divelab/Sys2Bench huggingface dataset:
Question: Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 30 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
Options:
A)1 hr 30 min
B)1 hr 45 min
C)2 hr
D)2 hr 20 min
E)3 hr
Rationale: Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3
second equation => M+2M =>1/30
converting it to hrs 3M=1/(30/60) =>1/(1/2) =>2
therefore M= 2/3 and P=2/3
Rate of Perry = 2/3
time= work/rate (work = 1 job)
Time= 1.5 hrs
Answer A
Answer: A
Question: Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 13 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
Options:
A)37.5 kilometers per hour
B)47.6 kilometers per hour
C)50 kilometers per hour
D)75 kilometers per hour
E)100 kilometers per hour
Rationale: Time taken to reach first 40 km is 40/60 = 2/3 hr
Time taken to reach next 40 km is 40/60 = 2/3 hr
Time taken to reach next 20 km is 20/60 = 1/3 hr
Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...
Each stop was of 13min , so two 13min break = 2*13/60 => 13/30 hr
Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+13/30 ) =21/10 hrs
So, Average speed is 100/(21/10) = 47.6km/hour
Answer will be B
Answer: B
Question: The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation?
Options:
A)1
B)5
C)7
D)8
E)11
Rationale: Let me define terms:
in g(p) = R
p is argument, R is result, g() is function,
in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification.
From definition of function g, we can deduce that:
If Result is even then two possibilities for argument = 1 Even 1 Odd
If Result is odd then one possibility for argument = 1 Even
Since final result = 19 = Odd
Possibilities:
g1:1 Even
g2: 1*(Even,Odd ) =1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8
Ans D it is!
Answer: D
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much Q does she have in her account after two years?
Options:
A)$10079.44
B)Q=$10815.83
C)$12652.61
D)$14232.14
E)$20598.11
Rationale: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%
Hence B the answer
Answer: B
Question: What is the least value of x. So that 30x55 is divisible by 3?
Options:
A)4
B)5
C)1
D)2
E)7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
3 + 0+ x + 5 + 5 = 13+ x
Least value of x may be 2
Therefore 13+ 2 = 15 is divisible by 3.
D
Answer: D
Question: For positive x and y if x/y is n% of y, then what percent must x be of y?
Options:
A)(y × n)%
B)(n/y)%
C)(√n)%
D)(n^2)%
E)(100 – n)%
Rationale: Solution -
The statement x/y is n% of y means that: x/y = (n / 100) × y
In order to find what percent must x be of y i.e., we need to divide x by y.
x/y %=(n / 100) × y *100 ---->(y*n)%
Therefore x/y is (y*n)%
ANSWER:A
Answer: A
Question: A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 800,000?
Options:
A)60
B)100
C)160
D)240
E)300
Rationale: The first digit and last digit are the same so the only possibility is 8.
The second and third digits can be any number from 0 to 9.
The total number of palindromic integers is 1*10*10 = 100
The answer is B.
Answer: B
Question: An amount of Rs.1560 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
Options:
A)Rs.390
B)Rs.368
C)Rs.380
D)Rs.360
E)Rs.311
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of C = 3/13 * 1560 = Rs. 360.
Answer: D
Answer: D
Question: There are some passengers riding on a bus. At the first stop, half the passengers get off and nobody gets on the bus. This pattern continues as the bus goes to the next stops. If only one passenger gets off at stop number 4, how many passengers were on the bus originally?
Options:
A)128
B)64
C)32
D)16
E)8
Rationale: Before stop 4, there were 2 passengers on the bus.
Before stop 3, there were 4 passengers on the bus.
Before stop 2, there were 8 passengers on the bus.
Before stop 1, there were 16 passengers on the bus.
The answer is D.
Answer: D
Question: In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 20% of the total number of children in the camp. How many more boys must she bring to make that happen?
Options:
A)35.
B)45.
C)40.
D)30.
E)25.
Rationale: Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to or 20%..
If we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it.
Now boys are 80% and girls are 20%. ( out of 100 students = 80 boys + 20 girls ).
IMO option A is correct.
Answer: A
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability taht the ticket drawn has a number which is a multiple of 3 or 5?
Options:
A)1/2
B)2/5
C)8/15
D)9/20
E)None
Rationale: Solution
Here S=(1,2,3,4,5,...,19,20).
Let E=event of getting a multiple of 3 or 5
= (3,6,9,12,15,18,5,10,20)
P(E)= n(E) / n(S)
= 9/20.
Answer D
Answer: D
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is?
Options:
A)2999
B)2778
C)7000
D)2889
E)6612
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 21000 = 7000
Answer:C
Answer: C
Question: The total cost of 100 paper plates and 200 paper cups is $4.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups?
Options:
A)$.90
B)$1.00
C)$1.20
D)$1.50
E)$1.60
Rationale: U dont need to go through all this
What u have with u is
100 P + 200 C = $4.50
Just divide the equation by 5 and you will get what u are looking for
20P + 40 C = $0.90
Therefore OA is A
Answer: A
Question: If two numbers are in the ratio 2:3. If 7 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)A)12
B)B)14
C)C)20
D)D)24
E)E)26
Rationale: 2:3
2x + 7 : 3x + 7 = 3 : 4
4[2x + 7] = 3[3x + 7]
8x + 28 = 9x + 21
9x - 8x = 28 - 21
x = 7
Then smallest number is = 2
2x = 14
Correct Option B
Answer: B
Question: What decimal of an hour is a second ?
Options:
A)0.00027
B)0.00029
C)0.00031
D)0.00025
E)0.00023
Rationale: Required decimal = 1/60x60 = 1/3600 = .00027
Answer is A.
Answer: A
Question: When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale?
Options:
A)17% increase
B)44% decrease
C)60% increase
D)66% increase
E)66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater.
ANSWER:A
Answer: A
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 7 robots altogether, if the robots build only one robot at a time?
Options:
A)70 1/7 min
B)94 1/7 min
C)110 1/7 min
D)112 1/7 min
E)131 1/7 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)
Now the 4 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 = 5/2
so they complete one robot in 2/5th of an hour - (3)
Now the 5 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2+1/2 = 3
so they complete one robot in 1/3th of an hour - (4)
Now the 6 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2
so they complete one robot in 2/5th of an hour - (5)
And now we have 7 robots
So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes
Answer - E
Answer: E
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 152 per Kg , the price of the third variety per Kg will be?
Options:
A)Rs. 147.50
B)Rs. 785.50
C)Rs. 174.50
D)Rs. 258.50
E)None of these
Rationale: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 152)
/ \
xâˆ’152 22.50
=>xâˆ’(152/22.50)=1.
=>xâˆ’152=22.50.
=>x= 174.50 Rs.
Answer : C
Answer: C
Question: One side of a triangle has length 5 and a second side has length 4. Which of the following could be the area of the triangle?
I. 15
II. 10
III. 5
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I, II and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 5 and 4 are the base and height of triangle .
Area = 1/2 * 5 * 4 = 10
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 10
The answer is D.
Answer: D
Question: One card is drawn from a pack of 52 cards. What is the probability that the card drawn is a ten or a spade?
Options:
A)3/7
B)4/13
C)4/15
D)7/19
E)11/31
Rationale: Out of 52 cards there will be 13 spades including 1 ten and there are 3 more tens. Total 16
probability= 16/52 = 4/13
Answer is B
Answer: B
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?
Options:
A) 120
B) 150
C) 180
D) 240
E) 600
Rationale: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
E
Answer: E
Question: There are m cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
Options:
A)n(n-1)
B)m(m-1)
C)n(n-1)/2
D)n(n+1)/2
E)n2
Rationale: First of all, the possible number of airlines is m. Then, the possible number of airlines departing from one city to another becomes (m-1). Hence, the answer is m(m-1), which makes A an answer choice.
B
Answer: B
Question: In how many ways can the integer 800 be expressed as a product of two different positive integers?
Options:
A)10
B)7
C)5
D)4
E)2
Rationale: 800=(2^5)*(5^2)
Since 800 is not a perfect square, no of ways=7
Answer B
Answer: B
Question: One day, Connie plays a game with a fair 6-sided die. Connie rolls the die until she rolls a 6, at
which point the game ends. If she rolls a 6 on her first turn, Connie wins 6 dollars. For each
subsequent turn, Connie wins 1
6 of the amount she would have won the previous turn. What is
Connie's expected earnings from the game?
Options:
A)32/31
B)33/31
C)34/31
D)36/31
E)0/31
Rationale: Connie has a 1
6 chance of winning 6 dollars her first turn. She has a 5/6
1/6 chance of
winning 1 dollar her second turn. Next, she has a 25
36
1/6 chance of winning 1/6 dollars her third turn.
Generalizing, Connie's expected earnings form a geometric series with initial term 1/6 *6 = 1 and
common ratio 5/6* 1/6 = 5/36 . Hence, Connie's expected earnings are
1/1- 5/36
=
36/31
correct answer D
Answer: D
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)Rs.6.00
B)Rs.5.50
C)Rs.5.00
D)Rs.7.00
E)Rs.8.00
Rationale: Answer: Option C
2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
average = 5
Answer: C
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 20,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got five times as many votes as the other candidate, how many people have voted in each round?
Options:
A)15,000
B)30,000
C)40,000
D)50,000
E)60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+20000 = 5(x-20000)
4x = 120000=>x=30000
2x=60000
IMO option E.
Answer: E
Question: The average weight of a group of boys is 30 kg. After a boy of weight 37 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Options:
A)A)4
B)B)8
C)C)6
D)D)2
E)E)1
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 37 kg joins the group, total weight of boys = 30x + 37
So 30x + 37 = 31(x + 1) = > x = 6.
Answer:C
Answer: C
Question: 6x – 5y + 3z = 23
4x + 8y – 11z = 7
5x – 6y + 2z = 11
Given the equations above, x + y + z = ?
Options:
A) 11
B) 12
C) 13
D) 14
E) 15
Rationale: (6x – 5y + 3z) - (5x – 6y + 2z ) = 23-11
or, x+y+z = 12
Option B is the ans
Answer: B
Question: If (1+z)y=y, which of the following must be true?
Options:
A)z=-1 or y=0
B)z=0 or y=-1
C)z=1 or y=1
D)z=-1 or y=-1
E)z=0 or y=0
Rationale: We have (1+z)y=y.
If x=0, y=y. True
If y=0, (1+z)*0=0 True
So, E will be the answer.
Answer: E
Question: Three coins are tossed. Find the probability of at least 2 tails ?
Options:
A)1/2
B)2/3
C)1/4
D)1/8
E)3/8
Rationale: n(s) = 2^3 = 8
let E is the event of getting at least 2 tails
n(E) = TTT, TTH , HTT, THT = 4
P(E) = n(E) / n(s)
= 4/8
= 1/2
Ans- A
Answer: A
Question: The amount of water (in ml) that should be added to reduce 12 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
Options:
A)8 ml
B)5 ml
C)4 ml
D)6 ml
E)1 ml
Rationale: 6 6
30% 70%
30% ----- 6
70% ------? => 14 - 6 = 8 ml
Answer:A
Answer: A
Question: Mary and Mike enter into a partnership by investing $550 and $450 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year?
Options:
A)$8000
B)$10000
C)$15000
D)$12000
E)$12500
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 5.5 : 4.5
i.e., 55% of 2x would go to Mary and 45% of 2x would go to Mike.
Hence, Mary would get (55 - 45)% of 2x more than Mike
Or10% of 2x = $1000
i.e.,(60/100)*2x = 1000
or 2x = 10000.
Hence, the profit made by the company during the year $3x = $15000.
Answer : C
Answer: C
Question: In an election, candidate A got 79% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.
Options:
A)357003
B)357090
C)37667
D)379888
E)287761
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357090
Answer:B
Answer: B
Question: A plane flies 660 km with the wind and 570 km against the wind in the same length of time. If the speed of the wind is 15 km/h, what is the speed of the plane in still air?
Options:
A)185 km/h
B)195 km/h
C)205 km/h
D)215 km/h
E)225 km/h
Rationale: The speed of the plane in still air = x km/h
The speed of the wind is 15 km/h
Speed with the wind = (x + 15) km/h
Speed against the wind = (x â€“ 15) km/h
Time = Distance/ Speed
660 / (x+15) = 570 / (x-15)
660(x-15) = 570(x+15)
66x - 990 = 57x + 855
9x = 1845
x = 205
Therefore, the speed of the plane in still air is 205 km/h.
The answer is C.
Answer: C
Question: Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
Options:
A)8/9
B)11/12
C)8/13
D)11/13
E)12/13
Rationale: We can take some easy numbers and make calculations simpler.
Let R ( Rex's income) = 100
Q (Quentin's income) = 40%R = 40
S (Sam's income) = 75% Q = (3/4)*40 = 30
Now, if Rex gives 40% to Quentin --> Q = 40 + 40 = 80
60% given to Sam --> S = 30+60 = 90
The ratio is : Q/S = 80/90 = 8/9
ANSWER:A
Answer: A
Question: Find 95 ×× 97
Options:
A)92/198
B)92/12
C)92/13
D)92/10
E)92/15
Rationale: Here both numbers are less than 100. So they are deficient of - 5 and - 3 compared with 100. So
Answer:	E
Answer: E
Question: What is the principal sum?
I. The sum amounts to Rs. 660 in 3 years at S.I.
II. The sum amounts to Rs. 700 at S.I.
III. The rate of interest is 6% p.a.
Options:
A)I and III only
B)II and III only
C)I and II only
D)Any two of the three
E)None of these
Rationale: Explanation:
Clearly, I and III is needed to solve this question where as II is not needed
Answer: A
Answer: A
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Options:
A)388
B)267
C)298
D)480
E)281
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480.Answer:D
Answer: D
Question: A shopkeeper wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10%. If his cost price is Rs. 95, then marked price is:
Options:
A)Rs. 100
B)Rs.110
C)Rs. 120
D)Rs. 130
E)None
Rationale: Solution: CP = Rs. 95.
Then SP = 95 + 10% of 95 = Rs. 104.5.
Let MP = X. He gives 5% commission on MP.
So,
SP = X - 5% of X
SP = 0.95X.
104.5 = 0.95X.
X = 104.5/0.95 = 110.
Thus, MP = Rs. 110.
Short-cut
95===10%(gain)===>104.5===5%(Commission)===>109.72( = 110)
Answer: Option B
Answer: B
Question: A and B together can do a work in 9 days. If A alone can do it in 18 days. In how many days can B alone do it?
Options:
A)10
B)99
C)18
D)55
E)21
Rationale: 1/9 – 1/18 = 1/18
=> 18
Answer: C
Answer: C
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 250. If legs are counted, there are 580. The number of hares in the zoo is?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: 250*2 = 500
580
-----
80
1----2
?----80 = 40
ANSWER:A
Answer: A
Question: The average age of 30 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher.
Options:
A)43
B)44
C)45
D)47
E)48
Rationale: Explanation:
If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15.
Age of teacher = Average age of all + Total increase in age
= 15 + (1 x 30 ) = 45 years
Answer:C
Answer: C
Question: There are 3 red paints and 1 white paint that can be mixed to make new red paint colors. The paints are labeled A for Red78/Red23, B for Red23/Red17, C for Red17/White001. When mixing the paint for the new paint Firehouse Red, the formula calls for 4A:1D. How many of each paint is in Firehouse Red?
Options:
A)none of the below options
B)one part White001 : four parts Red23
C)four parts Red78 : one part Red17
D)four parts Red23 : one part Red17
E)one part White001 : four parts Red78
Rationale: Solution
A : B = Red78 : Red23, B : C = Red23 : Red17, C : D = Red17 : White1
âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= Red78 : Red23 : Red17 : White001.
Thus, A : D = Red78 : White001
4A:1D = Red78, Red78, Red78, Red 78 : White001
Correct Option E
Answer: E
Question: A man can row 7.2 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
Options:
A)2.4 km/hr
B)12.5 km/hr
C)1 2.6 km/hr
D)22.5 km/hr
E)22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=7.2
3x = 14.4
x = 4.8
i.e., speed upstream = 4.8 km/hr
Rate of stream = 1/2(2x−x)=x/2=4.8/2=2.4 km/hr
Answer is A
Answer: A
Question: Two pipes A and B can fill a cistern in 75/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
Options:
A)5 min.
B)9 min.
C)10 min.
D)15 min
E)18 min
Rationale: If B is closed after x mins, then
30*2/75 + x/45 = 1
x/45 = 1 - 4/5 = 1/5
x= 45/5 = 9 mins
ANSWER:B
Answer: B
Question: During the months May through October, Teddy the bear sextuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
Options:
A)36m - 1300
B)36m - 1200
C)6m - 1300
D)6m - 1200
E)6m
Rationale: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 6m - 300
April' 75 = 6m - 400
Oct' 75 = 36m - 1200
April'76 = 36m - 1300
Hence answer will be (A) 36m - 1300
Answer: A
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 24m/h. what is the speedof the person while he was going to his office?
Options:
A)8km/h
B)10km/h
C)12km/h
D)16km/h
E)14km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=24
\inline \Rightarrow 1.5k = 24
\inline \Rightarrow k=16km/h
D
Answer: D