divelab/Sys2Bench huggingface dataset:
Question: The avg. age of a group of 16 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
Options:
A)22 years
B)23 years
C)24 years
D)25 years
E)26 years
Rationale: Total age of 16 students=16*20=320
If total age of 4 students=x
Then, (320+x)/(16+4) =(20+1), x=100
So average age of new students=100/4= 25 years
ANSWER:D
Answer: D
Question: M = {-6, -5, -4, -3, -2, -1}
T = {-5, -4, -3, -2, -1, 0, 1, 2}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
Options:
A)0
B)1/4
C)2/5
D)1/2
E)3/5
Rationale: We will have a negative product only if 1 or 2 are selected from set T.
P(negative product) = 2/8 = 1/4
The answer is B.
Answer: B
Question: A cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom.If the cistern is full, in what time will the leak empty it?
Options:
A)50hours
B)62hours
C)90hours
D)75hours
E)100hours
Rationale: Let the leak empty the full cistern in x hours
9x/x-9 = 9+1
x = 90 hours
Answer is C
Answer: C
Question: If the position of the first, sixth digits of the number 2796543018 are interchanged, similarly the positions of the the second and seventh digits are interchanged and so on, which of the following will be the left of seventh digit from the left end?
Options:
A)1
B)2
C)6
D)7
E)8
Rationale: Explanation:
The new number formed is 4 3 0 1 8 2 7 9 6 5
The seventh digit from the left is 7, the 3rd digit from the left of 7 is 1
Answer: A) 1
Answer: A
Question: A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 30% lemonade syrup?
Options:
A)1.5
B)1.75
C)2.14
D)2.34
E)2.64
Rationale: Let the total solution is 150 L with 80 L water70 L syrup.
To make 30% syrup solution, the result solution must have 105 L syrup and 45 L syrup.
Therefore we are taking 25 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
25 L syrup in 53.6 L solution
We started by multiplying 10
Now to get to the result we need to divide by 25 => amount of solution to be replaced with water = (53.6/25) = 2.14.
Correct option : C
Answer: C
Question: Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of milk. The pattern repeats after she leaves the morsel of milk. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
Options:
A)milk − wheat − wheat
B)wheat − wheat − white
C)white − milk − wheat
D)white − white − white
E)white − white − milk
Rationale: In a single round Lucy drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Answer: A
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
Options:
A)3
B)4
C)5
D)7
E)8
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
A
Answer: A
Question: If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: In this particular example length (10 meter) is just extraneous information.
The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc...
The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc...
The distances between marks are 3/12, 1/12, and 2/12.
The answer is C.
Answer: C
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 1 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
Options:
A)2.5 hours
B)4.5 hours
C)5.5 hours
D)1 hour
E)None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 1 hours, Tank A and B can effectively fill 1⁄12 × 1 = 1⁄12 of the tank.
Time taken to fill the remaining 1−(1/12) = 11/12 of the tank = (11/12)/(1/6) = 5.5 hours. Answer : Option C
Answer: C
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 149, what is the difference between the ages of Patrick and Monica?
Options:
A)27
B)64
C)45
D)72
E)18
Rationale: Ages of P and Mi=3x+5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=47x=149
x=4
Difference if ages of Pa and Mo=25x-9x=16x=16*4=64
Answer B
Answer: B
Question: What is the least number to be subtracted from 11, 15, 21 and 30 each so that the resultant numbers become proportional?
Options:
A)7
B)6
C)3
D)4
E)9
Rationale: Let the least number to be subtracted be 'x', then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.
<=> (11 - x):(15 - x) = (21 - x):(30 -x)(21 - x)
From the options, when x = 3
=> 8 * 27 = 12 * 18 => then x = 3. => (11 - x)(30 - x) = (15 - x)(21 - x)
Answer: C
Answer: C
Question: A triangle has three angles all with the same ratio to each other, 1:1:1. What is the angle measurement?
Options:
A)45Â°
B)60Â°
C)75Â°
D)90Â°
E)105Â°
Rationale: If the ratio is 1:1:1, and the total angle measurement is 180Â°, then the equation is
x + x + x = 180Â°
3x = 180Â°
x = 60Â°
Therefore the answer is 60Â° or B.
Answer: B
Question: Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $400, and exactly 12 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
Options:
A)10,000
B)11.0
C)12,000
D)13,200
E)14,000
Rationale: The average price of 25 products is $1,200 means that the total price of 25 products is 25*1,200=$30,000.
Next, since exactly 12 of the products sell for less than $1,000, then let's make these 12 items to be at $400 each (min possible).
Now, the remaining 12 items cannot be priced less than $1,000, thus the minimum possible price of each of these 12 items is $1,000.
Thus the minimum possible value of 24 products is 12*400+12*1,000=$16,800.
Therefore, the greatest possible selling price of the most expensive product is $30,000-$16,800=$13,200.
Answer: D.
Answer: D
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 60 percent on clothing, 10 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
Options:
A) 2.8%
B) 3.6%
C) 4.4%
D) 5.2%
E) 4.8%
Rationale: Let amount spent by Jill = 100
Clothing=50, Food=20, others=30
Tax on clothing= 2.4
Tax on others=2.4
Percentage= 4.8/100 =4.8%
Answer: E
Answer: E
Question: What is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22 ?
Options:
A)1386
B)1276
C)1566
D)1466
E)1577
Rationale: LCM of 12,14,18 and 22 = 2772
least no which will be exactly divisible by 12,14,18 and 22 = 2772
2772/2 = 1386
1386 is the number when doubled 2772
=>1386 is the least exactly divisible by 12,14,18 and 22.
ANSWER A
Answer: A
Question: All of the stocks on the over-the-counter market are designated by either a 3-letter or a 4-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Options:
A)27(26^3)
B)26(26^4)
C)27(26^4)
D)26(26^5)
E)27(26^5)
Rationale: Number of 4-letter codes: 26 * 26 * 26 = 26^3
Number of 5-letter codes: 26 * 26 * 26 * 26 = 26^4
Total Number of codes: 26^3 + 26^4 = 26^3 + 26*(26^3) = 27*(26^3)
Therefore, the answer is A: 27*(26^3).
Answer: A
Question: One dog tells the other that there are two dogs in front of me.The other one also shouts that he too had two behind him. How many are they?
Options:
A)3
B)4
C)1
D)6
E)78
Rationale: Explanation:
Dog
Dog
Dog
So there are 3 dogs.
They are in circle.
Answer: A
Answer: A
Question: L29Q,L31S,P37U,R41W,T43U,?
Options:
A)V43Y
B)U47Y
C)V47Z
D)V47Y
E)V46X
Rationale: L + Q = 29
L + S = 31
P + U = 37
R + W = 41
T + W = 43
29 , 31 , 37 , 41 , 43 ---> prime number number sequence
=> next number = 47
V + Y = 47 => V47Y
ANSWER:D
Answer: D
Question: A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 5 days. For how many number of days should A and C should work together to complete the remaining work ?
Options:
A)1/2
B)2/3
C)3/4
D)4/3
E)5/2
Rationale: b work 1/8 * 5=5/8
remaining work =1-5/8=3/8
a and c work together =1/6+1/12=3/12=1/4
take remaining work is done in =8/3 *1/4=2/3 days
ANSWER:B
Answer: B
Question: An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
Options:
A)18
B)30
C)64
D)6720
E)216
Rationale: Arrangement means permutations questions..
8P3 = 8!/3! = 6720
.
ANS option D is correct answer..
Answer: D
Question: How many randomly assembled people are needed to have a better than 50% probability that at least 1 of them was born in a leap year?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: (C) 3 , with 2 we will have exactly 50%, so for more than 50% should be 3.
Answer: C
Question: Find the no. of ways in which 8 different flowers can be stung to form a garland so that 4 particular flowers are never separated.
Options:
A)3!x3!
B)7!x3!
C)7!x4!
D)8!x4!
E)4!x4!
Rationale: Condsidering the 4 particular flowers as one unit we have 5 flowers, which can be arranged in garland in 4! ways. But the flowers can be arranged in 4! ways. Therefore required no. of ways is 4!x4!. Ans:(E )
Answer: E
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 6. If X invested Rs.5,000. the amount invested by Y is
Options:
A)Rs.45,000
B)Rs.50,000
C)Rs.60,000
D)Rs.15,000
E)None
Rationale: Solution
Suppose Y invested Rs.y
Then,	5000 /y = 2 / 6
â€¹=â€º y=(5000Ã—6 / 2).
â€¹=â€º y=15000.
Answer D
Answer: D
Question: If f(a)=2a, what is the value of (f(a-b)+f(a))/b ?
Options:
A)4a/b
B)3a+4b/b
C)(4a-2b)/b
D)5a-6b*b
E)8a-7b/b
Rationale: f(a)=2a
f(a-b)= 2(a-b)
(f(a-b)+f(a))/b = (2(a-b)+2a)/b = (4a-2b)/b
Answer is C
Answer: C
Question: How many factors does 36^2 have?
Options:
A)2
B)8
C)24
D)25
E)26
Rationale: 36^2 = 2^4 3^4
total factors = (4+1)(4+1) = 25.
Answer is D.
Answer: D
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Explanation:
=> 3(2x+9) = 75
=> 2x+9 = 25
=> x = 8
Option A
Answer: A
Question: If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 9 miles?
Options:
A)27/5
B)26/5
C)23/5
D)22/5
E)21/5
Rationale: 1 km is approxmately equal to 0.6 miles
So 9 km = 9*0.6 = 5.4 miles . Multiple & divide by 10
i.e 5.4*10/10 = 54/10 = 27/5
Answer : A
Answer: A
Question: Machine T takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine T to make 40 widgets?
Options:
A) 5
B) 6
C) 8
D) 10
E) 12
Rationale: i approached this one by plugging in numbers...started with C.
if 40 are made in 8 hours, then 20 are made in 4 hours. so time of T is 4, and time of B is 2.
rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and T reduces the time - the total # of widgets made will be even higher.
now between D and E -> try only one ..if it doesn't work, then the other one is the answer.
i picked E:
12h to make 40 widgets, and 6 hours to make 20. this is the time of T. time of B=4 hours.
20/6 + 20/4 = 10/3 + 20/4
find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:
40+60/12 = 100/12
divide by 4:
25/3
so this is the rate given.
E is the correct answer
Answer: E
Question: A train is 400 meter long is running at a speed of 60 km/hour. In what time will it pass a signal post?
Options:
A)28 seconds
B)30 seconds
C)40 seconds
D)24 seconds
E)18 seconds
Rationale: Speed = 60 Km/hr = 60*(5/18) m/sec = 150/9 m/sec
Total distance = 400 meter
Time = Distance/speed
= 400 * (9/150) = 24 seconds
Answer: D
Answer: D
Question: The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Ans: E - 4 pairs
(xˆ2)(yˆ2) = 900 [square root both sides]
xy = 30
20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15
Cancel the repeats
This leaves us with exactly 4 options.
Hence, E
Answer: E
Question: An archer is shooting arrows from various distances. She shoots at a target from 40 yards, 50 yards, and 60 yards. The probability that she hits within the bullseye from 40 yards is 4/5, the probability that she hits within the bullseye from 50 yards is 3/4, and the probability that she hits within the bullseye from 60 yards is 2/3. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
A)39/40
B)49/50
C)59/60
D)9/10
E)14/15
Rationale: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 40 yards)*(prob that she misses from 50 yards)*(prob that she misses from 60 yards)
Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3
Thus the probability that she misses all shots = (1/5)*(1/4)*(1/3) = 1/60
Thus the probability that she makes at least one shot = 1 - (1/60) = 59/60
C
Answer: C
Question: How many seconds will a 600 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)25
B)36
C)40
D)45
E)50
Rationale: Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=600*3/50=36sec
ANSWER:B
Answer: B
Question: Fortunes, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms?
Options:
A)34 km per hour
B)54 km per hour
C)49 km per hour
D)65 km per hour
E)67 km per hour
Rationale: Given that the diesel consumption is at the rate
1400×[1000x+x]1400×[1000x+x]
Cost of diesel = Rs 35 per litre
Payment to the driver = Rs 125 per hour.
Also given that the SUV is driven at the speed of xx km per hour.
Total cost (c)(c)
=1400×[1000x+x]×800×35+125×800x=1400×[1000x+x]×800×35+125×800x
=70000x+70x+100000x=70000x+70x+100000x
Now differentiating both sides in the above equation with respect to xx.
dcdx=−170,000x2+70=0dcdx=−170,000x2+70=0
⇒ x=49 km per hour.
C
Answer: C
Question: Find the annual income derived by investing $ 6800 in 40% stock at 136.
Options:
A)550
B)2000
C)250
D)3000
E)400
Rationale: By investing $ 136, income obtained = $ 40.
By investing $ 6800, income obtained = $ [(40/136)*6800] = $ 2000.
Answer B.
Answer: B
Question: Express the following as a Decimal 6%
Options:
A)0.6
B)6.0
C)0.006
D)6.6
E)0.06
Rationale: 6% = 6/100
=0.06
Answer is E.
Answer: E
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 8 minutes more to walk to work than to ride his bike to work, then x equals?
Options:
A)4
B)7
C)12
D)15
E)20
Rationale: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 480 (which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=480 ----> 40x=480--> x = 12.
Option C
Answer: C
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
Options:
A)40%
B)44%
C)80%
D)90%
E)100%
Rationale: Explanation:
A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer: Option C
Answer: C
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 525 what is the least possible value of k?
Options:
A)10
B)14
C)15
D)21
E)25
Rationale: 525 = 3*5*5*7
Thus k must include numbers at least up to the number 10 so that there are two appearances of 5.
The answer is A.
Answer: A
Question: Three models (P, Q, and R) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model P, 17 cars of Model Q, and 15 cars of Model R. What is the maximum number of cars of model P in any showroom ?
Options:
A)17
B)16
C)15
D)14
E)13
Rationale: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal 51/3=17).
Moreover that the number of model P is maximum means that the numbers of model Q and R should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.
So Maximum number of model P is 17-2= 15.
The answer is (C)
Answer: C
Question: Find the average of first 60 natural numbers?
Options:
A)50.5
B)52
C)30.5
D)75
E)65
Rationale: Sum of first 100 natural numbers = 60*61/2 = 1830Required average = 1830/60 = 30.5Answer is C
Answer: C
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of B.
Options:
A)240
B)288
C)277
D)390
E)361
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
13/21 * 630 = 390
Answer: D
Answer: D
Question: In a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.
Approximately how many faulty circuit boards exist in a group of 2,400 circuit boards where 64 fail inspection?
Options:
A)72
B)356
C)200
D)256
E)264
Rationale: Total of 2,400 boards. All that fail verification are indeed faulty. So the 64 are indeed faulty. 1/8 those that pass are also faulty.
From the 2,400 we know 64 fail. So 2,336 must pass. Of these 1/8 are faulty. 2,336 divided by 8 gives you 292.
What one must do now is to add to the 292 which were not detected the actually detected faulty ones, namely the 64.
Total faulty: 356.
Answer: B
Answer: B
Question: A, B and C start at the same time in the direction to run around a circular stadium. A completes a round in 252 seconds and C in 198 seconds, all starting at the same point. after what time will they meet again at the starting point ?
Options:
A)26 minutes 18 seconds
B)42 minutes 36 seconds
C)45 minutes
D)46 minutes 12 seconds
E)58 minutes
Rationale: Solution
L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec. i.e, 46 minutes 12 seconds. Answer D
Answer: D
Question: Diana is painting statues. She has 7/16 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?
Options:
A)7
B)20
C)28
D)14
E)19
Rationale: number of statues=all the paint÷amount used per statue
=7/16 ÷ 1/16
=7/16*16/1
=7/1
=7
Answer is A.
Answer: A
Question: A can do a piece of work in 30 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Options:
A)30 days
B)65 days
C)86 days
D)45 days
E)17 days
Rationale: 10/30 + 10/30 + 10/x = 1
x =30 days
Answer:A
Answer: A
Question: In the new budget , the price of kerosene oil rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
Options:
A)10
B)20
C)30
D)40
E)None of them
Rationale: Reduction in consumption = [((R/(100+R))*100]%
=[(25/125)*100]%=20%.
Answer is B.
Answer: B
Question: If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
Options:
A)3%
B)6%
C)75%
D)94%
E)97%
Rationale: Probability of getting no heads = 1/64
Probability of getting at least 1 head = 63/64
Probability of getting no tails = 1/64
Probability of getting at least 1 tail = 63/64
Probability of getting at least 1 head and at least 1 tail = 63*63/64*64
63/64 is greater than 98%... So squaring that should be greater than 96%. Answer is E.
Answer: E
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 7 years, Arun's age will be 19 years. What is the age of Deepak at present?
Options:
A)16
B)14
C)12
D)9
E)15
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 7 = 19 => x = 12
Deepak's age = 3x = 9 years.
Answer: D
Answer: D
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.10 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)399
B)272
C)732.6
D)277
E)311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1.1 = 732.6 Answer: C
Answer: C
Question: The average of 65 numbers is 40. If two numbers, 83 and 30 are discarded, then the average of the remaining numbers is nearly
Options:
A)28.32
B)39
C)38.78
D)29
E)39.47
Rationale: Explanation :
Total sum of 63 numbers = (65 * 40) - (83 +30) = 2600 - 113= 2487
Average = 2487/63 = 39.47
Answer : E
Answer: E
Question: If W is the set of all the integers between 69 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Options:
A)20
B)32
C)33
D)34
E)35
Rationale: Multiples of 2 from 69 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 68=[99/2]-[68/2]=49-34=15
Multiples of 3 from 69 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 68=[99/3]-[68/3]=33-23=10
Multiples of2 and 3 bothi.e.6 from 69 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 68=[99/6]-[68/6]=16-11=5
These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3
i.e. Total Numbers in W = 15 + 10 - 5 = 20
Answer Option A
Answer: A