mathewhe/aqua_rat huggingface dataset:
Question: In how many ways Chief Minister and Minister be elected from a team of 6 members?
(A) 28
(B) 20
(C) 36
(D) 30
(E) 32
Rationale: To do this, if captain is elected first, then we have 6 ways of doing this.
For election of vice-captain, we have only 5 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 6*5 = 30 ways.
D
Answer: (D) 30
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 2 min, then the length of the tunnel is?
(A) 2898
(B) 1800
(C) 500
(D) 297
(E) 435
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 2 min = 120 sec.
Let the length of the train be x meters.
Then, (800 + x)/120 = 65/3
x = 1800 m.
Answer: B
Answer: (B) 1800
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 80 miles apart. One and a half hours later, they are again 80 miles apart, driving away from each other. If Otto drives at a speed of m miles per hour, then, in terms of m, Han drives at a speed of how many miles per hour?
(A) a) 106.67-m
(B) b) 40-m
(C) c) 80-2m
(D) d) 120-m
(E) e) 40-m/2
Rationale: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 60 mi, then move away from each other another distance of 60 miles. That's a total distance of 160 miles in 1.5 hr, which gives a rate of:
R = (160 mi)/(1.5) = 106.67 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is m, and let's call the other n. We want n.
m + n = 106.67
n = 106.67 - m
Answer =(A)
Answer: (A) a) 106.67-m
Question: The no. of girls in a class are 7times the no. of boys, which value cannever be the of total students?
(A) 20
(B) 35
(C) 30
(D) 40
(E) 42
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: (C) 30
Question: The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 150 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
(A) 30
(B) 50
(C) 70
(D) 80
(E) 90
Rationale: Let x be the number of new boarders.
The ratio changed from 5:12 up to 1:2 = 6:12.
150 / (150+x) = 5/6
x = 30
The answer is A.
Answer: (A) 30
Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there ?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Explanation:
Let number of horses = number of men = x.
Then, number of legs = 4x + 2 x (x/2) = 5x.
So, 5X = 70 or x = 14.
Answer: C
Answer: (C) 14
Question: Look at this series: 544, 509, 474, 439, ... What number should come next?
(A) 206
(B) 408
(C) 306
(D) 507
(E) 404
Rationale: E
404
This is a simple subtraction series. Each number is 35 less than the previous number.
Answer: (E) 404
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (5,7), (12,7), (2,3), (9,3) ?
(A) 21
(B) 28.
(C) 35.
(D) 49.
(E) 52.
Rationale: Area of parallelogram = b*h.
Base = Distance in x coordinates between (2,3) and (9,3) = 7
Height = Difference in y coordinates between (5,7) and (2,3) = 3.
Area = 7*3 = 21.
ANSWER:A
Answer: (A) 21
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 7.2
(B) 4.2
(C) 6.1
(D) 7.2
(E) 8.2
Rationale: Explanation:
distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time = 600/300 = 2m/s
= 2×185 km/hr = 365 km/hr = 7.2 km/hr
Answer: Option A
Answer: (A) 7.2
Question: A photo-mat shop charges $0.50 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos?
(A) 2 films and 6 photos
(B) 5 films and 6 photos
(C) 5 films and 14 photos
(D) 6 films and 4 photos
(E) 6 films and 28 photos
Rationale: 1st photo = 0.50
Subsequent = 0.50*0.6=0.3
Price of 1 full film=0.50+0.3*35=11
Price of 2 full film = 11*2=22
24-22=2
2=0.5+0.3x
x=5
24--->2 full films and 1+5=6 photos
Answer: A
Answer: (A) 2 films and 6 photos
Question: In the Biotechnology class of 2000, there were Q graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is Q equal to?
(A) 69.
(B) 71.
(C) 73.
(D) 75.
(E) 76.
Rationale: Total = 32 +45 -13 +9 = 73 .... My first post on the forum... I hope I am correct
C is correct choice.
Answer: (C) 73.
Question: The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is
(A) 1677
(B) 1683
(C) 2523
(D) 3363
(E) None of these
Rationale: Explanation:
L.C.M of 5, 6, 7, 8 = 840
therefore Required Number is of the form 840k+3.
Least value of k for which (840k+3) is divisible by 9 is k = 2
therefore Required Number = (840 x 2+3)=1683. Answer: B
Answer: (B) 1683
Question: A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
(A) 300 m
(B) 400 m
(C) 200 m
(D) 100 m
(E) 700 m
Rationale: Speed=40 km/hr =40Ã—5/18=100/9 m/s
Time =18 seconds
Distance Covered
=100/9Ã—18
=200 m
Therefore, length of the train =200 m
Answer: C
Answer: (C) 200 m
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.
(A) 1/128
(B) 1/127
(C) 1/125
(D) 1/121
(E) 1/126
Rationale: Explanation:
Out of nine, five are good and four are defective. Required probability
= 4C4/9C4 = 1/126
Answer: E
Answer: (E) 1/126
Question: The price of a book is increased from $300 to $330. What is the % of increase in its price?
(A) 10%
(B) 20%
(C) 40%
(D) 50%
(E) 60%
Rationale: Explanation: Change in the price = Rs 330 â€“ Rs 300
= Rs 30
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 30 300
) *100 = 10%
A
Answer: (A) 10%
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability y that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: In order to determine the probability y that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Answer: (D)  68.75%
Question: For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence -1, -3, 2,-5, 4, -6,10,-3?
(A) 6
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.
-3*2=-6=negative;
2 * -5 = -10 > negative
-5*(4)=-20=negative.
4 * (-6) = -24 > negative
-6 * 10 = -60 > negative
-3 * 10 = -30 > negative
So there are 6 pairs of consecutive terms.
Answer: A.
Answer: (A) 6
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer: A
Answer: (A) 4
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $40 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
(A) $5
(B) $10
(C) $14
(D) $4
(E) $28
Rationale: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $40
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 40
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 40
i.e. x = 36
i.e. Fixed Monthly Charge, y = 4
Answer: Option
D
Answer: (D) $4
Question: On sport’s day, if 12 children were made to stand in each column, 98 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed ? After a certain music being played the plan was that the children have to stand in concentric circles such that the innermost circle will have one student, the next circle will have two students, the third circle will have 3 students and so on. How many circles will be formed in this manner.
(A) 48
(B) 20
(C) 50
(D) 29
(E) 19
Rationale: no of students will be 98*12=1176
let us consider n circles then 1+2+3+....+n=1176
n(n+1)/2=1176
n=48 circles
ANSWER:A
Answer: (A) 48
Question: How many 5 no. digit no. can be formed with digits 1,2,3,4,5,6 which are divisible by 4 and digits not repeated
(A) 144
(B) 168
(C) 192
(D) 186
(E) none
Rationale: last 2 digits can be 12,16,24,32,36,52,56,64.
so total possible 5 digit numbers = 8*4*3*2= 192 numbers
ANSWER:C
Answer: (C) 192
Question: If log3N+log9Nlog3N+log9N is whole number, then how many numbers possible for N between 100 to 100?
(A) 1, 9, 81
(B) 1, 9, 89
(C) 1, 9, 88
(D) 1, 9, 22
(E) 1, 9, 11
Rationale: log3N+log9Nlog3N+log9N = log3N+log32Nlog3N+log32N = log3N+12log3Nlog3N+12log3N =32log3N32log3N
Now this value should be whole number.
Let 32log3N32log3N = w
⇒log3N=23w⇒log3N=23w
N=3(23w)N=3(23w)
As N is a positive integer, So for w = 0, 3, 6 we get N = 1, 9, 81.
Answer:A
Answer: (A) 1, 9, 81
Question: The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is
(A) 33
(B) 278
(C) 75
(D) 978
(E) 27
Rationale: Explanation:
The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.
Answer: C) 75
Answer: (C) 75
Question: 6000, 1200, 300, 60...
(A) 30
(B) 15
(C) 20
(D) 36
(E) 46
Rationale: 6000/5=1200
1200/4=300
300/5=60
60/4=15
ANSWER:B
Answer: (B) 15
Question: Which of the following describes all values of x for which 9-x^2 ≥ 0 ?
(A) x ≥ 1
(B) x ≤ -1
(C) 0 ≤ x ≤ 1
(D) x ≤ -1 or x ≥ 1
(E) -3 ≤ x ≤ 3
Rationale: 9-x^2 >= 0 ---> x^2-9<=0
--> (x+3)(x-3)<=0
Above equation true for
i) x+3<=0 and x-3>=0 ---> x<= -3 and x>=3 ---> this is not possible ---Strike out this solution
ii) x+3>=0 and x-3<=0 ---> x>=-3 and x<=3 --> -3<=x<=3
Answer E
Answer: (E) -3 ≤ x ≤ 3
Question: A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.
(A) 100
(B) 110
(C) 120
(D) 140
(E) None of above
Rationale: In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.x/6 = (30+x)/8x = 90. So distance from start after which B will catch A = 90+30 =120km Answer : C
Answer: (C) 120
Question: The surface of a cube is 150sq cm. Find its volume?
(A) 8cc
(B) 9cc
(C) 125cc
(D) 4cc
(E) 6cc
Rationale: 6a2 = 150 = 6*25
a = 5 => a3 = 125cc
Answer: C
Answer: (C) 125cc
Question: The sum of four consecutive even numbers is 292. What would be the smallest number?
(A) 22
(B) 27
(C) 70
(D) 28
(E) 11
Rationale: Explanation:
Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
Answer: C
Answer: (C) 70
Question: The present population of a town is 3456. Population increase rate is 20% p.a. Find the population of town before 2 years?
(A) 2400
(B) 2100
(C) 3500
(D) 3600
(E) 2050
Rationale: P = 3456
R = 20%
Required population of town = P/(1 + R/100)^T
= 3456/(1 + 20/100)^2
= 3456/(6/5)^2
= 2400(approximately)
Answer is A
Answer: (A) 2400
Question: Average of 10 matches is 32, How many runs one should should score to increase his average by 3 runs.
(A) A)65
(B) B)76
(C) C)78
(D) D)80
(E) E)88
Rationale: Explanation:
Average after 11 innings should be 35
So, Required score = (11 * 35) - (10 * 32)
= 385 - 320 = 65
Answer: Option A
Answer: (A) A)65
Question: Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 22
(B) 16
(C) 27
(D) 28
(E) 20
Rationale: Speed Ratio = 1:4/3 = 3:4
Time Ratio = 4:3
1 -------- 4
4 --------- ? 16 m.Answer:B
Answer: (B) 16
Question: The population of a town increases by 12% during first year and decreased by 10% during second year. If the present population is 50,400, what it was 2 years ago?
(A) 40,000
(B) 35,000
(C) 50,000
(D) 60,000
(E) none of these
Rationale: Here A = 50400, x = 12, y = - 10
Therefore, the population 2 years ago
= A /[( 1 + x/100) ( 1 + y/100)]
= 50400 / [( 1 + 12/100) ( 1 - 10/100)]
= (50400 x 100 x 100) / (112 x 90)
= 50,000.
ANSWER:C
Answer: (C) 50,000
Question: A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability Y that all 3 jellybeans removed from the bag are blue?
(A) 9/100
(B) 2/19
(C) 1/8
(D) 3/20
(E) 3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability Y= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B
Answer: (B) 2/19
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
(A) 1500
(B) 1300
(C) 1200
(D) 1000
(E) 5000
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
ANSWER D
Answer: (D) 1000
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
(A) 6 hrs 21 min
(B) 6 hrs 71 min
(C) 6 hrs 32 min
(D) 6 hrs 27 min
(E) 6 hrs 23 min
Rationale: Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer:A
Answer: (A) 6 hrs 21 min
Question: Bert left the house with N dollars. He spent 1/3 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $10.50 left in his pocket. What was the value of N?
(A) $42
(B) $44
(C) $52
(D) $60
(E) $68
Rationale: started to test answer A
if he had 42, then he spent 13 2/3 at hardware store
now he was left with 27 1/3$
he spent 7 dollars on cleaning, thus he remained with 20 1/3$
he then spent 1/2 of 20 1/3 or 10.5,
hence,right OPTION is A.
Answer: (A) $42
Question: The average weight of 49 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?
(A) 51 1⁄3
(B) 52 30/49
(C) 52 1⁄49
(D) 43.42
(E) None of these
Rationale: Total weight of 49 students
= 49 × 52 = 2548 kg
Total weight of 5 students who leave
= 5 × 48 = 240 kg
Total weight of 5 students who join
= 5 × 54 = 270 kg
Therefore, new total weight of 49 students
= 2548 – 240 + 270 = 2578
⇒ New average weight = 2578⁄49 = 52 30/49 kg
Answer B
Answer: (B) 52 30/49
Question: Seven children â€” A, B, C, D, E, F, and G â€” are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?
(A) 240
(B) 480
(C) 720
(D) 1440
(E) 3600
Rationale: There are five different â€œthree in a rowâ€ locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B â€” just those two orders. This means the total number of configurations for these three children is 5*2 = 10.
Now, consider the non-restricted elements, the other four. Once A & B & G are seated, the remaining four children can be seated in any order among the remaining four seats â€” thatâ€™s a permutation of the 4 items â€”- 4P4 = 4! = 24. For any single configuration of A & B & G, there are 24 ways that the other children could be seated in the remaining seats.
Finally, weâ€™ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. Thatâ€™s a total number of configurations of 24*10 = 240. Answer = A
Answer: (A) 240
Question: Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number?
(A) 6/3
(B) 3/8
(C) 1/2
(D) 5/8
(E) 1/8
Rationale: There are 4! i.e. 24 ways in which four objects can be arranged in four places. There are a total of 9 instances where the objects are not occupying the place corresponding to the given number. They are as follows:
(2, 1, 4, 3) (2, 3, 4, 1) (2, 4, 1, 3) (3, 1, 4, 2) (3, 4, 1, 2) (3, 4, 2, 1) (4, 1, 2, 3) (4, 3, 1, 2) (4, 3, 2, 1)
Hence, the required probability = 9/24 = 3/8.
ANSWER:B
Answer: (B) 3/8
Question: In order to fulfill a local school’s request for x cakes, a parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?
(A) px/a
(B) px/(a(a-p))
(C) px
(D) pxa
(E) px(p-a)
Rationale: No of cakes each parent has to bake : x/a
No of parents did not bake cake = p
No of cakes that were not baked by p parents = p*x/a
No of parents has to bake additional cakes = a-p
additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(a(a - p))
Answer B
Answer: (B) px/(a(a-p))
Question: By selling a watch for Rs.720/-, a man loses 20% what is that watch cost price?
(A) s. 600/-
(B) s. 700/-
(C) s. 800/-
(D) s. 850/-
(E) s. 900/-
Rationale: 80 % ------> 720 (80 * 9= 720)
100 % ------>900 (100 * 9 = 900)
Cost price = Rs. 900/-
E)
Answer: (E) s. 900/-
Question: What is the difference between local value & face value of 6 in the numeral 65793?
(A) 58453
(B) 58956
(C) 58994
(D) 59894
(E) 59994
Rationale: (Local value of 6) - (Face value of 6)
= (60000 - 6) = 59994
E
Answer: (E) 59994
Question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
(A) 7 kmph
(B) 8 kmph
(C) 9 kmph
(D) 7 kmph
(E) 6 kmph
Rationale: Speed in still water = (10 + 4)1/2 kmph = 7 kmph.
answer :A
Answer: (A) 7 kmph
Question: Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-2) = 0, then b + c =
(A) 18
(B) 15
(C) -16
(D) -21
(E) -24
Rationale: f(x) = x^2 + bx + c. If f(6) = 0 and f(-2) = 0, then b + c =
f(6) = 0= 36+6b+c--- Taking 36 to the other side
-> 6b+c= -36
f(-2) =0= 4-2b+c --- taking -2b+c to the other side
-> 2b-c=4
When we add these 2 equations, we get 8b= -32---> b= -4
And while substituting b= -4 we get c= -12.
b+c= -16--- Answer C
Answer: (C) -16
Question: If 9^y = 3^16, what is y?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: 9^y = 3^2y = 3^16
2y=16
y = 8
The answer is E.
Answer: (E) 8
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
(A) 20 min
(B) 30 min
(C) 45 min
(D) 40 min
(E) 70 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: (D) 40 min
Question: The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.9.00, Rs.7.00, Rs.4.50 and Rs.5.50 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 20 rupees notes on the counter payment. How many notes did Rahul give?
(A) 8
(B) 9
(C) 10
(D) 9
(E) 13
Rationale: Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=> 5a + 5b + 10c + 10d = 20*x.
=> a + b + 2(c+d) = 4 * x . -----------------------------(i)
Since, a + b = 9+7 = 16
And,
=> c + d = 4.50+5.50= 10 .
Putting these values in (i), we get :-
=> 16 + 2 *10 = 4 * x.
=> x = 9 .
Answer : D
Answer: (D) 9
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.76 less, he could have gained 25%. What is the cost price?
(A) s.380
(B) s.375
(C) s.375
(D) s.350
(E) s.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
76 ----- ? => 380
ANSWER:A
Answer: (A) s.380