divelab/Sys2Bench huggingface dataset:
Question: The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1980 in revenue from the sales. How many orchestra tickets did they sell?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Let x be the number of orchestra tickets.
Then 90-x is the number of upper tier tickets.
30x + 12(90-x) = 1980
18x = 1980-1080
x = 50
The answer is D.
Answer: D
Question: If, 6 years ago, Jamie was half as old as he is now, how old will he be in x years?
Options:
A)x + 12
B)x + 5
C)x + 2
D)x – 5
E)2x
Rationale: let his age be a. a-6=a/2 hence a=12. 12 years hence, a =x+12
Answer A
Answer: A
Question: Evaluate: 20 - 16÷4×3 =
Options:
A)16
B)10
C)4
D)8
E)6
Rationale: According to order of operations, 16÷4×3 (division and multiplication) is done first from left to right
16÷4×3 = 4 × 3 = 12
Hence
20 - 16÷4×3 = 20 - 12 = 8
correct answer D) 8
Answer: D
Question: The incomes of A and B are in the ratio 3:2 and their expenditure are in ratio 5:3. If each saves Rs. 1000, then, A's income can be:
Options:
A)Rs. 3000
B)Rs. 4000
C)Rs. 6000
D)Rs. 9000
E)Rs. 4500
Rationale: Solution: Let income of A and B be 3x and 2x respectively. Also, their expenditure is 5y and 3y.
Now, according to question,
3x-5y = 1000 ------- (i)*3
2x-3y = 1000	---------- (ii)*5
9x-15y-10x+15y = 3000-5000;
Or, -x = -2000;
Or, x = 2000;
Then, income of A = 3x = 3*2000 = Rs. 6000.
Answer: Option C
Answer: C
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 6 days and B in 18 days, then C alone can do it in?
Options:
A)1
B)7
C)8
D)9
E)36
Rationale: C = 1/4 - 1/6 – 1/18 = 1/36 => 36 days'
Answer: E
Answer: E
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent W of her bushes have only yellow roses?
Options:
A)20
B)30
C)50
D)70
E)80
Rationale: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, W=0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers
OA B
Answer: B
Question: A shopkeeper fixes the marked price of an item 25% above its cost price. The percentage of discount allowed to gain 8% is
Options:
A)11.59%
B)12.59%
C)13.59%
D)14.59%
E)None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 125
Required gain = 8%,
So Selling price = Rs 108
Discount = 125 - 108 = 17
Discount% = (17/135)*100 = 12.59%
Option B
Answer: B
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Options:
A)23
B)5
C)9
D)28
E)6
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
ANSWER C
Answer: C
Question: 2 persons can finish a job in 8 days. First person alone can finish the work in 24 days. How many days does the second person take to finish the job?
Options:
A)10 days
B)12 days
C)14 days
D)16 days
E)18 days
Rationale: 2 persons can do work in 1 day = 1/8
First person can do work in 1 day = 1/24
Second person can do work in 1 day = 1/8-1/24 = 1/12
So Second person can finish work in 12 days
ANSWER:B
Answer: B
Question: Mother, daughter and an infant combined age is 74, and mother's age is 46 more than daughter and infant. If infant age is 0.4 times of daughter age, then find daughters age.
Options:
A)22
B)10
C)37
D)38
E)32
Rationale: Assume M + D + I = 74; .................(1)
Also given M - D - I = 46 ⇒⇒ M = D + I + 46
Also I = 0.4 D ⇒⇒ I = 2/5 D
Substituting M and I values in the first equation we get D - 2525D - 46 + D + 2525D = 74
Solving D = 10
Answer:B
Answer: B
Question: On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 125 + 83d = 90(d+1).
7d = 35.
d = 5.
The answer is B.
Answer: B
Question: Walking at 8KMPH From Point T to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point T to Railway station?
Options:
A)A)9KM
B)B)6.66KM
C)C)7.25KM
D)D)12.40KM
E)E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point T and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point T and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: B
Question: A number is doubled and 7 is added. If resultant is trebled, it becomes 99. What is that number
Options:
A)8
B)10
C)14
D)13
E)16
Rationale: Explanation:
=> 3(2x+7) = 99
=> 2x+7 = 33
=> x = 13
Option D
Answer: D
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 780. If each member of the club paid at least $ 42, then what is the greatest possible number of members in the club?
Options:
A)19
B)20
C)21
D)23
E)25
Rationale: Given: Each person spends $42.
By looking at the options, we see that if there were 20 members, each person will spend atleast $42.
Hence the greatest number of members = 19. Option A
Answer: A
Question: x is a positive integer less than 300. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=300
n=22.13
or n= 22
Answer:- B
Answer: B
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 1800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
Options:
A)9000
B)98000
C)10000
D)11000
E)12000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 1800 ( 18 × 100 = 1800)
100% -------> 10000 votes (100 × 100 = 10000)
C
Answer: C
Question: If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)9:6:7
B)9:6:9
C)9:2:4
D)9:6:4
E)3:6:4
Rationale: A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
Answer:D
Answer: D
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 9 family members in a row for the picture?
Options:
A)7x8!
B)9×8!
C)8×9!
D)10!/2!
E)10!
Rationale: In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, 5, 6, 7, which can be arranged in 8! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 8!*2! ways.
Total - Restriction =
= 9! - 8!*2! =
= 8!(9 - 2!) =
= 7*8!.
Answer: A.
Answer: A
Question: A group of three women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
Options:
A) 7! – 2!3!2!
B)6! – 4!3!
C) 7! – 5!3!
D) 7 × 2!3!2!
E) 2!3!2!
Rationale: 6 people can sit in 6! different ways. But because 3 men cannot sit together, we take them as a unit.
This unit of men, among themselves can sit in 3! ways.
Hence, 6! - 3!.
This unit of men along with3 women can sit in 4! different ways which also needs to be eliminated.
Hence 6! - 4!3!
B
Answer: B
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 480 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
A)32/15
B)3/8
C)8/5
D)5/8
E)5/3
Rationale: Distance traveled by Eddy = 480 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 480/3 = 160 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 160/75 = 32/15
Answer A
Answer: A
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)21 (1/3) kmph
B)25 (1/3) kmph
C)29 (1/3) kmph
D)20 (1/3) kmph
E)24 (1/3) kmph
Rationale: A
Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.
Answer: A
Question: P invested $2000 in a business and Q invested $4000 in a business. At the end of the year they got $6000 as the profit. Find their share?
Options:
A)$1000,$2000
B)$2000,$4000
C)$3000,$4000
D)$2000,$3000
E)$4000,$5000
Rationale: P:Q = 2000:4000
P:Q = 1:2
P's share = 6000*1/3 = $2000
Q's share = 6000*2/3 = $4000
Answer is B
Answer: B
Question: A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 50 percent of its games that season, what was the total number of games that the team played?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: 50% is 10%-points above 40% and 30%-points below 80%.
Thus the ratio of "the first 30 games" to "remaining games" is 3:1.
So the team played a total of 30+10 = 40 games.
The answer is A.
Answer: A
Question: Solve the equation for x : 8(x + y + 2) = 8y - 8
Options:
A)-3
B)-2
C)-1
D)1
E)2
Rationale: A
-3
8(x + y + 2) = 8y - 8
8x + 8y + 16 = 8y - 8
8x + 16 = -8
8x = -24
=> x = -3
Answer: A
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)73 1/3%
B)63 1/3%
C)33 1/3%
D)93 1/3%
E)33 1/3%
Rationale: Explanation:
675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: C
Question: A candidate got 34% of the votes polled and he lost to his rival by 640 votes. How many votes were cast?
Options:
A)2000
B)2400
C)2800
D)3200
E)3600
Rationale: Let x be the total number of votes.
0.34x + 640 = 0.66x
0.32x = 640
x = 640/0.32 = 2000
The answer is A.
Answer: A
Question: A rope of which a calf is tied is increased from 10 m to 20 m, how much additional grassy ground shall it graze?
Options:
A)540
B)128
C)100
D)942
E)942.86
Rationale: π (202 – 102) = 942.86
Answer: E
Answer: E
Question: In a certain city each of 15 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)
Options:
A)3
B)4
C)6
D)5
E)7
Rationale: D.5:
if we have 5 colors we can choose pairs in 5C2 ways = 10 and single color flags are 5. Therefore total number of flags = 15.
ANS D.
Answer: D
Question: If 'z' is a positive integer exactly divisible by 2 or 5 but not divisible by 4 .What could possibly be the value of 'z' ?
Options:
A)40
B)20
C)12
D)18
E)10
Rationale: 40 and 20 are both divisible by 2 and 5 but also by 4. so they are not the right answer.
12 and 18 are both clearly not divisible by 5(not correct)
10 is both divisible by 2 and 5 but not by 4.
answer : (E) 10
Answer: E
Question: A jar contains 6 black and 2 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?
Options:
A)2/7
B)5/7
C)4/7
D)3/15
E)3/14
Rationale: P(1st black, 2nd white) = 6/8*2/7 = 12/56;
P(1st white, 2nd black) = 2/8*6/7 = 12/56.
P = 12/56 + 12/56 = 24/112 = 12/56 = 6/28 = 3/14.
Answer: E.
Answer: E
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.6 years, The ratio of the number of boys to the number of girls in the class is
Options:
A)7 : 3
B)1 : 3
C)9 : 3
D)6 : 3
E)2 : 5
Rationale: Explanation:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.6 = (k + 1) * 15.8
<=> (16.4 - 15.8) k = (15.8 - 15.6) <=> k = 0.2/0.6 = 1/3.
Required ratio = 1/3 : 1 = 1 : 3.
Answer: B
Answer: B
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?
Options:
A)40
B)42
C)44
D)48
E)50
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 7
7[2x + 10] = 5[3x + 10]
14x + 70 = 15x + 50
15x - 14x = 70 - 50
x = 20
Then the first number is = 2
2x = 40
A
Answer: A
Question: Pipes A and B can fill a tank in 5 and 6 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?
Options:
A)60/17 hr
B)13/12 hr
C)52/11 hr
D)6 hr
E)63/19 hr
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hr
Answer is A
Answer: A
Question: In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 4 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
Options:
A)168.
B)80.
C)56.
D)48.
E)16.
Rationale: ways to select one shelf = 2
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 4+3 = 7
ways to select all of them together = 2*4*7 = 56
Hence, C is the answer.
Answer: C
Question: √(9)^2
Options:
A)3
B)14
C)9
D)21
E)None of these
Rationale: explanation
√(9)^2 =?
or, ? = 9
Answer C
Answer: C
Question: A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead and yellow bead. If the necklace begins with a red bead and ends with a white bead, then N could be:
Options:
A)38
B)77
C)68
D)29
E)112
Rationale: The pattern is R G W B Y R G W B Y R .......
So, White bead comes at these positions 3rd, 8th, 13th, 18th...
If we take this as a arithmetic progression, then this series can be expressed as 3 + (n - 1) 5. ( From the formula for general term of AP = a + (n-1)d).
This can be expressed as 5n - 2
We check the answer options so only 68 satisfy the condition.
Answer:C
Answer: C
Question: What is the speed of the stream if a canoe rows upstream at 8 km/hr and downstream at 12km/hr
Options:
A)1 kmph
B)4 kmph
C)3 kmph
D)2 kmph
E)1.9 kmph
Rationale: Sol.
Speed of stream = 1/2(12 -8) kmph = 2 kmph.
Answer D
Answer: D
Question: Two men A and B working together complete a piece of work which it would have taken them
respectively 12 and 18 days to complete if they worked separately. They received Rs.149.25 as
their payment. Find the share of A in the amount they received?
Options:
A)Rs. 89.55
B)Rs. 59.70
C)Rs. 85.56
D)Rs. 88.56
E)None of these
Rationale: lcm of 12 and 18 is 36
no of untits of a is 3units
no of units of b is 2 units
then 5-->149.25
3--->?
( 3*149.25)/5
=89.55
ANSWER:A
Answer: A
Question: In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:2:2, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?
Options:
A) $900
B) $720
C) $675
D) $400
E) $225
Rationale: To solve this question, it will be best to first express the given ratio using variable multipliers. Thus, we have:
Household Expenses : Food : Miscellaneous = 5x : 2x : 2x
Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:
5x + 2x + 2x = 1,800
9x = 1,800
x = 200
Thus, the total amount allocated to food is 2 x 200= $400.
Answer D.
Answer: D
Question: A car covers a distance of 900 km in10 hrs. What is its speed in mps.
Options:
A)40 m/s
B)25 m/s
C)20 m/s
D)15 m/s
E)16 m/s
Rationale: Explanation:
Distance = Speed x Time
Speed = (900/10) = 90 kmph
Spees in mps = 90 x 5/18 = 5 x 5 = 25 mps.
Answer: Option B
Answer: B
Question: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits D can does Grace have available during her trip?
Options:
A) 2,520
B) 1,260
C) 620
D) 360
E) 120
Rationale: The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).
This gives you D=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
Answer: B
Question: P started from his house towards west. After walking a distance of 25 m. He turned to the right and walked 10 m. He then again turned to the right and walked 15 m. After this he is to turn right at 135o and to cover 30 m. In which direction should he go?
Options:
A)South-We3
B)11
C)South-West
D)112
E)21
Rationale: Answer: C
Answer: C
Question: How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 7%?
Options:
A)0—1.5 gal
B)1.5—3 gal
C)3—4.5 gal
D)4.5—6 gal
E)6+ gal
Rationale: Let amount of water that must be added in gallons to dilute concentration of brine solution = x
Amount of brine already present = 10/100 * 10 = 1 gallon
1/(10+x) *100 = 7
=>100 = 70 + 7x
=> x= 30/7 = 4.2
Answer C
Answer: C
Question: After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.75 cubic inches, what is the original volume of the cubic ice, in cubic inches?
Options:
A)2.5
B)3.0
C)4.0
D)6.5
E)12.0
Rationale: Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.75
x = 12
Alternate solution: Try to backsolve.
Initial volume = 12
After one hour --> (1/4)12 = 3
After two hours --> (1/4)3 = 0.75
Answer: E
Answer: E
Question: A day-trader plans to invest a total of $23,100 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment?
Options:
A)$2,800
B)$3,000
C)$3,500
D)$3,800
E)$3,900
Rationale: We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice).
Total of 14 minimized investments = (14)(1400) = $???600
The 15th investment + $???600 = $23,100
So, the HUNDREDS DIGITS of the 15th investment must be 5
Answer: C
Answer: C
Question: The C.P of 10 pens is equal to the S.P of 15 pens. Find his gain % or loss%?
Options:
A)loss 16 2/8%
B)loss 16 6/3%
C)loss 16 2/3%
D)loss 18 2/3%
E)loss 33.33%
Rationale: 10 CP = 15 SP
15 --- 5
100 --- ? => 33.33% (Loss)
Answer:E
Answer: E
Question: If 3y + x > 2 and x + 2y <= 3 , What can be said about the value of y?
Options:
A)y = -1
B)y >-1
C)y <-1
D)y = 1
E)y = 0
Rationale: 3y + x > 2 -----(1)
x + 2y < = 3
=> x + 2y + y < = 3 + y
=> x + 3y < = 3 + y -----(2)
from (1)&(2)
2 < 3y + x < 3 + y
=> 2 < 3 + y
=> -1 < y
=> y > -1
ANSWER:B
Answer: B
Question: A train traveling at 216 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds. What is the length of the platform in meters?
Options:
A)240 meters
B)360 meters
C)420 meters
D)720 meters
E)Cannot be determined
Rationale: Answer
Distance covered by the train when crossing a man and when crossing a platform
When a train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.
However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.
The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover. i.e., length of the platform.
Compute length of platform
Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 216 kmph * 12 seconds
Convert 216 kmph into m/sec
1 kmph = 5/18 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 216 kmph = 5/18∗216 = 60 m/sec
Therefore, length of the platform = 60 m/s * 12 sec = 720 meters.
Choice D
Answer: D
Question: A part of certain sum of money is invested at 9% per annum and the rest at 18% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)4:2
B)2:1
C)4:3
D)4:0
E)4:9
Rationale: 18:9
= 2:1
Answer: B
Answer: B
Question: There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?
Options:
A)30
B)46
C)40
D)44
E)36
Rationale: Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1)
Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get
=> 2r = 72 => r = 36.
ANSWER:E
Answer: E
Question: Find the odd man out
1, 2, 5, 14, 41, 121
Options:
A)2
B)121
C)124
D)41
E)21
Rationale: 1*3-1 =2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3 -1 = 122
ANSWER:B
Answer: B
Question: what is the minimum possible range in scores of the three test-takers?Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 18, 26 and 32.
Options:
A)26
B)32
C)18
D)20
E)30
Rationale: I simply looked at the 3 different possible scores for each individual test: 18,32,26
We have to find the minimum range:
32-18=14
32-26=6
26-18=8
The find the minimum range, you have to make the set of the 5 scores as small as possible.
Which means that 4 of the 5 scores of each individual person is zero.
6*5 = 30
Answer:E
Answer: E
Question: A man walks 6 km at a speed of 1 1/2 kmph, runs 8 km at a speed of 2 kmph and goes by bus another 32 km. Speed of the bus is 8 kmph. Find the average speed of the man.
Options:
A)4 (5/6) kmph
B)3 (5/6) kmph
C)5 (7/6) kmph
D)6 (7/6) kmph
E)None of these
Rationale: Man walked 6 km at 1.5 kmph, again he walked 8 km at speed of 2 kmph and 32 km at a speed of 8kmph
time taken indivisually:
=> 6/1.5 = 4 m
=> 8/2 = 4 m
=> 32/8 = 4 m
Average speed of man= total distance/ total time
=> 46/12 = 3 (5/6)
ANSWER:B
Answer: B
Question: Two pipes A and B can separately fill a tank in 16 and 10 minutes respectively. A third pipe C can drain off 60 liters of water per minute. If all the pipes are opened, the tank can be filled in 10 minutes. What is the capacity of the tank?
Options:
A)590 liters
B)960 liters
C)740 liters
D)560 liters
E)580 liters
Rationale: 1/16 + 1/10 - 1/x
= 1/10
x = 12
16 * 60 = 960
Answer:B
Answer: B