mathewhe/aqua_rat huggingface dataset:
Question: Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 7 on the two dice?
(A) 7/12
(B) 5/12
(C) 11/36
(D) 7/36
(E) 5/36
Rationale: There are 36 possible outcomes for two dice.
The number of outcomes with an even number on the first die is 3*6=18.
The number of outcomes with a sum of 7 is 6.
We need to subtract the outcomes that have both an even number on the first die and a sum of 7 because we have counted those outcomes twice. This number of outcomes is 3.
The number of outcomes with either an even number on the first die or a sum of 7 is 18+6-3=21.
The probability is 21/36=7/12.
The answer is A.
Answer: (A) 7/12
Question: Submarine P and Submarine Q are equipped with sonar devices that can operate within a 5,000 yard range. Submarine P remains in place while Submarine Q moves 4,700 yards south from Submarine P. Submarine Q then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Q continue to move and still be within the sonar range of Submarine P? I. North II. South III. West
(A) I only
(B) I and III only
(C) II only
(D) III only
(E) I,II only
Rationale: It's evident if we make a diagram for the Movement of Q respect to P.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : B
Answer: (B) I and III only
Question: The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?
(A) 20 sq. ft
(B) 27 sq. ft
(C) 37 sq. ft
(D) 47 sq. ft
(E) 57 sq. ft
Rationale: Other side	=
15 2	- 9 2
2	2
ft
=
225	-	81
4	4
ft
=
144
4
ft
=	6 ft.
Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
B)
Answer: (B) 27 sq. ft
Question: A card is drawn from a pack of 52 cards. The probability of getting a face card?
(A) 2/15
(B) 2/13
(C) 1/15
(D) 4/13
(E) 5/7
Rationale: Clearly in the 52 cards out of which there are 16 face cards.
probability of getting a face card = 16/52 = 4/13
correct option is D
Answer: (D) 4/13
Question: A cube of edge 6 cm is cut into cubes each of edge 3 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
(A) 1:4
(B) 1:25
(C) 1:52
(D) 1:522
(E) None
Rationale: Sol.
Required ratio = 6 * 3 * 3 / 6 * 6 * 6 = 1/4= 1:4.
Answer A
Answer: (A) 1:4
Question: If shares of two persons in profits are Rs.400 and Rs.600 then ratio of their capitals is
(A) 3:4
(B) 2:3
(C) 4:3
(D) 1:3
(E) 1:5
Rationale: total profit =1000
ratio=400/600
=2:3
ANSWER:B
Answer: (B) 2:3
Question: 385, 462, 572, 396, 427, 671, 264
(A) 385
(B) 427
(C) 671
(D) 264
(E) None of these
Rationale: Solution
In each number except 427,the middle digit is the sum of the other two. Answer B
Answer: (B) 427
Question: Obra drove 200π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
(A) 6.67%
(B) 12.5%
(C) 41.66%
(D) 25%
(E) 33.3%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 200π/480π =41.66%
Hence, answer is C.
Answer: (C) 41.66%
Question: Can you find a number such that if we multiply that number by 1 or 2 or 3 or 4 or 5 or 6 , then the resultant number contains same all digits, different places
(A) 143857
(B) 142857
(C) 144857
(D) 142853
(E) 142854
Rationale: Correct Answer : B
142857 * 1= 142857
142857 * 2= 285714
142857 * 3= 428571
142857 * 4= 571428
142857 * 5= 714285
142857 * 6= 857142
Answer: (B) 142857
Question: The avg weight of A,B & C is 80 kg. If D joins the group, the avg weight of the group becomes 82 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 81 kg. What is the weight of A?
(A) 56
(B) 65
(C) 75
(D) 89
(E) 95
Rationale: A + B + C = 3 *80 = 240
A + B + C + D = 4 * 82 = 328 ---- (i)
So, D = 88& E = 88 + 3 = 91
B + C + D +E = 81 * 4 = 324 --- (ii)
From Eq. (i) & (ii)
A-E = 328 – 324 = 4
A = E +4 = 91 + 4 = 95
Answer : E
Answer: (E) 95
Question: Shaquan has 5 playing cards, each one is ordered by the number on it, but one card is flipped over.
They are numbered 8, 16, 24, x , 40. If X is the card flipped over, what number will be on the other side?
(A) 22
(B) 30
(C) 32
(D) 26
(E) 28
Rationale: The answer is C) 32 because the cards are numbered by multipliers of 8.
8x2 is 16,
8x3 is 24,
8x4 is 32,
and 8x5 is 40.
Answer: (C) 32
Question: A pair of articles was bought for $810 at a discount of 10%. What must be the marked price of each of the article?
(A) $300
(B) $500
(C) $350
(D) $450
(E) $600
Rationale: S.P. of each of the article = 810/2 = $405
Let M.P = $x
90% of x = 405
x = 405*100/90 =$450
Answer is D
Answer: (D) $450
Question: What is the probability that a number selected from number 1 to 30 is prime number,when each of the given numbers is equally likely to be selected?
(A) 10/30
(B) 20/30
(C) 1
(D) 5/30
(E) 15/30
Rationale: x={2,3,5,7,11,13,17,19,23,29}
n(x)=10
n(s)=30
Hence required probability=n(x)/n(s)=10/30
Option A is answer
Answer: (A) 10/30
Question: Carol is four times Alice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?
(A) 6
(B) 8
(C) 12
(D) 18
(E) 24
Rationale: ans B..8
given that C=4A=2B..AND A=C-12..=4A-12
substituting the values A=4, C=12 AND B=8..
Answer: (B) 8
Question: A certain manufacturer sells its products	to stores in 113 different	regions worldwide, with an average (arithmetic mean) of 182 stores per region. If last year these stores sold an	average of 51,752 units of the manufacturer’s product per store, which of the following is closest to the total number of units of manufacturer’s product	sold	worldwide last	year?
(A) 10^5
(B) 10^6
(C) 10^7
(D) 10^8
(E) 10^9
Rationale: 51752*182*113 or
51000*180*113 or
50000*200*100
=10^9
E
Answer: (E) 10^9
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
D
Answer: (D) 24
Question: Find odd one among 2,3, 4, 4, 6, 8, 9,12, 16 ?
(A) 9
(B) 8
(C) 77
(D) 65
(E) 212
Rationale: ANSWER: A
Answer: (A) 9
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $140
(B) $141
(C) $142
(D) $147
(E) $145
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
correct answer E)$145
Answer: (E) $145
Question: A bus 15 m long is running with a speed of 40 km/hr. In what time will it pass a man who is skateboarding at 8 km/hr in the direction opposite to that in which the car is going?
(A) 1.125
(B) 1.5
(C) 1.75
(D) 1.25
(E) 1
Rationale: Speed of bus relative to man = 40 + 8 = 48 km/hr.
= 48 * 5/18 = 40/3 m/sec.
Time taken to pass the man = 5 * 3/40
= 1.125 sec.
Answer: A
Answer: (A) 1.125
Question: The population of a town is 10000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
(A) 4300
(B) 4500
(C) 8100
(D) 5230
(E) 5366
Rationale: 10000 × 90/100 × 90/100 = 8100
Answer : C
Answer: (C) 8100
Question: A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?
(A) 30/100
(B) 32/100
(C) 35/100
(D) 41/100
(E) None of these
Rationale: Explanation :
Let A = Event that A speaks the truthB = Event that B speaks the truthThen P(A) = 75/100 = 3/4P(B) = 80/100 = 4/5P(A-lie) = 1-3/4 = 1/4P(B-lie) = 1-4/5 = 1/5Now ,A and B contradict each other =[A lies and B true] or [B true and B lies]= P(A).P(B-lie) + P(A-lie).P(B)= (3/5*1/5) + (1/4*4/5) = 7/20= (7/20 * 100) % = 35%
Answer : C
Answer: (C) 35/100
Question: The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $50 and other expenses per hous is $ 50, then what would be the minimum expenditure required to cover a distance of 500 Km?
(A) 800
(B) 950
(C) 900
(D) 1000
(E) 1250
Rationale: 50 kmph consumption is 1 lt/hr
so 500 km will take 10 hrs and the consumption is 10 lt for entire distance.
1 lt costs $50
so 10 lt costs $500
extra expenses for 1 hr - $50
10 hrs - $500
total expense - $500 + $500 = $1000
Answer : D
Answer: (D) 1000
Question: here are 5 Rock songs, 6 Karnatic songs and 3 Hindi pop songs. How many different albums can be formed using the above should contain at least 1 Rock song and 1 karnatic song?
(A) 45133
(B) 15384
(C) 63215
(D) 15624
(E) 45123
Rationale: There are 2n ways of choosing ‘n’ objects. For e.g. if n = 3, then the three objects can be chosen in the following 23 ways - 3C0 ways of choosing none of the three, 3C1 ways of choosing one out of the three, 3C2 ways of choosing two out of the three and 3C3 ways of choosing all three.
In the given problem, there are 5 Rock songs. We can choose them in 25 ways. However, as the problem states that the case where you do not choose a Rock song does not exist (at least one rock song has to be selected), it can be done in 25 - 1 = 32 - 1 = 31 ways.
Similarly, the 6 Carnatic songs, choosing at least one, can be selected in 26 - 1 = 64 - 1 = 63 ways.
And the 3 Indi pop can be selected in 23 = 8 ways. Here the option of not selecting even one Indi Pop is allowed.
Therefore, the total number of combinations = 31 * 63 * 8 = 15624
Ans: D
Answer: (D) 15624
Question: A person took some amount with some interest for 8 years, but increase the interest for 1%, he paid Rs.640/- extra, then how much amount he took?
(A) Rs.5500/-
(B) Rs.8000/-
(C) Rs.4000/-
(D) Rs.7000/-
(E) None of these
Rationale: Explanation:8 years = Rs.640/-year = 640/8Rate of Interest = 1%100/1% × 640/8 = Rs.8000/-P = Rs.8000/- Answer: Option B
Answer: (B) Rs.8000/-
Question: Machine A working alone can complete a job in 10 hours. Machine B working alone can do the same job in 12 hours. How long will it take both machines working together at their respective constant rates to complete the job?
(A) 50/11
(B) 60/11
(C) 40/11
(D) 47/11
(E) 57/15
Rationale: Machines ( A ) ( B ) (A+B)
---Time - 10 - ( 12 ) -
---Rate 12--- 10-- 22
--Work 120 --120 -120
A+B = (120/22) = 60/11
B
Answer: (B) 60/11
Question: The average of five natural numbers is 150. A particular number among the five exceeds another by 100. The rest three numbers lie between these two numbers and they are equal. How many different values can the largest number among the five take?
(A) 59
(B) 19
(C) 21
(D) 18
(E) 42
Rationale: We basically have 5 positive numbers - x, y, y, y, x+100 with sum = 750
so 2x + 3y = 650 and x<y<x+100.
Take extreme cases of inequality and we get for x=y case, 5x=650 so x = 130.
Another case, y=x+100, 5x+300 = 650. x=70.
BOTH THESE CASES are not allowed since y lies between x and x+100. But these are the bounds.
Once we have that, it is only a matter of finding the allowed values of x. (650-2x) should be divisible by 3, so changes allowed in x should be only in factors of 3. Start writing numbers from 73, 76....upto 127 and we get 19!
Answer is B,
Answer: (B) 19
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
(A) 1/5
(B) 1/7
(C) 1/0
(D) 1/2
(E) 1/3
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:B
Answer: (B) 1/7
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 70
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
(A) 51
(B) 88
(C) 90
(D) 125
(E) 108
Rationale: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 70 + (35-15) + (40-10-12) = 70+20+18 = 108
Hence, Answer will be E.
Answer: (E) 108
Question: A can do a work in 4 days. B can do the same work in 12 days. If both A & B are working together in how many days they will finish the work?
(A) 3
(B) 5
(C) 4
(D) 2
(E) 6
Rationale: A rate = 1/4
B rate = 1/16
(A+B) rate = (1/4)+(1/12) = 1/3
A & B finish the work in 3days
correct option is A
Answer: (A) 3
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 20 per square m?
(A) s.43000
(B) s.19000
(C) s.57000
(D) s.60000
(E) s.62000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 20 * 950
= Rs.19000
B
Answer: (B) s.19000
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
(A) 2277
(B) 2999
(C) 1000
(D) 2651
(E) 1971
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C
Answer: (C) 1000
Question: Convert the following unit:
4 hectares in mÂ²
(A) 50000 mÂ²
(B) 40000 mÂ²
(C) 60000 mÂ²
(D) 45000 mÂ²
(E) 55000 mÂ²
Rationale: 4 hectares in mÂ²
1 hectare = 10000 mÂ²
Therefore, 4 hectares = 4 Ã— 10000 mÂ²
= 40000 mÂ²
ANSWER : OPTION B
Answer: (B) 40000 mÂ²
Question: When 242 is divided by a certain divisor the remainder obtained is 6. When 698 is divided by the same divisor the remainder obtained is 13. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?
(A) 11
(B) 14
(C) 18
(D) 23
(E) None of these
Rationale: let that divisor be x
since remainder is 6 or 13 it means divisor is greater than 13.
now 242-6=236 =kx (k is an integer and 234 is divisble by x)
similarly 698-13=685 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (236+685)+6+13
=x(k+l) + 19
when we divide this number by x then remainder will be equal to remainder of (19 divided by x) = 5 hence x = 19-5 = 14
hence B
Answer: (B) 14
Question: Robinson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.49
(B) 0.52
(C) 0.48
(D) 0.6
(E) 0.45
Rationale: probability of adams approval = 0.7
baker approval =0.5
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4
=0.14+0.21+0.14
=0.49
A
Answer: (A) 0.49
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 112 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 98
(C) 105
(D) 120
(E) 210
Rationale: Set up equation:
x = total number of workers
112 = 0,4 * 2/3 * x + 0,8 * 1/3 * x
112 = 16/30 x
x = 210
210 - 112 = 98
Answer B
Answer: (B) 98
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?
(A) 17 hours
(B) 95 hours
(C) 14 hours
(D) 19 hours
(E) 18 hours
Rationale: Part filled in 2 hours = 2/6 = 1/3.
Remaining part = 1 - 1/3 = 2/3
(A + B)'s 1 hour work = 2/21
C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]
= (1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours.
Answer:C
Answer: (C) 14 hours
Question: Of the 6 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Given:
Total number of wires = 6
Number of cable wires = 2
Number of telephone wires = 3
To find:
Number of combination which has at least one cable wires
Solution:
No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2
Since it is a combination of wires, the arrangement is not important
Approach 1:
Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)
Selection 1
Number of ways of selecting one cable wire = 2C1 = 2
Number of ways of selecting 2 telephone wires = 3C2 = 3
Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 2
Number of ways of selecting one cable wire = 2C2 = 1
Number of ways of selecting 2 telephone wires = 3C1 = 3
Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire
Approach 2
Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)
Total number of ways of selecting 3 wires out of 5 = 5C2 = 10
Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1
Selection X - Selection Y = 8
Answer is Option C
Answer: (C) 8
Question: What will be the fraction of 12%
(A) 1/20
(B) 1/50
(C) 1/75
(D) 3/25
(E) None of these
Rationale: Explanation:
12*1/100 = 3/25.
Option D
Answer: (D) 3/25
Question: A rectangular circuit board is designed to have width w inches, perimeter p inches, and area n square inches. Which of the following equations must be true?
(A) w^2 + pw + n = 0
(B) w^2 - pw + 2n = 0
(C) 2w^2 + pw + 2n = 0
(D) 2w^2 - pw - 2n = 0
(E) 2w^2 - pw + 2n = 0
Rationale: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.
Now, assume:
Width =w = 1 inchand length = 1 inch;
Perimeter =p = 4 inches;
Area =n = 1 square inches.
Plug the values of w, p, and n into the answer choices: only for E 2w^2 - pw + 2n= 2 - 4 + 2 = 0.
Answer: E.
Answer: (E) 2w^2 - pw + 2n = 0
Question: A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 10 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?
(A) 2:5
(B) 3:5
(C) 2:3
(D) 3:2
(E) 7:13
Rationale: ............................... Milk ............... Water ....................... Total
Initial ...................... 24 .................... 16 .............................. 40
10 Lts mix. taken out 24-6 ............... 16-4 ........................... 40-10
10 Lts milk added..... 18+10 ................ 12 .............................. 40
20 Lts mix. taken out 28-14 ............... 12-6 ........................... 40-20
20 Lts water added..... 14................ 6+20 .............................. 40
New ratio = 14:26 = 7:13
E
Answer: (E) 7:13
Question: How many positive integers less than 5,000 are evenly divisible by neither 16 nor 21?
(A) 4,514
(B) 4,475
(C) 4,521
(D) 4,428
(E) 4,349
Rationale: integers less than 5000 divisible by 16 5000/16 =333.something , so 333
integers less than 5000 divisible by 21 5000/21 = 238.## , so 238
we have double counted some, so take LCM of 16 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 16 and 21 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4514 answer A.
Answer: (A) 4,514
Question: A special municipal payroll tax charges not tax on a payroll less than $250,000 and only 0.1% on a company’s payroll above $250,000. If Belfried Industries paid $200 in this special municipal payroll tax, then they must have had a payroll of
(A) $450,000
(B) $202,000
(C) $220,000
(D) $400,000
(E) $2,200,000
Rationale: ANSWER : A , ( with different approach) :
The 200 paid is 0.1% of the additional amount above 250,000. Let it be X
Now 0.1% of X = 200
Therefore X= 200,000
Total = 250,000 + X= 450,000
Answer: (A) $450,000
Question: If (m-8) is a factor of m^2-qm-24, then q=
(A) 3
(B) 5
(C) 6
(D) 11
(E) 16
Rationale: (m-8)(m-a)=m^2-qm-24
A=-3
q=8+a=5=B
Answer: (B) 5
Question: At a special sale, 6 tickets can be purchased for the price of 3 tickets. If 6 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 6 tickets?
(A) 20%
(B) 33.3%
(C) 40%
(D) 50%
(E) 66.6%
Rationale: let the price of a ticket be Rs.100, so 3 tickets cost 300 & 6 tickets cost 600
6 tickets purchased at price of 3 tickets ie., for 300, so amount saved s Rs.300,
% of 6 tickets = (300 /600)*100 =50 %
ANSWER:D
Answer: (D) 50%
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs. 40,000, the amount invested by Y is
(A) 33488
(B) 63809
(C) 60000
(D) 37887
(E) 77824
Rationale: Explanation:
Suppose Y invested Rs. y. Then 40000/y = 2/3 or y = 60000 .
Answer: C) 60000
Answer: (C) 60000
Question: There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
(A) 1/5
(B) 2/3
(C) 3/5
(D) 4/7
(E) 7/11
Rationale: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5
A
Answer: (A) 1/5
Question: If the three points A, B and C with the coordinates (4, 2), (3, 1) and (2, a) respectively lie on a line, what is the value of a?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The Line will have the same slope irrespective of which two points are taken into account
i.e. Slope of Line using Points (4, 2), (3, 1) = Slope of Line using Points (4, 2), (2, a)
CONCEPT: Slope between two points (a, b) and (c, d) = (d-b)/(c-a)
i.e. (1-2)/(3-4) = (a-2)/(2-4)
i.e. (a-2) = -2
i.e. a = 0
Answer: option A
Answer: (A) 0