divelab/Sys2Bench huggingface dataset:
Question: The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is?
Options:
A)22
B)27
C)18
D)19
E)11
Rationale: Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :
Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice
(20-x)/(x-15) = 2/3 60 - 3x = 2x - 30
5x = 90 x = 18.
Answer: C
Answer: C
Question: 5,6,8,11,?,20,26,33
Options:
A)10
B)13
C)15
D)8
E)19
Rationale: The Pattern is + 1, + 2, +3, ...
11+4=15
Answer :C
Answer: C
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)Rs.6850
B)Rs.7268
C)Rs.6871
D)Rs.6150
E)Rs.6381
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs. 6150.
Answer:D
Answer: D
Question: 20 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
Options:
A)10
B)6
C)4
D)7
E)5
Rationale: Required number of machines = 20*10/40 = 5
Answer is E
Answer: E
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Options:
A)31
B)35
C)32
D)38
E)40
Rationale: A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.
ANSWER A
Answer: A
Question: If |x|/6 < 1, which of the following must be true?
Options:
A)x>6
B)x<6
C)x=6
D)x=12
E)x=-12
Rationale: if x <6, then If |x|/6 < 1
Like x=2
Then |2|/6 < 1
1/3<1
ANSWER B x<6
Answer: B
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 140?
Options:
A)3
B)6
C)28
D)42
E)70
Rationale: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)
140 = 4*5*7
The GCF could be 4 or 28
The answer is C.
Answer: C
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Options:
A)11 min
B)56 min
C)13 min
D)20 min
E)19 min
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio
= 4:51 -------- 5 4 --------- ? è 20
Answer:D
Answer: D
Question: A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But
whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11
mornings and 12 afternoons. How many days did they stay there totally?
Options:
A)16
B)18
C)20
D)13
E)14
Rationale: Explanation :
Clearly 11 mornings and 12 afternoons = 23 half days
=> Since 13 days raining means 13 half days.
=> So 23-13 =10 halfdays ( not effecetd by rain )
=> So 10 halfdays =5 fulldays
Hence ,
Total no. of days = 13+5 =18 days
Answer : B
Answer: B
Question: Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
Options:
A)1.5
B)1.7
C)2.3
D)2.5
E)3.0
Rationale: Ratio of A to B in the final mixture = 50-30 : 30-15 = 4:3
Gallons of A used = 4/7*4 = 2.28
ANSWER:C
Answer: C
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)32 6/7%
B)22 6/7%
C)72 6/7%
D)42 6/7%
E)12 6/7%
Rationale: Explanation:
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: D
Question: If the remainder is 8 when positive integer n is divided by 12, what is the remainder when n is divided by 6?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Assume x is quotient here,
n=12x+8 ----------(1)
and n=6x+ ?
We can also write equation (1) as:
n=(12x+6)+2.
ie 6(2x+1)+2 ie the first term is perfectly divisible by 6.
So,the remainder left is 2.
So,answer (C) is right choice.
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)175 m
B)180 m
C)185 m
D)170 m
E)190 m
Rationale: Explanation:
Length of the train be â€˜Xâ€™
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
ANSWER IS B
Answer: B
Question: A and B start a business with Rs.5000 and Rs.7000 respectively. How should they share their profits at the end of one year?
Options:
A)3:5
B)3:4
C)5:7
D)3:2
E)3:9
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
5000 : 7000 => 5:7
Answer:C
Answer: C
Question: In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots?
Options:
A)-12
B)-6
C)12
D)6
E)24
Rationale: Explanation:
The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12.
we get, sum of the roots = 1 / a = 1
a = 1
Product of the roots = -12 / 1 =-12
ANSWER: A
Answer: A
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 5. What are the coordinates of P?
Options:
A)(5/2, 5/2)
B)(7/2, 7/2)
C)(9/2, 9/2)
D)(11/2, 11/2)
E)(15/2, 15/2)
Rationale: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
The x, y coordinates are 5/6 of the distance from 3 to 6.
x = 3 + (6-3)*(5/6) = 3 + 5/2 = 11/2 = y
The answer is D.
Answer: D
Question: Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company M last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Options:
A)5/22
B)4/22
C)3/22
D)9/22
E)7/22
Rationale: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22
E
Answer: E
Question: A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Options:
A)1243 toys
B)1375 toys
C)1543 toys
D)1212 toys
E)1598 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
5500 * 4 = 1375 toys
correct answer B
Answer: B
Question: A 6 litre sol is 40% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
Options:
A)A.0.6
B)B.1.2
C)C.2.1
D)D.3
E)E.5.4
Rationale: 40% of 6 = 2.4
50% of 6 = 3
shortage is 0.6
so we need to have 0.6/50% to get 50% alcohol content.
= 1.2 B
Answer: B
Question: The average age of 44 students in a group is 12 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
Options:
A)cannot be determined
B)None of these
C)55
D)56
E)57
Rationale: Age of the teacher = (45 × 13 – 44 × 12) years
= 57 years.
Answer E
Answer: E
Question: The fourth proportional to 5, 8, 15 is:
Options:
A)24
B)20
C)23
D)16
E)None
Rationale: Answer: Option A
Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
5x = (8 x 15)
x =	(8 x 15) /5 = 24
Answer: A
Question: The greatest common factor of positive integers m and n is 15. What is the greatest common factor of (2m^2, 2n^2)?
Options:
A)15
B)30
C)150
D)450
E)900
Rationale: m = 15j and n = 15k, where the greatest common factor of j and k is 1.
2m^2 = 2*15*15*j^2 and 2n^2 = 2*15*15*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*15*15 = 450
The answer is D.
Answer: D
Question: What number has a 5:1 ratio to the number 10?
Options:
A)11
B)50
C)17
D)12
E)18
Rationale: 5:1 = x: 10
x = 50
Answer: B
Answer: B
Question: In a dairy farm, 34 cows eat 34 bags of husk in 34 days. In how many days one cow will eat one bag of husk ?
Options:
A)34 days
B)40 days
C)46 days
D)50 days
E)None of these
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 34
Bags 34 1]::34:x
=>x∗34∗1=34∗1∗34
=>x=34
Option A
Answer: A
Question: It costs $2 for the first 1/5 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 2 hours and 15 minutes, how much will it cost him?
Options:
A)$25.
B)$26.
C)$29.
D)$30.
E)$31.
Rationale: 2 hrs 15 min = 135 min
First 12 min ------> $2
Time left is 135 min...
Now, 60 min costs $ 12
1 min costs $ 12/60
135 min costs $ 12/60*135 => $ 27
So, Total cost will be $27 + $2 => $ 29
Hence answer will be C
Answer: C
Question: x, y, and z are all unique numbers. If x is chosen randomly from the set {10, 11} and y and z are chosen randomly from the set {20, 21, 22, 23}, what is the probability that x and y are prime and z is not?
Options:
A)1/5
B)3/20
C)1/8
D)3/10
E)1/10
Rationale: P(x is prime) = 1/2
P(y is prime) = 1/4
If y is prime, then z is not prime since y and z are unique.
Then the probability is 1/2*1/4 = 1/8
The answer is C.
Answer: C
Question: Debini normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Debini averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
Options:
A)135
B)105
C)95
D)75
E)45
Rationale: Debini normally drives to work in 45 minutes at an average speed of 40 miles per hour.
Use formula D = RT
Car:
T1: 45 min
R1: 40 mph
D1: [(40*45)/60] = 30 miles
Bike:
T1:?
R2: 12 - 16 mph
D2: 08*D1 = 24 miles
T1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)
Therefore, Deb has to leave 120 min - 45 min = 75 min early
ANSWER: D
Answer: D
Question: In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?
Options:
A)10.7%
B)20%
C)25%
D)33 1/3
E)58 1/3
Rationale: No of bank customers in 1985 = 60 x .45 = 27
No of bank customers in 1987 = 144 x .25 = 36
increase in % = 100 X 9/27 = 100/3 or 33 1/3
D is the correct answer
Answer: D
Question: A sum fetched total simple interest of 4016.25 at the rate of 12 p.c.p.a. in 5 years. What is the sum?
Options:
A)6693.75
B)8032.5
C)4462.5
D)8900
E)None of these
Rationale: Let the sums be P.
Now, 60% of P = 4016.25
or, P = 6693.75
Answer A
Answer: A
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Options:
A)121km
B)242km
C)224km
D)112km
E)115km
Rationale: Explanation:
Average Speed =2Ã—21Ã—24/21+24=22.4 km/hr
Total distance =22.4Ã—10=224 km
ANSWER IS C
Answer: C
Question: A train 70 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)4 sec
B)16 sec
C)6 sec
D)20 sec
E)8 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 70 * 2/35 = 16 sec
ANSWER: A
Answer: A
Question: A man buys an article for $100. and sells it for $130. Find the gain percent?
Options:
A)10%
B)15%
C)25%
D)20%
E)30%
Rationale: C.P. = $100
S.P. = $130
Gain = $30
Gain% = 30/100 *100 = 30%
Answer is E
Answer: E
Question: There are 8 books in a shelf that consist of 3 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
A)40
B)45
C)50
D)55
E)65
Rationale: 8C4 [Select any four] - 6C4 [Select all hard backs] =65.
E
Answer: E
Question: Simplify the following equation
[(p - q)2 - (p + q)2] / 4p = b/a
Options:
A)a b = q
B)q b = a
C)a q = b
D)a q = -b
E)None of these
Rationale: [(p - q)2 - (p + q)2] / 4p = b/a
=> [p2 + q2 - 2pq - (p2 + q2 + 2pq)] / 4p = b/a
=> - 4pq/4p = b/a
=> q = - b/a
=> a q = -b
ANSWER:D
Answer: D
Question: A bag contains 12 white and 18 black balls. Two balls are drawn in succession without replacement. What is the probability that first is white and second is black?
Options:
A)20/145
B)18/145
C)35/120
D)36/145
E)40/145
Rationale: The probability that first ball is white:
=12C1/30C1
12/30
=>2/5
Since, the ball is not replaced; => the number of balls left in bag- 29.
the probability the second ball - BLACK
18C1/29C1 = 18/29
req = 2/5 * 18/29 = 36/145
ANSWER D
Answer: D
Question: The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $62,500, how much profit did the business make?
Options:
A)$100,000
B)$125,000
C)$150,000
D)$200,000
E)$250,000
Rationale: Majority owner + two partners = 0.25*P + 2*(0.25)*(0.75)*P = 0.25*P + (0.5)*(0.75)*P = 0.25*P + (0.375)*P = (0.625)*P
This equals $62,500.
(0.625)*P = 62,500 ----- divide both sides by 625
(0.001)*P = 100 ------ multiply by 1000
P = 100,000
Answer = A
Answer: A
Question: A thief steals at a car at 3.00 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
Options:
A)1 p.m
B)3 p.m
C)4 p.m
D)5.30 p.m
E)6 p.m
Rationale: D
5.30 p.m
Suppose the thief is overtaken x hrs after 3.00 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 5.30 p.m.
Answer: D
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
Options:
A)1/6
B)1/9
C)1/5
D)1/1
E)1/3
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability
= 3!4!/6! = 1/5
Answer:C
Answer: C
Question: A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
Options:
A)24
B)72
C)720
D)336
E)420
Rationale: The left window will have permutations of the 5 fiction books, so the number of possibilities for that window is
permutations = 5! = (5)(4)(3)(2)(1) = 120
The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 120*6 = 720
Answer: C.
Answer: C
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.1 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?
Options:
A)8.1
B)12.
C)12.5.
D)14.
E)15.4.
Rationale: Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.1 *5= 5.5 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (5.5^2+ 6^2)^1/2= 8.1 KM
A is the answer
Answer: A
Question: The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability W that 3 of Sam’s 4 funds grew by at least 10% over last year?
Options:
A) 6C3 / 10C4
B) 6C3 * 4C1 / 10C4
C) 6C3 * 4C1 / 10P4
D) 6P3 * 4P1 / 10C4
E) 6P3 * 4P1 / 10P4
Rationale: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.
We know this is a combination, not a permutation. This rules out choices C, DE.
A clearly isn't the answer because W=6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.
B it is.
Answer: B
Question: D, B, C are three consecutive positive integers (D>B>C). What is the value of the expression 2D +B +3C?
Options:
A)6A+7.
B)5A+1.
C)5A-1.
D)6A-5.
E)6D-7.
Rationale: => D+D+(D-1)+3(D-2)
=6D-7=E
Answer: E
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 2 employees to 5 different offices?
Options:
A)5
B)6
C)7
D)25
E)9
Rationale: Ans. Each employee can go into any of the two offices. Thus we have
=> 5 * 5 = 25
Answer : D
Answer: D
Question: The length of a train and that of a platform are equal. If with a speed of 36 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)752
B)799
C)300
D)750
E)712
Rationale: Speed = [36 * 5/18] m/sec = 10 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 10 Ã¨ x = 10 * 60 / 2 = 300
Answer: C
Answer: C
Question: The operation # is defined for all nonzero f and y by f#y = f + f/y. If a>0, then 1#(1#a) =
Options:
A)a
B)a+1
C)a/(a+1)
D)(a+2)/(a+1)
E)(2a+1)/(a+1)
Rationale: f#y = f + f/y. If a>0, then 1#(1#a) =
You can see that a stands for y and 1 stands for f. I like to work with numbers so I did f=1 a=2 and a=y so y=2
1#a= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3
So now you can check by filling in a, which is 2:
A. a --> 2
B. a+1 --> 2+1=3
C. a/(a+1)-->2/(2+1)=2/3
D. (a+2)/(a+1)-->(2+2)/(2+1)=4/3
E. (2a+1)/(a+1)-->(2*2+1)/(2+1)=5/3
So E is the answer.
Answer: E
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 10 months, find for how much time did Q invest the money?
Options:
A)11
B)10
C)20
D)16
E)12
Rationale: 7*5: 10*x = 7:10
x = 20
Answer:C
Answer: C
Question: In triangle PQR, the angle Q = 90 degree, PQ = 4 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
Options:
A)1.2 cm
B)2.4 cm
C)4.8 cm
D)2.16 cm
E)3.2 cm
Rationale: Look at the diagram below:
Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:4=8:10 --> QY=3.2.
Answer: E
Answer: E
Question: Insert the missing number
..., 4, 8, 16, 32, 64, 128, 256
Options:
A)6
B)5
C)2
D)3
E)8
Rationale: series is 2* Previous Number.
ANSWER:C
Answer: C
Question: 20 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
Options:
A)33.33
B)34.01
C)26.32
D)28.33
E)19.21
Rationale: Explanation:
Let the two parts be (20 - x) and x.
Then, 10 (20 - x) + 22x = 780
=> 12x = 580
=> x = 48.33.
Bigger part = (20 - x) = 28.33.
Answer: D) 28.3
Answer: D
Question: Mixture V is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture V, how many kilograms of mixture V must be added to make a 70% material B in the new mixture?
Options:
A)A)6
B)B)7
C)C)8
D)D)9
E)E)10
Rationale: Can be done with weighted avg method.
if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil .
V1=20(initial mix.)
Avg. is what we need..ie 70% of material B means 30% of oil
V2=36(36% of 10 kg mix)
w1/w2=(V2-Avg)/(Avg-V1)
(36-30)/(30-20)
6/10
means for every 10 kg of new mix. we need 6 kg of mix V
Ans A
Answer: A
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)12, 9
B)10, 5
C)12, 7
D)11, 6
E)14, 3
Rationale: Explanation:
x – y = 5
4x – 6y = 6
x = 12 y = 7
ANSWER IS C
Answer: C
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
Options:
A)5 : 1
B)10 : 5
C)15 : 2
D)20 : 2
E)25 : 2
Rationale: Ratio of US to Indian stamps is 5:2
U/I = 5:2
= 25:10
ratio of Indian to British stamps is 5 : 1
I/B = 5:1
=10:2
Now , Ratio of US to British stamps
U/B = 25:2
Answer E
Answer: E
Question: What is the next number of the following sequence
1,3,4,5,1,9,16...
Options:
A)14
B)25
C)16
D)17
E)18
Rationale: (1, 3 ,4,5) (1, 9, 16, x)
square of 1st group gives 2nd group
1^2 = 1
3^2 = 9
4^2 = 16
5^2 = 25
ANSWER:B
Answer: B
Question: If a certain sample of data has a mean of 22.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)13.5
C)14.5
D)23.5
E)26.5
Rationale: The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is C.
Answer: C
Question: It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn
Options:
A)16
B)90
C)36
D)45
E)20
Rationale: 1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min..
only A and B are left..
if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins..
ans 20 E
Answer: E
Question: If x≠2 and (x^2 - 4)/(2y) = (x - 2)/4, then in terms of y, x = ?
Options:
A)(y - 6)/2
B)(y - 3)/2
C)(y - 4)/2
D)y - 6
E)(y + 6)/2
Rationale: Since (x^2 – 4)=(x-2)(x+2) the original equation can be changed into 4*(x-2)(x+2) = 2y *(x-2).
By cancelling 2(x-2) (we can do it because x≠2) we get :
2*(x+2)=y.
So x=(y-4)/2. So the answer is C).
Answer: C
Question: A man buys 54 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
Options:
A)7.6 %
B)7.7 %
C)16.21 %
D)13.6 %
E)7.8 %
Rationale: Explanation:
Let Marked price be Re. 1 each
C.P. of 54 pens = Rs. 46
S.P. of 54 pens = 99% of Rs. 54= Rs. 53.46
Profit % = (Profit /C.P.) x 100
Profit% = (7.46/46) x 100 = 16.21 %
ANSWER: C
Answer: C
Question: A motorist travel to a place 150 km away at an average speed of 60 km/hr and returns at 30 km/hr.His average speed for the whole journey in km/hr is
Options:
A)36 km/hr
B)37 km/hr
C)40 km/hr
D)44 km/hr
E)None of these
Rationale: Explanation:
Average speed will be
2xy/x+y km/hr
= {2(60)(30)}/{60+30} km/hr
= 40 km/hr
Answer: Option C
Answer: C