mathewhe/aqua_rat huggingface dataset:
Question: In how many ways can the letters of the word SPENCER be arranged if the S and P must always be together and the N and C must always be together?
(A) 12
(B) 24
(C) 60
(D) 120
(E) 240
Rationale: There are 7 letters in the word SPENCER are 2E , SP , NC , R
We will consider SP and NC as a group and there are 2 E's
No of arrangements in which S and P must always be together and the N and C must always be together
= (5! *2 *2)/2!
= 5!*2
= 120 *2
= 240
Answer E
Answer: (E) 240
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 26 seconds. The ratio of their speeds is?
(A) 3/1
(B) 9/1
(C) 3/3
(D) 3/5
(E) 5/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 26 ==> 27 x + 17 y = 26 x + 26 y
==> 1 x = 9 y ==> x/y
= 9/1.
Answer:B
Answer: (B) 9/1
Question: A person has to make 146 pieces of long bar. he take $ seconds to cut piece.what is total time taken by him to make 146 pieces?
(A) 580 seconds
(B) 680 seconds
(C) 500 seconds
(D) 540 seconds
(E) 560 seconds
Rationale: if it is 4 seconds, as u have mistaken with SHIFT key, then....
we'll have to make 145 cuts for 146 pieces.
so 145 * 5 = 580 seconds
ANSWER:A
Answer: (A) 580 seconds
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
(A) 17 litres
(B) 21.3 litres
(C) 11 litres
(D) 07 litres
(E) 38 litres
Rationale: 262.85(32)+3,104.35x = 1,399.45(32 + x)
Solve the equation.
262.85(32)+3,104.35x = 1,399.45(32 + x)
8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x
8,411.2 + 1,704.9x = 44,782.4
1,704.9x = 36,371.2
x ≈ 21.3
Answer is B.
Answer: (B) 21.3 litres
Question: The cost price of 14 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/91%
(B) 18 2/11%
(C) 27 3/11%
(D) 18 2/91%
(E) 12 2/11%
Rationale: 14 CP = 11 SP
11 --- 2 CP
100 --- ? =>27 3/11%
Answer:C
Answer: (C) 27 3/11%
Question: There are 7 Physics and 1 Chemistry book in shelf A and 5 Physics books in Shelf B, one book is moved from shelf A to shelf B. A student picks up a book from shelf B. Find the probability that the Chemistry book is taken by the student.
(A) 7/8
(B) 1/8
(C) 1/48
(D) 5/48
(E) 5/6
Rationale: I)Probability that the book moved from A to B is Chemistry=1/8.
II)Probability that the boom taken from B is Chemistry=1/6
P=1/8∗1/6=14/8
ANSWER: C
Answer: (C) 1/48
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 38
(B) 27
(C) 40
(D) 77
(E) 21
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: (C) 40
Question: Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 15hrs
(B) 20hrs
(C) 25hrs
(D) 30hrs
(E) 32hrs
Rationale: Part filled by A in 1 hour = 1/50
part filled by B in 1 hour = 1/75
Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30
Both the pipes will together will fill the tank in 30 hours.
Answer is D
Answer: (D) 30hrs
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:
(A) 240
(B) 120
(C) 280
(D) 160
(E) 200
Rationale: Let C's share = Rs. x
Then, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6
Therefore, x/6 + x/4 + x = 1360
=17x/12 = 1360
x = 1360 x 12/17= Rs. 960
Hence, B's share = Rs. (960/4)= Rs. 240.
Answer is A.
Answer: (A) 240
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/6%
(B) 16 3/3%
(C) 16 2/3%
(D) 16 2/9%
(E) 12 2/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: The average (arithmetic mean) of six numbers is 10. If 3 is subtracted from each of four of the numbers, what is the new average?
(A) 1.5
(B) 2
(C) 3
(D) 8
(E) 4.5
Rationale: Sum of 6 numbers = 6*10 =60
If 3 is subtracted from each of four of the numbers , we subtract 3*4=12 from the total sum
Sum of 6 number after subtracting 3 from each of four of the numbers = 60 - 12 = 48
New average = 48/6 = 8
Answer D
Answer: (D) 8
Question: The speeds of 3 trains in the ratio 2:4:6. The ratio between time taken by them to travel the same distance is?
(A) 6:4:3
(B) 1:2:3
(C) 4:8:9
(D) 6:3:2
(E) 4:8:7
Rationale: Ratio of time taken is = 1/2 : 1/4 : 1/6 = 6:3:2
Answer is D
Answer: (D) 6:3:2
Question: How many diagonals does a 62-sided convex polygon have?
(A) 1829
(B) 2356
(C) 3458
(D) 3843
(E) 4820
Rationale: A 62-sided convex polygon has 62 vertices.
If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829.
The answer is A.
Answer: (A) 1829
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 7 years, son's age will be:
(A) 12 years
(B) 14 years
(C) 18 years
(D) 20 years
(E) 21 years
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 7 years = (x+ 7) = 21 years..
Answer: E
Answer: (E) 21 years
Question: A person travels from P to Q a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
(A) 62.5
(B) 77
(C) 48
(D) 99
(E) 21
Rationale: Speed on return trip = 150% of 50 = 75 km/hr.
Average speed of trip = 50 + 75 /2 =125/2 = 62.5 km/hr
Answer : A
Answer: (A) 62.5
Question: Express 5 mps in kmph?
(A) 22
(B) 88
(C) 90
(D) 18
(E) 24
Rationale: 5 * 18/5 = 18 kmph
Answer: D
Answer: (D) 18
Question: In your classes you counted 126 hands. How many students were at the class?
(A) 63
(B) 61
(C) 85
(D) 86
(E) 88
Rationale: Total number of hands = 126
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 126 by 2
126 ÷ 2 = 63
Therefore, there were 63 students at the class.
ANSWER IS A
Answer: (A) 63
Question: A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after 1year service. He served only for 9 months and receiveduniform and Rs.650, find the priceof the uniform?
(A) Rs.90
(B) Rs.100
(C) Rs.120
(D) Rs.150
(E) Rs.160
Rationale: 9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
B
Answer: (B) Rs.100
Question: In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted?
(A) 72%
(B) 47%
(C) 42%
(D) 34%
(E) 28%
Rationale: Town A is 40%, therefore town B must be 60%
Town A registered voters:0.70∗0.40=0.28
Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent
ANSWER:B
Answer: (B) 47%
Question: A volunteer organization is recruiting new members. In the fall they manage to increase their number by 4%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
(A) 16.16%
(B) 15.76%
(C) 14.14%
(D) 13.13%
(E) 12.12%
Rationale: (100%+4%)*(100%-19%) = 1.04*.81 = 0.8424.
1-0.8424 = 15.76% lost = -15.76%
The Answer is B
The organization has lost 15.76% of its total volunteers from fall to spring.
Answer: (B) 15.76%
Question: Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?
(A) 1/3
(B) 1/5
(C) 1/6
(D) 1/7
(E) 2/5
Rationale: Total number of ways to go home, considering that the order order matters =
Options: SSSEEE
Slots : ------
total permutations of 6 options in 6 slots: 6P6 = 6! = 6*5*4*3*2
Total ways to select "South" in the first 2 positions and anything else in the subsequent 4 positions =
Options: SS ????
Slots: -- ----
Permutations of 3 "S" in 2 slots AND Permutations of 4 Choices in 4 slots =
3P2 * 4P4 = 3! * 4! = 3*2*4*3*2
The probability is therefore:
3P2 * 4P4 = 6P6
3*2*4*3*2= 1/5
ANSWER:B
Answer: (B) 1/5
Question: There are 4 more women than men on Centerville's board of education. If there are 4 members on the board, how many are women?
(A)  3
(B)  4
(C)  6
(D)  7
(E)  8
Rationale: Given: M=W-4 so, W+(W-4)=4 --> W=4.
Answer: B.
Answer: (B)  4
Question: If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?
(A) 25/√π
(B) 30/√π
(C) 20
(D) 25
(E) 30
Rationale: 60/360 = 1/6
1/6 of total area = 5
5/6 of total area = 5*5 =25
ANSWER:D
Answer: (D) 25
Question: What quantity of water should taken out to concentrate 27 liters of 40% acidic liquid to 60% acidic liquid?
(A) 5liters
(B) 10liters
(C) 15liters
(D) 9liters
(E) 6liters
Rationale: Required answer is = 27(60-40)/60 = 9 liters
Answer is D
Answer: (D) 9liters
Question: A rectangular grass field is 75 m * 55 m, it has a path of 3.2 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) s.1350
(B) s.1327
(C) s.1328
(D) s.1364
(E) s.1927
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +3.2 * 2) 2*2.5 => 682
682 * 2 = Rs.1364
Answer: D
Answer: (D) s.1364
Question: Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 6
II. 12
III. 24
(A) I, II, and III
(B) I and II only
(C) II and III only
(D) I and III only
(E) II only
Rationale: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Answer: (A) I, II, and III
Question: A 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
(A) 260m
(B) 220m
(C) 230m
(D) 240m
(E) 250m
Rationale: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+240/9=500/9
x=260
Ans is 260m
ANSWER: A
Answer: (A) 260m
Question: A rower can row upstream at 7 km/hr and downstream at 15 km/hr. What is the rower's rate in still water?
(A) 9 km/hr
(B) 10 km/hr
(C) 11 km/hr
(D) 12 km/hr
(E) 13 km/hr
Rationale: The rate in still water is 1/2 * (15 + 7) = 11 km/hr
The answer is C.
Answer: (C) 11 km/hr
Question: If W is the set of all the integers between 49 and 88, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 11
(B) 44
(C) 48
(D) 28
(E) 26
Rationale: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 87, the smallest is 51): 87 - 51 = 36
Step 2. Divide by 3: 36 / 3 = 12
Step 3. Add 1: 12 + 1 = 13.
So there are 13 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 88, the smallest is 50): 88 - 50 = 38
Step 2. Divide by 2: 38 / 2 = 19
Step 3. Add 1: 19 + 1 = 20.
So there are 19 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 13 multiples of 3 and the 19 multiples of 2: 13+19=32.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 13+19=32. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 32:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 84 - 54 = 30
Step 2. Divide by 6: 30 / 6 = 5
Step 3. Add 1: 5 + 1 = 6.
So there are 6 multiples of 6 within the range: we counted 6 numbers twice.
Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:
=13+19 - 6
= 32 - 6
= 26
Therefore, the final number of multiples of 2, 3 or 6 is 26.
Hence, this is the correct answer. (E)
Answer: (E) 26
Question: Two vertical pole of 2 m and 8 m stand apart on a horizontal plane.The height in meters at the point of intersection of the line joining the top of each pole to the bottom of other pole is ....
(A) 1.8
(B) 1.6
(C) 1.4
(D) 5.4
(E) cannot be determined without knowing the distance bw the bottom of the pole
Rationale: formula is...(p*q)/p+q
here p=2,q=8
height in meters=(8*2)/8+2=16/10=1.6
ANSWER:C
Answer: (C) 1.4
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 11
(B) 61
(C) 88
(D) 66
(E) 35
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer:E
Answer: (E) 35
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 760 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
(A) 191
(B) 190
(C) 193
(D) 212
(E) 213
Rationale: Total movies submitted are 760.
As per question we need to take 1/4 of 760 to be considered for top 10 movies = 190
approximate the value we 190.
IMO option B is the correct answer...
Answer: (B) 190
Question: If 4 people are selected from a group of 8 married couples, what is the probability that none of them would be married to each other?
(A) 1/33
(B) 2/33
(C) 8/13
(D) 16/33
(E) 11/12
Rationale: If we are to select 4 people from 8 couples WITHOUT any restriction, how many ways can we make the selection? 16!/4!12! = 1820
If we are to select 4 people from 8 couples WITH restriction that no married couple can both make it to the group, only a representative?
8!/4!4! = 70
But we know that to select a person from each couple, take 2 possibilities
70*2*2*2*2 = 1120
Probability = Desired/All Possibilities = 1120/1820 = 8/13
Answer: C
Answer: (C) 8/13
Question: The cost of 3 chairs and 10 tables is Rs 9856. What is the cost of 6 chairs and 20
tables?
(A) Rs 17227
(B) Rs 18712
(C) Rs 19172
(D) Rs 19712
(E) None
Rationale: Let the cost of one chair be Rs x and that of a table be = Rs y
According to the question,
3x + 10y = Rs 9856
⇒ 2 × (3x + 10y) = 2 × 9856
∴ 6x + 20y = Rs 19712
Answer D
Answer: (D) Rs 19712
Question: A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 7 times per hour, and both clocks chirp for the first time at 2:03 pm, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?
(A) 2:53 pm
(B) 3:03 pm
(C) 3:13 pm
(D) 3:23 pm
(E) 3:33 pm
Rationale: The question is asking when the first clock will have chirped 21 times (3*7 chirps).
The first clock chirps once every 3 minutes.
If the first chirp is at 2:03, then the 21st chirp is at 63 minutes after 2:00.
The answer is B.
Answer: (B) 3:03 pm
Question: How many cubes of 10cm edge can be put in a cubical box of 1m edge
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) 100000
Rationale: Number of cubes=(100x100x100)/(10x10x10)=1000 Answer: C) 1000
Answer: (C) 1000
Question: Which greatest possible length can be used to measure exactly 10 meter 40 cm, 14 meter 10 cm and 7 meter 90 cm
(A) 45cm
(B) 25cm
(C) 24cm
(D) 15cm
(E) 10cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1040 cm, 1410cm, 790cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 10.
Option E
Answer: (E) 10cm
Question: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).
How many subsets of the set {w, x, y, z} contain w?
(A) Four
(B) Five
(C) Seven
(D) Eight
(E) Sixteen
Rationale: The number of ways of selecting 0 or more from n elements is 2^n.
Hence here, once you select w , the number of ways of selecting 0 or more from x,y and z ( 3 elements) is 2^3 = 8.
The same applies for {w, x, y}. If you select w here, the number of ways of selecting 0 or more from x and y = 2^2 = 4
ANSWER:A
Answer: (A) Four
Question: The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 6!?
(A) 3(5!)
(B) 5(5!)
(C) 4(5!)
(D) 6(5!)
(E) 7(5!)
Rationale: GCF is the product of common factors of the numbers involved.
GCF = 5!
a = 6! = 6*5!
b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)
Looking at the answers only 5 (5!) and 6! will have GCF as 5!
Ans B
Answer: (B) 5(5!)
Question: There are twelve consecutive flags at an equal interval of distance. A man passes the 8th flag in 8 seconds. How many more seconds will he take to pass the remaining 4 flags ?
(A) 2.57 seconds
(B) 3.57 seconds
(C) 4.57 seconds
(D) 5.57 seconds
(E) 6.57 seconds
Rationale: let the 1st flag i placed at the origin and the remaining on the X-axis.......then the coordinate on 8th flag is (7,0)..therefore distance travelled is 7 units in 4 second ......and coordinate of 12th flag is (11,0)..there r 4 units ....so time taken is (8*4)/7=4.57 seconds
ANSWER:C
Answer: (C) 4.57 seconds
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
(A) 125/129
(B) 125/122
(C) 125/126
(D) 125/128
(E) 125/112
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer: C
Answer: (C) 125/126
Question: If a number is exactly divisible by 11 and 13, which of the following types the number must be?
(A) Divisible by (11 + 13)
(B) Divisible by (13 - 11)
(C) Divisible by (11 x 13)
(D) Divisible by (13 ÷ 11)
(E) None
Rationale: Answer
LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13).
Correct Option: C
Answer: (C) Divisible by (11 x 13)
Question: A dance delegation of 4 people must be chosen from 5 pairs of dance partners. If 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?
(A) 20
(B) 30
(C) 60
(D) 70
(E) 80
Rationale: Since 2 dance partners can never be together, lets select 4 pairs from 5 pairs of dance partners to fill the 4 positions. Now, in each position, each pair can be selected in 2 different ways.
Therefore number of ways of forming a delegation such that the 2 dance partners are never together = 5C4*(2C1)^4 = 5 * 16 = 80
Answer: E
Answer: (E) 80
Question: If x = 1- 2t and y = 2t - 2, then for what value of t does x = y?
(A)  5/2
(B)  3/2
(C)  3/4
(D)  2/5
(E)  0
Rationale: We are given x = 1 – 2t and y = 2t – 2, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 2t for x and 2t – 2 for y in the equation x = y. This gives us:
1 – 2t = 2t – 2
3 = 4t
3/4 = t
The answer is C.
Answer: (C)  3/4
Question: If x and y are positive integers, and 4x^2=2y, then which of the following must be a multiple of 9?
I. x^2
II. y^2
III. xy
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: 4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is B
Answer: (B) II only
Question: The average (arithmetic mean) of 20, 40, and 60 is 8 more than the average of 10, 70, and what number?
(A) 16
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: a1 = 120/3 = 40
a2 = a1 -8 = 32
sum of second list = 32*3 = 96
therefore the number = 96 -80 = 16
ANSWER:A
Answer: (A) 16
Question: Anil had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product?
(A) 1590
(B) 1600
(C) 1950
(D) 1630
(E) 1760
Rationale: Explanation :
Let the number that Anil wanted to multiply be 'Y'.
He was expected to find the value of 35Y.
Instead, he found the value of 53Y.
The difference between the value that he got (53Y) and what he was expected to get (35Y) is 540.
=> 53Y - 35Y = 540
=> (53 - 35) * Y = 540
=> Y = 30
Therefore, the correct product = 53 * 30 = 1590
Answer : A
Answer: (A) 1590
Question: Murali travelled from city A to city B at a speed of 50 kmph and from city B to city C at 50 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/50 + (3x)/50
= (2x + 3x)/50 = 5x/100
= x/20 Average speed
= (2x + 3x)/(x/20) = 100 kmph.
Answer: B
Answer: (B) kmph
Question: A city council will select 2 of 9 available firefighters and 1 of 4 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
(A) 36
(B) 72
(C) 144
(D) 216
(E) 432
Rationale: OA D
9C2 * 4C1
using the combination formula to choose 2 from 9 and 1 from 4
C
Answer: (C) 144
Question: you need to pict any number from 1, 3,5,7,9,11,13 and 15 to make below equation true.
()+()+()=30
can you solve it?
(A) 7+15+9
(B) 6+15+9
(C) 6+14+9
(D) 6+15+8
(E) 8+15+9
Rationale: Correct Answer : B
3x+15+9=30
3x =3*2*1 =6
therefore :- 6+15+9= 30
Answer: (B) 6+15+9