^2)=3, x^4+(1/x^4)=?
A.7
B.11
C.12
D.14
Answer: A.7
Explanation: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=3^2-2=7.
Thus, the answer is A.
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
A.2
B.5
C.9
D.6
Answer: C.9
Explanation: 9 a.m.
Answer: C
Question: Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?
A.4225
B.4096
C.4356
D.Insufficient Data
Answer: C.4356
Explanation: DETAILED SOLUTION
Let the area of backyard be x2 this year and y2 last year
∴ X2- Y2 = 131
=) (X+Y) (X-Y) = 131
Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.
=) (X+Y) (X-Y) = 131 x 1
=) X+Y = 131
X-Y = 1
=) 2X = 132 =) X = 66
and Y = 65
∴ Number of tomatoes produced this year = 662 = 4356
Correct Choice (C)
Question: A football team lost 5 yards and then gained 9. What is the team's progress?
A.2
B.4
C.5
D.6
Answer: B.4
Explanation: For lost, use negative. For gain, use positive.
Progress = -5 + 9 = 4 yards
Question: Pipe A can fill a tank in 8 hours. Due to a leak at the bottom, it takes 12 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
A.5
B.24
C.78
D.90
Answer: B.24
Explanation: Let the leak can empty the full tank in x hours 1/8 - 1/x = 1/12
=> 1/x = 1/8 - 1/12 = (3 - 2)/24 = 1/24
=> x = 24.
Answer: B
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
A.10 hours
B.23 hours
C.18 hours
D.20 hours
Answer: A.10 hours
Explanation: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours =10 hours.
Answer: A
Question: A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?
A.115
B.117
C.116
D.114
Answer: B.117
Explanation: Explanation:
Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.
ANSWER IS B
Question: If a - b = 3 and a2 + b2 = 29, find the value of ab.
A.10
B.12
C.15
D.18
Answer: A.10
Explanation: 2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10.
Answer: A
Question: A rectangular field is 20 yards long and 18 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)
A.330 ft
B.336 ft
C.430 ft
D.330 ft
Answer: B.336 ft
Explanation: 20 + 18 + 20 + 18 = 76 yds. for
outside of field.
18 + 18 = 36 yds. for dividing sections
76 + 36 = 112 yds. of fencing
112 x 3 = 336 ft. of fencing
correct answer B
Question: On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 45 percent of the sales representatives prefer to stay at Hotel XYZ and 55 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?
A.36
B.39
C.42
D.45
Answer: D.45
Explanation: 18 people stay in XYZ and 42 people stay in ABC.
27 people prefer XYZ and 33 people prefer ABC.
Let's put all 27 people who prefer XYZ in hotel ABC.
Then 18 people who prefer ABC will stay in XYZ.
The highest possible number who are not given their preference is 27+18=45.
The answer is D.
Question: A does a work in 20days and B does the same work in 5days. In how many days they together will do the same work?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: A+B can finish =AB/A+B = 20*5/(20+5) = 4days
Answer is D
Question: A park shaped like a rectangle has a length of 24 meters and a width of 18 meters. If trees are planted on its sides with gaps of 2 meters between them, how many trees are needed?
A.32 trees.
B.42 trees.
C.52 trees.
D.62 trees.
Answer: B.42 trees.
Explanation: Solution:
The perimeter of the rectangle is 2 × (24 + 18) = 2 × 42 = 84 meters, so there will be 84 ÷ 2 = 42 trees.
Answer B
Question: Of the 8 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 8 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
A.30
B.35
C.56
D.70
Answer: A.30
Explanation: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 8 ways to select one man
so 5*4*3*3 = 180
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 180/3!= 180/6= 30
A
Question: If equation |x/5| + |y/5| = 2 encloses a certain region on the coordinate plane, what is the area of this region?
A.20
B.50
C.200
D.100
Answer: C.200
Explanation: The equation can be reduced to intercept form as |x/10| + |y/10| = 1, so these are lines in four quadrants with x and y intercept as 10, so it is a rhombus with diagonals of 20 each and hence area = 1/2*d1*d2 = 1/2*20*20 = 200. Answer C.
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 15 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
A.67
B.45
C.60
D.90
Answer: C.60
Explanation: I believe there is a better way to do it.
Basically one of the options should satisfy the given criteria.
60 did
1/5 *60 =12
2/3*60=40
so total distance
52 + remaining 15 =67
Question: Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, B and Chris be 27 years, then how old is Bruce ?
A.7 years
B.10 years
C.12 years
D.13 years
Answer: B.10 years
Explanation: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, Bruce's age = 2x = 10 years.
B
Question: A, B and C start a business each investing 20,000. After 5 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 69,900 was recorded. Find the share of B
A.20,000
B.21,200
C.28,200
D.20,500
Answer: C.28,200
Explanation: Ratio of the capitals of A, B and C
= 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7
= 205000 : 212000 : 282000 = 205 : 212 : 282.
B’s share = (69900 × 212⁄699) = 21200;
Answer C
Question: If x is an integer such that 1 < x < 9, 2 < x < 15, 7 > x > –1, 4 > x > 0, and x + 1 < 5, then x is
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: 1 < x < 9,
2 < x < 15,
-1< x < 7
0< x< 4
x+1<5
From above: 2< x < 4 --> x = 3.
Answer: A.
Question: If a 3-member subcommittee is to be formed from a certain 9-member committee, how many different such subcommittee are possible?
A.6
B.18
C.20
D.84
Answer: D.84
Explanation: Another way:
1st member can be selected in 9 ways
2nd can be selected in 8 ways
3rd can be selected in 7 ways
So total ways : 504
But to avoid the similar scenarios 504/3!=84
D
Question: The average (arithmetic mean) of 20, 40, and 60 is 7 more than the average of 10, 70, and what number?
A.19
B.25
C.35
D.45
Answer: A.19
Explanation: a1 = 120/3 = 40
a2 = a1 -7 = 33
sum of second list = 33*3 = 99
therefore the number = 99 -80 = 19
ANSWER:A
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 22 households had a both a car and a bike and 44 had a car, how many had bike only?
A.30
B.35
C.20
D.18
Answer: B.35
Explanation: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-22+11 --> {Bike}=57 --> # those who have bike only is {Bike}-{Both}=57-22=35.
Answer: B.
Question: Country X imposes a two-tiered tax on imported cars: the first tier imposes a tax of 30% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 20%. If Ron imported a $50,000 imported car and ended up paying $12000 in taxes, what is the first tier's price level?
A.$22000
B.$20000
C.$23000
D.$24000
Answer: B.$20000
Explanation: Let T be the tier price, P be total price = 50000
Per the given conditions:
0.30T + 0.20(P-T) = 12000
0.30T+0.20*50000-0.20T =12000
0.10T +10000 =12000
0.10T =12000-10000 = 2000
T = 2000/0.10 =20000
Answer B
Question: The difference between a two digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
A.2
B.3
C.four
D.8
Answer: C.four
Explanation: Solution
Let the ten's digit be x and units digit be y.
Then, (10x+y) - (10y+x)= 36	‹=›9(x - y) = 36
‹=›x - y = 4.
Answer C
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
A.992
B.389
C.500
D.277
Answer: C.500
Explanation: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Question: The sum of the ages of 5 children born at the intervals of 3 year each is 40 year. what is the age of the youngest child ?
A.2 year
B.8 year
C.10 year
D.None of these
Answer: A.2 year
Explanation: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 40 â‡” 5 x = 10 â‡” x= 2.
âˆ´ Age of the youngest child = x = 2 years. Answer A
Question: If a and b are odd integers, which of the following must be an even integer?
A.a(b – 2)
B.ab + 4
C.(a + 2)(b – 4)
D.3a + 5b
Answer: D.3a + 5b
Explanation: 3a+5b==0dd*odd + odd*odd =odd+odd = even.
ANSWER:D
Question: Rs.3150 is divided so that 5 times the first share, thrice the 2nd share and six times the third share amount to the same. What is the value of the third share?
A.s529
B.s527
C.s570
D.s750
Answer: D.s750
Explanation: A+B+C = 3150
5A = 2B = 6C = x
A:B:C = 1/5:1/2:1/6 = 6:15:5
5/21 * 3150=Rs750
Answer:D
Question: For 600km 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 bus and the rest bycar. The ratio of the speed of the train to that of the cars is?
A.1:3
B.3:4
C.2:5
D.3:7
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: 9 - 3 ÷ 1/3 + 3 = ?
A.1
B.3
C.6
D.9
Answer: B.3
Explanation: 9 - 3 1/3 + 3
=9-3÷1/3+3
=9-(3X3) +3
=9-9+3
=3
CORRECT ANSWER : B
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1051. Find the cost of each ice-cream cup?
A.25
B.40
C.77
D.99
Answer: B.40
Explanation: Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 1051
96 + 225 + 490 + 6x = 1051
6x = 240 => x = 40.
Answer: B
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 25 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
A.50%
B.53%
C.54%
D.55%
Answer: D.55%
Explanation: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
60*0.75=45 Democrats are expected to vote for Candidate A;
40*0.25=10 Republicans are expected to vote for Candidate A.
Thus total of 45+10=55 registered voters are expected to vote for Candidate A, which is 55% of the total number of registered voters.
Answer: D.
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 6 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
A.60 gallons
B.100 gallons
C.240 gallons
D.180 gallons
Answer: C.240 gallons
Explanation: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 6 gallons\
Volume of whole = 6 * 40 = 240 gallons.
ANSWER:C
Question: A sum of Rs.4400 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.2860
B.Rs.3120
C.Rs.3320
D.Rs.2760
Answer: A.Rs.2860
Explanation: Let A be the amount received at the end of the three years.
A = 4400[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4400 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7260
So the interest = 7260 - 4400 = Rs.2860
ANSWER:A
Question: Beth received 1/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
A.1/5
B.4/7
C.3/10
D.7/20
Answer: B.4/7
Explanation: Let the total votes be 10. Beth received 1 votes, other votes 10-1=9. In order to have received 1/2 of the votes she needed 5 votes so 4 more, which is 4/7 of the other votes.
Answer: B.
Question: In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ?
A.64
B.1/8
C.1
D.4
Answer: D.4
Explanation: Say r=2 => V1 = 1/16
when r=1; V2 = 1/4
V2 = 4*V1.
Answer : D
Question: A metallic hemisphere is melted and recat in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then :
A.H = 2R
B.H = 4R
C.H = √4R
D.H = 2/3 R
Answer: A.H = 2R
Explanation: Sol.
2/3 ∏R³ = 1/3 ∏R²H ⇒ H = 2R.
Answer A
Question: If n is a positive integer, which one of these following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6?
A.125n + 3
B.240n + 3
C.380n + 3
D.590n + 3
Answer: B.240n + 3
Explanation: The numbers 4, 5, and 6 all divide 240 so they all divide 240n.
When we divide (240n + 3) by 4, 5, or 6, the remainder must be 3.
The answer is B.
Question: The fourth proportional to 6, 11, 36 is:
A.64
B.66
C.68
D.70
Answer: B.66
Explanation: Let the fourth proportional to 6, 11, 36 be x.
Then, 6 : 11 : 36 : x
6x = (11 x 36)
x =	(11 x 36)/6
x=396/6 =66
Answer: Option B
Question: Rahul will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
A.5
B.6
C.9
D.24
Answer: A.5
Explanation: Rahul will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases....A
Question: In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many R eggs does the plant process per day?
A. 100
B. 300
C. 400
D. 3,000
Answer: C. 400
Explanation: Straight pluggin in for me. As usual, I started with C and got the answer.
Lets' back calculate and see what we get
Let us consider eggs processed each day to be 400
So Initial ratio of eggs processed and rejected is 96:4 or 24:1
So out of 400 eggs, there will be 384 eggs processed and 16 rejected.
Now if the no. of eggs inspected remain and 12 more eggs get accepted that means there R=384+12=396 eggs accepted and 4 rejected...and the ratio will be 99:1
Bingo...this is what the questions says....
Its always a good idea to start with C.
Question: 15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
A.87
B.18
C.17
D.16
Answer: B.18
Explanation: Binders Books Days
15 1400 21
x 1600 20
x/15 = (1600/1400) * (21/20) => x = 18
Answer:B
Question: How many multiples of 10 are there between 11 and 1001?
A.98
B.99
C.100
D.97
Answer: B.99
Explanation: 10 * 2 = 20
10 * 100 = 1000
Total multiples = (100 - 2) + 1
= 99
Answer B
Question: A can do a piece of work in 18 days, B in 27 days, C in 36 days. They start worked together . But only C work till the completion of work. A leaves 4 days and B leaves 6 days before the completion of work. In how many days work be completed?
A.12
B.11
C.99
D.27
Answer: A.12
Explanation: Let the work be completed in x days
(x-4)days of A + (x-6)days of B + x days of C = 1
\inline \Rightarrow \inline \frac{x-4}{18}+\frac{x-6}{27}+\frac{x}{36}=1
\inline \Rightarrow \frac{13x-48}{108}=1
x = 12
\inline \therefore Total time = 12 days
Answer:A
Question: Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability R that Jane will be on the same committee as Albert?
A. 12%
B. 20%
C. 33%
D. 40%
Answer: D. 40%
Explanation: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20
No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8
Probability R= (8/20) *100 =40%.
+1 for me.. :D