mathewhe/aqua_rat huggingface dataset:
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
(A) 7 days
(B) 8 days
(C) 5 days
(D) 4 days
(E) 2 days
Rationale: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: B
Answer: (B) 8 days
Question: In a class 30 students play cricket, 40 students play football and 20 play none of the two games.
If there are 80 students exactly in the class, how many play exactly ONE of the two games?
(A) 40
(B) 50
(C) 80
(D) 85
(E) 90
Rationale: n(C) = 30, n(F) = 40 and n(C' or F') = 20
=> n(C or F) = 80 - 20 = 60
also, n(C or F) = n(C) + n(F) - n(C and F)
=> 60 = 30 + 40 - n(C and F)
i.e. n(C and F) = 10
so, 30 - 10 = 20 students play just football and 40 - 10 = 30 students play just cricket
=> 20 + 30 = 50 students play exactly ONE game
B)
Answer: (B) 50
Question: 47% of the students in a class of 40 students has glasses or contacts. How many students in the class have either glasses or contacts?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: a=r⋅b
47%=0.47a
=0.47⋅40
a≈19
Option E is correct.
Answer: (E) 19
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 70?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 17
Rationale: four wheeler=17*4=68(max)
2 wheel=1
so no of 4 wheeler=17
ANSWER:E
Answer: (E) 17
Question: A problem is given to 3 students A, B and C whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the chance that the problem is solved.
(A) 2/3
(B) 1/2
(C) 1/4
(D) 3/4
(E) 3/7
Rationale: Explanation :
P(A) = 1/2, P(~A) = 1 - (1/2) = 1/2. [ Prob. of not solving A ]
P(B) = 1/3, P(~B) = 1 - (1/3) = 2/3. [ Prob. of not solving B ]
P(C) = 1/4, P(~C) = 1 - (1/4) = 3/4. [ Prob. of not solving C ]
The problem is solved means atleast one of A,B and C will solve the problem.
Whenever 'at least one' is present it is easier to do the problem by using the complement of the event (opposite of the event i.e problem not solved )
P (problem is not solved)
= P(~A~B~C)
= P(~A) x P(~B) x P(~C).
= (1/2) x (2/3) x (3/4).
= 1/4.
P (problem is solved i.e atleast one solves)
= 1 - P(~A~B~C).
= 1 - (1/4).
= 3/4.
Answer : D
Answer: (D) 3/4
Question: In one hour a boat goes 6 km/hr along the stream and 14 km/hr against the stream. The speed of the boat in still water(in km/hr) is?
(A) 20 km/hr
(B) 10 km/hr
(C) 15 km/hr
(D) 30 km/hr
(E) 40 km/hr
Rationale: Explanation:
Speed of boat in still water = 1/2 (Speed downstream + speed up stream)
= 1/2 (6 + 14) = 1/2 x 20
= 10 km/hr
Answer: Option B
Answer: (B) 10 km/hr
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be ?
(A) 8 days
(B) 10 days
(C) 12 days
(D) 14 days
(E) 16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
A)
Answer: (A) 8 days
Question: Average age of A and B is 24 years and average age of B, C and D is 22 years. The sum of the ages of
A, B, C and D is
(A) 90
(B) 98
(C) 120
(D) Data is not adequate
(E) None of these
Rationale: Answer: Option D
Answer: (D) Data is not adequate
Question: If a man can cover 10 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 135 km
(B) 125 km
(C) 115 km
(D) 105 km
(E) 235 km
Rationale: 10 m/s = 10 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 10 * 18/5 * 15/4 km = 135 km.
ANSWER:A
Answer: (A) 135 km
Question: In a group of ducks and cows, the total number of legs are 30 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 11
(B) 12
(C) 14
(D) 15
(E) 18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 30
=> 2x = 30 => x = 15
D
Answer: (D) 15
Question: There are 10 points on a circle. A hexagon can be formed by linking 6 of the 10 points. How many such hexagons are possible?
(A) 60
(B) 120
(C) 200
(D) 210
(E) 600
Rationale: 6 points can be selected out of 10 points in 10C6 ways
=10 !/6!*4!=210
Ans D
Answer: (D) 210
Question: One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 4 robots altogether, if the robots build only one robot at a time?
(A) 70 min
(B) 94 min
(C) 110 min
(D) 112 min
(E) 120 min
Rationale: First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
And now we have 4 robots
So Total = (1) + (2) = 70 minutes
Answer - A
Answer: (A) 70 min
Question: After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 73%?
M13-03.
(A) N−35
(B) N+72
(C) 2N+70
(D) 2N+74
(E) 2N−35
Rationale: Say N=1.
So, after 1 test John has 70 correct answers.
In 2 tests, so in 200 questions he needs to have 0.73*200=146 correct answers, so in the second test he must get 146-70=76 questions correctly.
Now, plug N=1 into the answer choices to see which one yields 76. Only option D fits.
Answer: D.
Answer: (D) 2N+74
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5760. What is the average monthly balance maintained by John in his
account during the year?
(A)  2840
(B)  28800
(C)  6840
(D)  7540
(E)  28400
Rationale: bank balance is doubled with accumulation of interest tp 5760..
this means INTEREST is 5760/2=2880 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 28800..
B
Answer: (B)  28800
Question: A Cuban cigar would cost 4 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
(A) 11.8$.
(B) 23$.
(C) 13.7$.
(D) 35$.
(E) 37.4$.
Rationale: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options A,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.
Therefore C is the answer.
Answer: (C) 13.7$.
Question: Set Q consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set Q, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: A = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of Q = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C
Answer: (C) 0
Question: A car traveled from San Diego to San Francisco at an average speed of 66 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
(A) 24.
(B) 32.
(C) 36.
(D) 42.
(E) 44.
Rationale: Let the time taken be = x
One way distance = 66x
Total distance traveled = 2 * 66x = 132x
Total time taken = x + 2x = 3x
Average speed = 132x/3x = 44
Answer: E
Answer: (E) 44.
Question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours Q will it take if Jim types the report and Mary edits it immediately after he is done?
(A) 41.4
(B) 34.1
(C) 13.4
(D) 12.4
(E) 10.8
Rationale: Break down the problem into two pieces: typing and editing.
Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);
Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23 in theory below)--> x=150/7;
Jim needs 12 hours to edit the report--> Jim's editing rate = 1/12;
Mary and Jim can edit a report in 7.5and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;
How many Q hours will it take if Jim types the report and Mary edits it immediately after he is done--> x+y=150/7+20=~41.4
Answer: A.
Answer: (A) 41.4
Question: 10(150) ÷ 10(146) = ?
(A) 10(6)
(B) 100000
(C) 1000
(D) 10000
(E) None of these
Rationale: 10(150) ÷ 10(146) = ?
or ? = 10(150)/10(146)=10(150−146)
i.e, [m(x)/m(y)=m(x−y)]
= 10(4) = 10000
Answer D
Answer: (D) 10000
Question: P, Q and R have Rs.6000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
(A) 2388
(B) 3722
(C) 2400
(D) 2872
(E) 1231
Rationale: Explanation:
Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(6000 - r) => 3r = 12000 - 2r
=> 5r = 12000 => r = 2400.
Answer: C
Answer: (C) 2400
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 2/7
(B) 1/7
(C) 6/8
(D) 1/4
(E) 2/9
Rationale: Explanation:
Original share of 1 person =1/8
New share of 1 person =1/7
Increase =(1/7-1/8)=1/56
Required fraction =(1/56)/(1/8)=(1/56*8/1)=1/7
Answer:B
Answer: (B) 1/7
Question: A 180 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train?
(A) 54 kmph
(B) 108 kmph
(C) 176 kmph
(D) 134 kmph
(E) 161 kmph
Rationale: S = 180/12 * 18/5
= 54 kmph
Answer: A
Answer: (A) 54 kmph
Question: A number is doubled and 8 is added. If the resultant is trebled, it becomes 84. What is that number?
(A) 10
(B) 6
(C) 8
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let the number be x.
Then, 3(2x + 8)	‹=› 84
‹=› 2x+8 = 28
‹=› 2x= 20
x= 10.
Answer A
Answer: (A) 10
Question: If the height of a cone is increased by 100% then its volume is increased by?
(A) 100
(B) 777
(C) 998
(D) 729
(E) 2879
Rationale: 100%
Answer:A
Answer: (A) 100
Question: How many positive integers less than 120 are there such that they are multiples of 13 or multiples of 12 but not both?
(A) 13
(B) 19
(C) 15
(D) 16
(E) 17
Rationale: for 13: 13...117=13*9 = 117
for 12: 12...120=12*10 =120
but there is one integer 13*12. so
N=(9)+(10)=19
B
Answer: (B) 19
Question: A survey was sent to 75 customers, 7 of whom responded. Then the survey was redesigned and sent to another 60 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
(A) 2%
(B) 5%
(C) 14%
(D) 60%
(E) 73%
Rationale: Rate of first survey = 7/75
Rate of second survey = 9/60
% Response rate increase (9/60-7/75)/(7/75) = 60%
Answer is D = 60%
Answer: (D) 60%
Question: A committee is composed of w women and m men. If 3 women and 3 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by
(A) w/m
(B) w/(w+m)
(C) (w+3)/(m+3)
(D) (w+3)/(w+m+3)
(E) (w+3)/(w+m+6)
Rationale: The number of women is w+3.
The total number of people is w+m+6.
P(a woman is selected) = (w+3) / (w+m+6)
The answer is E.
Answer: (E) (w+3)/(w+m+6)
Question: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 20 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
(A) 1/125
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
Rationale: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 20/100 = 1/5
Three are independent;probability of rich and fair complexioned girl is:
(1/4) Ã—(1/5) Ã— (1/5) = 1/125
Answer: A
Answer: (A) 1/125
Question: If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number?
(A) 601
(B) 238
(C) 293
(D) 298
(E) 272
Rationale: If the word started with the letter A then the remaining 5 positions can be filled in 5! Ways.
If it started with c then the remaining 5 positions can be filled in 5! Ways.Similarly if it started with H,I,N the remaining 5 positions can be filled in 5! Ways.
If it started with S then the remaining position can be filled with A,C,H,I,N in alphabetical order as on dictionary.
The required word SACHIN can be obtained after the 5X5!=600 Ways i.e. SACHIN is the 601th letter.
Answer: A
Answer: (A) 601
Question: In a certain parking lot, 5% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
5%*x = 20%*y
y/x = 1/4 = 25%
The answer is B.
Answer: (B) 25%
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
(A) 4!*3!
(B) 3!*8!*4!*4!
(C) 3!*8!
(D) 5!*3!
(E) 8!*4!
Rationale: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
Ans: B
Answer: (B) 3!*8!*4!*4!
Question: How many even number in the range between 10 to 150 inclusive are not divisible by 3
(A) 15
(B) 30
(C) 31
(D) 33
(E) 47
Rationale: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
10,12,14...150
using AP formula, we can say 150 = 10 + (n-1) *2
or n=71.
For 6,
12,18,...96
using AP formula, we can say 150 = 12 + (n-1) *6
or n=24.
Hence, only divisible by 2 but not 3 = 71-24 = 47. hence, Answer E
Answer: (E) 47
Question: How many cases do you need if you have to pack 112 pairs of shoes into cases that each hold 28 shoes?
(A) 6
(B) 9
(C) 8
(D) 12
(E) 10
Rationale: C
8
112 pairs of shoes = 224 shoes.
= 224 ÷ 28
= 8.
Answer: (C) 8
Question: 6 points are marked on a straight line and another 5 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
(A) 21
(B) 91
(C) 168
(D) 196
(E) 135
Rationale: Solution: select 2 from 5 and one from 6 + select 2 from 6 and 1 from 5
5C2*6C1 + 6C2*5C1
= 135
Answer : E
Answer: (E) 135
Question: 4,7,11,18,29,47,...?..,123,199
(A) 84
(B) 102
(C) 76
(D) 70
(E) none of the above
Rationale: the addition of difference between each no. is equal to latter no.
so, difference between 47 and 76 is 29 which is previous no. of 47
answer C
Answer: (C) 76
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.60 a kg to produce a mixture worth Rs. 6.30 a kg
(A) 2:0
(B) 2:3
(C) 2:1
(D) 2:2
(E) 7:9
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 70 : 90 = 7 : 9
Answer: E
Answer: (E) 7:9
Question: We invested a total of $1,000. We invested one part of the money at 5% and the rest of the money at 6%. The total investment with interest at the end of the year was $1,054.50. How much money did we invest at 5%?
(A) $400
(B) $450
(C) $500
(D) $550
(E) $600
Rationale: Let x be the money invested at 5%.
1.05x+1.06(1000-x)=1054.50.
0.01x=1060-1054.50.
0.01x=5.50.
x=550.
The answer is D.
Answer: (D) $550
Question: James 5 days earnings are {500, 650, 750, 800, 850 }, how much less is the mean of the earnings of James than the median of the earnings of James?
(A) 50
(B) 55
(C) 60
(D) 40
(E) 85
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (500+ 650+ 750+ 800+ 850 )/5 = 710
Median = 750
Difference = 40
Option D
Answer: (D) 40
Question: Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations,and she can try 100 different possibilities,what is the probability that she does not pick the one correct combination.
(A) 1
(B) 159/160
(C) 0.975
(D) 0.775
(E) 0
Rationale: If Denise does not pick the correct combination in first 100 try, then the correct combination is one of remaining 3900. So Probability = 3900/4000 = 0.975.
answer is C.
Answer: (C) 0.975
Question: A metallic sheet is of rectangular shape with dimensions 50 m x 30 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 5 m, the volume of the box (in m cube) is:
(A) 4120 m cube
(B) 4140 m cube
(C) 5140 m cube
(D) 5120 m cube
(E) None of these
Rationale: Explanation:
l = (50 - 10)m =40 m, [because 5+5 = 10]
b = (30 -10)m = 20 m,
h = 5 m.
Volume of the box = (40 x 20 x 5) m cube
= 4000 m cube.
Option E
Answer: (E) None of these
Question: How many multiples of 6 are less than 3600, and also multiples of 36?
(A) 94
(B) 100
(C) 625
(D) 832
(E) 833
Rationale: The LCM of 6 and 36 is 36. Divide 3600/36 = 100.xxx. So B is your answer.
Answer: (B) 100
Question: A can finish a work in 12days and B can do the same work in half the time taken by A. Then, working together what part of the same work they can finish in a day?
(A) 1/2
(B) 1/3
(C) 2/5
(D) 1/4
(E) 3/7
Rationale: 1days work of A+B = (12+6)/12*6 = 1/4
Answer is D
Answer: (D) 1/4
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 40% are drinking beer, 30% are drinking mixed drinks, and 30% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
(A) 2/5
(B) 4/7
(C) 12/17
(D) 7/24
(E) 7/10
Rationale: Suppose there are 100 students
Group A : 40% = 40 students
40% drink beer = 16
30% mixed = 12
30% both = 12
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 16+18 =34 and both = 20
thus 24/34 = 12/17
Hence C
Answer: (C) 12/17
Question: V and B are integers. The expression (V+1)(B+1) is even. What can be said about V and B?
(A) They are both even numbers.
(B) At least one of them is even.
(C) At least one of them is odd.
(D) They are both odd.
(E) Nothing can be said surly on V and B
Rationale: Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (V+1) or (B+1) needs to be Even
So either V or B needs to be odd
Or At least one of them is odd.
At least one of them is odd=C
Answer: (C) At least one of them is odd.
Question: A certain company charges $10 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $10 plus $3 per pound. If the company charged $31 to ship a certain package, which of the following was the weight of the package, in pounds?
(A) 8
(B) 5
(C) 7
(D) 4
(E) 6
Rationale: Let the weight of the package be X. Then the cost is 3*X + 10= 31 ---> 3X=21 ---> X=7
Answer : C
Answer: (C) 7
Question: A mother said to her daughter, “I was as old as you are at now at the date of your birth.” If the mother’s age is 38 years now, the daughter’s age 5 years back was?
(A) 16 years
(B) 19 years
(C) 24 years
(D) 14 years
(E) 21 years
Rationale: D
14 years
Daughter’s current age = A years
Then, (38 – A) = A
2A = 38
A = 19 years
Daughter’s age Five years back = (19 – 5) years
= 14 years
Answer: (D) 14 years
Question: In the class of 100 students, 50 speak Hindi and 70 speak English. What is the lowest possible number of students who
speak both the languages?
(A) A)8
(B) B)10
(C) C)20
(D) D)30
(E) E)32
Rationale: let the student who speaks hindi-x
let the student who speaks english-y
as (xuy)-(xny)=total
50+70-(xny)=100
=20
C)
Answer: (C) C)20
Question: In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N?
(A) (N-M)
(B) MN/(M + N)
(C) (NM)
(D) (N-M)/(M+N)
(E) NONE OF THESE
Rationale: The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N).
Answer: B
Answer: (B) MN/(M + N)
Question: A batsman in his 10th innings makes a score of 85, and thereby increases his average by 3. What is his average after the 10th innings? He had never been ’not out’.
(A) 47
(B) 53
(C) 39
(D) 43
(E) 42
Rationale: Average score before 10th innings
= 85 - 3 × 10= 50
Average score after 10th innings
=> 50+ 3 = 53
ANSWER:B
Answer: (B) 53
Question: The sum of two numbers is 20 and their difference is 10. Find their product.
(A) 104
(B) 114
(C) 75
(D) 325
(E) 335
Rationale: Let the numbers be x and y.
Then x + y = 20 and x - y = 10
x = 15; y = 5
xy = 15 * 5 = 75
ANSWER: C
Answer: (C) 75
Question: Of the 150 people at a party, 70 were women, and 30 women tried the appetizer. If 60 people did not try the appetizer, what is the total number of men who tried the appetizer?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Total people at party=150
Women=70
so Men 150-70=80
No. of pple who tried appetizer=150-60 (given info)=90
No of women who tried appetizer=30
So Remaining ppl(men) who tried the appetizer =90-30=60
Correct Option C
Answer: (C) 60
Question: In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
40 = 20 + 30 + 10 - (10) - 2x
x = 5
So, answer will be A
Answer: (A) 5
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many ways can they selected that at least one boy should be there?
(A) 123
(B) 253
(C) 209
(D) 124
(E) 541
Rationale: We may have( 1 black and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4boys)
=(6c1 x 4c3)+(6c2 x 4c2)+(6c3 x 4c1)+6c4
=24+90+80+15
=209
ANS: C
Answer: (C) 209
Question: Rounded to three decimal places, 1.006^4 =
(A) 1.024
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016
Rationale: As compared to 1, 0.006 is a very small quantity. Thus, we can write (1+0.006)^4 is nearly equal to (1+4*0.006) = 1.024.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.
A.
Answer: (A) 1.024
Question: The least number which when add 3 to it, completely divided 8, 12 and 18 is?
(A) 71
(B) 70
(C) 69
(D) 68
(E) 67
Rationale: LCM = 72
72 - 3 = 69
ANSWER:C
Answer: (C) 69