divelab/Sys2Bench huggingface dataset:
Question: 5 + 5 + 5 + 5 +5 + 4 x 5^2 + 4 x 5^3 + 4 x 5^4 + 4 x 5^5 + 4 x 5^6 + 4 x 5^7 + 4 x 5^8 + 4 x 5^9 =
Options:
A) 5^20
B) 5^18
C) 5^14
D) 5^10
E) None of above
Rationale: Let's see that 5 + 5 + 5 + 5 +5 is 5^2, then: 5^2 + 4 x 5^2 becomes 5 x 5^2 that is 5^3. You follow with the next element: 5^3 + 4 x 5^3 is equal to 5 x 5^3 that is 5^4. Then is assumed right before 4 x 5^9: 5^9 + 4 x 5^9 becomes 5 x 5^9 that is 5^10. Thus, the correct answer is the option D, 5^10.
Answer: D
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 15% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
Options:
A)$113
B)b $115
C)c $125
D)d $130
E)e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 15% less than the price each head sold for on the day before i.e , (85/100)*0.5 = $ 0.425
Hence selling cost for the remaining cabbage = 500 * 0.425 = $ 212.5
Total selling cost = 500 + 213 = $ 713
Gross profit = $ 713 - $ 600 = $ 113
Hence Answer is A.
Answer: A
Question: A rectangular park 60 m long and 40 m wide has 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)338
B)278
C)260
D)278
E)111
Rationale: Answer:B
Answer: B
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm?
Options:
A)189 cm2
B)150 cm2
C)127 cm2
D)177 cm2
E)90 cm2
Rationale: 1/2 * 20(5 + 4)
= 90 cm2
Answer: E
Answer: E
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
Options:
A)4x+6y
B)x+y+4
C)X+2
D)4X-9Y
E)Y-5
Rationale: Explanation:
By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
ANSWER:D
Answer: D
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)76 Kmph
B)68 Kmph
C)86 Kmph
D)45 Kmph
E)56 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: B
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 18 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
Options:
A)84.
B)72.
C)86.
D)98.
E)112.
Rationale: All of them catch fishes in relation to number 18....
2/3*18+2*18+2*1.5*18*2/3=84
Answer is A
Answer: A
Question: Two athletes starting from same place walk in the same direction at a rate of 8 km/hr and 6 km/hr. What time will they take to be 10 km apart ?
Options:
A)10 hours
B)15 hours
C)5 hours
D)4 hours
E)None of these
Rationale: Explanation :
The relative speed of athletes = 8-6 = 2 km/hr.
Distance between them = 10 km
Time=10/2 = 5 hours
Answer : C
Answer: C
Question: Using all the letters of the word "NOKIAS", how many words can be formed, which begin with N and end with S?
Options:
A)24
B)80
C)160
D)80
E)100
Rationale: There are five letters in the given word.
Consider 6 blanks ....
The first blank and last blank must be filled with N and S all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
Answer: A
Answer: A
Question: Series till 50 terms: 2+3-5 +2+3-5+.
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5.........+2+3.
series is repeat +2 +3 -5 continously..
So, till 48th term it will repeat +2+3-5..
49th term = +2
50thterm = +3
ANSWER:A
Answer: A
Question: Anil brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?
Options:
A)220
B)420
C)250
D)700
E)500
Rationale: E
C.P. be Rs. x. Then, 20% of x = 1100
20/100 * x = 1100 => x = 5500
C.P. = Rs. 5500, expenditure on repairs = 10%
Actual price = Rs. (100 * 5500)/110 = Rs. 5000
Expenditures on repairs = (5500 - 5000) = Rs. 500.
Answer: E
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
Options:
A)76.5
B)36.5
C)46.5
D)16.5
E)26.5
Rationale: Explanation:
Correct Sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = = 1825/50 = 36.5
Answer: B
Answer: B
Question: The roof of an apartment building is rectangular and its length is 5 times longer than its width. If the area of the roof is 720 feet squared, what is the difference between the length and the width of the roof?
Options:
A)38.
B)40.
C)42.
D)44.
E)48.
Rationale: Answer is E : 48
Let w be the width , so length is 5w. Therefore : w*5w = 720, solving for, w = 12 , so 5w-w = 4w = 4*12 = 48
Answer: E
Question: Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 40% of his income to Sam and 60% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
Options:
A)	11/12
B)	13/17
C)	13/19
D)	12/19
E)	27/19
Rationale: MAKE R = 10
P = 0.6R = 6
Q = 0.8P = 4.8
S= 0.6P = 3.6
FOR THAT WE GET S = 7.6
AND Q 10.8
SO 10.8/7.6 = 2.7/ 1.9
Ans:E
Answer: E
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)21
D)23
E)24
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B
Answer: B
Question: A and B together can complete a work in 3 days. They start together but after 2 days,B left the work.If the work is completed after two more days, find the B alone could do the work?
Options:
A)8
B)20
C)6
D)21
E)10
Rationale: A and B(one day work)=1/3 part
(A+B) works 2 days together=2/3 part
Remaining work=1-(2/3) part=1/3 part
1/3 part of the work is completed by A in two days=(1/3)*(1/2)
One day's work of A=1/6 part
One day's work of B=(1/3)-(1/6)=1/6
So,B alone can do the work in 6 days
Answer is option C
Answer: C
Question: Train C and D, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train C left at 4 pm traveling at a speed of 60 miles per hour, and train D left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?
Options:
A)9:05 pm
B)9:06 pm
C)9:07 pm
D)9:08 pm
E)9:09 pm
Rationale: First, since C has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles
Then remaining distance to be traveled will be 455 - 105 = 350 miles
Now, using relative rates (105)(t) = 350
This gives 10/3 hours
Now 5.45pm + 10/3 hours gives us 9.05pm
Hence answer is A
Answer: A
Question: Find the average of the series : 312, 162, 132, 142 and 122?
Options:
A)298
B)269
C)927
D)174
E)291
Rationale: Average = (312 + 162 + 132 + 142 + 122)/5 = 870/5 = 174.Answer: D
Answer: D
Question: During one month at a particular restaurant, 1/6 of the burgers sold were veggie burgers and 1/5 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
Options:
A)x
B)x/2
C)2x/3
D)3x/4
E)4x/5
Rationale: T/6 - Veggi
(1/5)[T - (T/6)] = double meat = x = 5T/30
=> Veggie = T/6 = 5x/5=x
Answer is A.
Answer: A
Question: In case M is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
A)V and U
B)V and T
C)U and S
D)N and O
E)T and U
Rationale: N and O should serve on A
ANSWER:D
Answer: D
Question: When 2/3 of the garments in the shipment were inspected, 15 of the garments passed inspection and the remaining 5 garments failed. How many of the uninspected garments must pass inspection in order that 80 percent of the garments in the shipment pass?
Options:
A)10
B)9
C)8
D)7
E)5
Rationale: B = 9
2/3x= 20
x=30
for 80% approval we need 24 garments approved.
already approved = 15
we need 9 more.
Answer : B
Answer: B
Question: If w<0, which of the following must be true?
Options:
A)–100 < w < 100
B)w ≤ –1
C)w ≤ 1
D)w^2 ≥ 1/4
E)–100 < w < 0
Rationale: w is a negative number.
A. –100 < w < 100w can be a negative number less than -100
B. w ≤ –1w can be a fraction, in which case it would be greater than -1
C. w ≤ 1must be true since 1 is positive and w is negative
D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5
E. –100 < w < 0w can be a negative number less than -100=C
Answer: C
Question: If 5 spiders make 2 webs in 8 days, then how many days are needed for 1 spider to make 1 web?
Options:
A)10
B)15
C)30
D)20
E)16
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)5:1
(webs) 1:8}::x:2
â‡’5Ã—1Ã—8=1Ã—2 Ã— x
â‡’x=20
Answer: Option D
Answer: D
Question: We made a down payment of $25 and borrowed the balance on a new sofa which cost $250. The balance with interest was paid in 23 monthly payments of $11 each and a final payment of $17. The amount of interest paid was what percent of the amount borrowed?
Options:
A)20%
B)22%
C)25%
D)27%
E)30%
Rationale: We borrowed $225.
To pay back this loan, we paid 23*$11 + $17=$270.
The interest was $270-$225=$45.
The percentage was $45/$225=0.2=20%.
The answer is A.
Answer: A
Question: Rs.500 amounts to Rs.670 in 5 years at simple interest. If the interest is increased by 2%, it would amount to how much?
Options:
A)150
B)550
C)760
D)450
E)260
Rationale: (500*5*2)/100 = 50
500+ 50 = 550
Answer: B
Answer: B
Question: A Man travelled a distance of 51 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on
bicycle at 9 km/hr. What is the distance travelled on foot?
Options:
A)16 km
B)24 km
C)12 km
D)10 km
E)None of these
Rationale: Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 51 km
So,
4x + 9(9-x) = 51
=> 5x = 30
=> x = 6
So distance traveled on foot = 4(6) = 24 km
Answer: Option B
Answer: B
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)17
B)25
C)88
D)26
E)27
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer:B
Answer: B
Question: If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
Options:
A)50%
B)75%
C)120%
D)133 1/3%
E)150%
Rationale: The price on June 1st = 12 (assume);
The price on May 1st = 2/3*12 = 8;
The price on July 1st = 8*1.50 = 12.
The average price of the bond on May 1st and July 1st = (8+12)/2 = 10.
The price of the bond on June 1st (12) is 6/5 times (120%) the average price of the bond on May 1st and July 1st.
Answer: C.
Answer: C
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000?
Options:
A)6620
B)2888
C)2776
D)9930
E)2718
Rationale: A = 30000(11/10)^3
= 39930
= 30000
----------
9930.Answer: D
Answer: D
Question: At what rate percent per annum will a sum of money double in 8 years.
Options:
A)12.5%
B)12.9%
C)18.5%
D)11.5%
E)12.3%
Rationale: Explanation:
Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum.
Answer: A) 12.5%
Answer: A
Question: Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?
Options:
A)240
B)180
C)160
D)140
E)120
Rationale: 3x + 4x = 420
x = 60 => 3x = 180
ANSWER:B
Answer: B
Question: A train covers a distance of 12 km in 10 minutes. If it takes 8 seconds to pass a telegraph post, then the length of the train is
Options:
A)100m
B)120m
C)140m
D)160m
E)170cm
Rationale: Explanation:
Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.
Length of the train = (Speed x Time) = (20 x 8) m = 160 m
Answer: Option D
Answer: D
Question: A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 5
II. 1
III. -3
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
Answer: C
Question: A father was as old as his son's present at the time of your birth. If the father's age is 44 years now, the son's age 5years back was?
Options:
A)10 years
B)12 years
C)14 years
D)16 years
E)17 years
Rationale: Let the son's present age be x years. Then, (44 - x) = x
2x = 44.
x = 22.
Son's age 5 years back (22 - 5) = 17 years.
E
Answer: E
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 5, how many people got on at the first stop?
Options:
A)128
B)64
C)32
D)16
E)8
Rationale: 7 - > 1
6 - > 2
5 - > 4
4 - > 8
3 - > 16
2 - > 32
1 - > 64
because people get off after the first stop
=> the formula will be : 2^(n-1) where n is the stop number
in this case n = 5
=> 2^(5-1) = 2^4 = 16
=> answer is D
Answer: D
Question: If a is an odd integer and b is an odd integer and a > b which of the following must be an odd integer :
Options:
A)a/b
B)ab
C)2a+b
D)2(a+b)
E)option A B and C
Rationale: a= odd = e.g 9
b= odd = e.g 3
A. odd/odd for example 9/3 = 3 odd
B. odd * odd = 3 * 9 = 27 odd
C. 2*odd + odd = even + odd odd
D. 2(odd + odd) = 2(even) even
Hence E it is.
Answer: E
Question: The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Also note here the relevance of 'K must be less than 400'.
21K is 180n (a multiple of 180).
180n = 2^2 * 3^2 * 5 * n = 3*7*K
n must have a 7 at least.
K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60.
So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 60*7 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 60*2 or 60*3*2 or 60*5 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has.
Answer (C)
Answer: C
Question: If f(x)=x^2 and x is a natural number, what CANNOT be the solution to f(f(f(x)))?
Options:
A)16384
B)65536
C)6561
D)256
E)1
Rationale: Answer A is equal to 4^7 and cannot be a solution because f(f(f(x)) is equivalent to x^8 and 4^7 cannot equal to anything to the power of 8.
Answer: A
Question: The speed of a boat in still water in 22 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:
Options:
A)9.4 km
B)10.2 km
C)10.4 km
D)9.2 km
E)None of these
Rationale: Explanation :
Speed downstream = (22 + 4) = 26 kmph
Time = 24 minutes = 24/60 hour = 2/5 hour
distance travelled = Time × speed = (2/5)×26 = 10.4 km. Answer : Option C
Answer: C
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 1/2 hours; pumps A and C, operating simultaneously, can fill the tank in 1/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
Options:
A)1/3
B)1/2
C)1/4
D)1
E)5/6
Rationale: A+B =1/2 ; A+C =1/2 ,B+C =2 ; ADD THEN 2*(A+B+C) = 3
A+B+C = 3/2 HRS
E
Answer: E
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
Options:
A)1.6
B)1
C)0.4
D)0.16
E)0.016
Rationale: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*16*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 160/10,000 = 16/1000 = 0.016 ft
The answer is E.
Answer: E
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
Options:
A)1261
B)1868
C)6286
D)2678
E)1524
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer: A
Answer: A
Question: The diagonals of a rhombus are 16 cm and 20 cm. Find its area?
Options:
A)160
B)288
C)150
D)238
E)31
Rationale: 1/2 * 16 * 20 = 160
Answer: A
Answer: A
Question: A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected ?
Options:
A)17/42
B)18/27
C)5/42
D)3/15
E)15/47
Rationale: 3 letters can be choosen out of 9 letters in 9C3 ways
(2 vowels + 1 constant or 3 vowels) -> 4C2*85C1) + 4C3 ways
=> req probability = (4C2 * 5C1)+4C3/9C3 = 17/42
ANSWER A
Answer: A
Question: A shopkeeper sells 600 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
Options:
A)12
B)27
C)29
D)35
E)21
Rationale: SP per metre = 18000/600 = Rs. 40 Loss per metre = Rs. 5 CP per metre = 40 + 5 = Rs. 45.Answer: D
Answer: D
Question: each interior angle of a regular polygon is 120 degrees greator than each exterior angle.how many sides are there in the polygon
Options:
A)6
B)8
C)12
D)16
E)18
Rationale: Interior angle = 180 - (360/n)
Exterior angle = (360/n)
Given: IA = 120 + EA
=> 180 - (360/n) = 120 + (360/n)
=> n = 12
ANSWER:C
Answer: C
Question: A person borrows Rs. 8000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
Options:
A)100 rs
B)150 rs
C)160 rs
D)180 rs
E)200 rs
Rationale: Gain in 2 years =
[(8000*6*2)/100]-[(8000*4*2)/100]
960-640=320
Gain in 1 year =(320/2)=160 rs
ANSWER:C
Answer: C
Question: Insert the missing number
3, 4, 7, 16, 43, 124, ...
Options:
A)367
B)356
C)125
D)1222
E)1322
Rationale: Series is having difference between susequest next number and the nuber with multiplication by 3
3, 4, 7, 16, 43, 124, ...
Differnce between 4 and 3 is 1, multiply with three and add 4 to it. 7 will come
Differnce between 7 and 4 is 3, multiply with three and add 7 to it. 16 will come
differnce between 16 and 7 is 9, multiply with three and add 16 to it. 43 will come
differnce between 43 and 16 is 27, multiply with three and add 43 to it. 124 will come
differnce between 124 and 43 is 81, multiply with three and add 124 to it. 367 will come
ANSWER:A
Answer: A
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
A. 32 km B. 25 km
Options:
A)65 km
B)88 km
C)44 km
D)02 km
E)20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer: E
Answer: E
Question: If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A^B is also a prime number.
Options:
A)1 only.
B)2 only.
C)3 only.
D)2 and 3 only.
E)1, 2 and 3.
Rationale: (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A x B is also a prime number. : Beats the property of primes, so false
(3) A^B is also a prime number. : Beats the property of primes, so false
Answer : 2 and 3 only
ANSWER:D
Answer: D
Question: A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
Options:
A)4/19
B)7/19
C)12/19
D)21/99
E)26/77
Rationale: Solution
P( None is defective)
= 18C2 / 22C2
= 51/77
P( at least one is defective)
= (1- 51/77)
= 26/77.
Answer E
Answer: E
Question: How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3?
Options:
A)3/10
B)4/10
C)6/10
D)7/10
E)9/10
Rationale: arrangement = 5!/3!=20
Probability of getting all 3 balls=
3 from 5=5c3
1 from 3 red ball,1 green,1 yellow
(3c1*1c1*1c1)/5c3 =3/10
ANSWER:A
Answer: A
Question: Fresh grapes contain 60% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 30kg of fresh grapes?
Options:
A)10 kg
B)15 kg
C)20 kg
D)25 kg
E)40 kg
Rationale: From the question we know: 30kg * 60% = 18 kg of water in the fresh grapes
30kg - 18kg of water = 12kg of non-water mass
We are looking for the weight of the dry grapes (X).
Since the question tells us that 20% of the weight of the dry graps is water and we know that 12kg is non-water mass we can set up the following equation:
X = 1/5(X) + 12kg
4/5(X) = 12kg
X = 15 kg
Answer- B
Answer: B
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
Options:
A)15
B)10
C)20
D)18
E)12
Rationale: 1/6 â€“ 1/15 = 1/10 => 10
ANSWER B
Answer: B
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 28,000. What was Simran's share in the profit?
Options:
A)Rs. 9423
B)Rs. 10,250
C)Rs. 12,000
D)Rs. 14,000
E)None of these
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 28000 * 3/7 = Rs. 12000
ANSWER:C
Answer: C
Question: A library has 360 math books; 60 Calculus books, 120 Geometry books, and 180 Algebra books. What percentage of books are Geometry books ?
Options:
A)33.3 %
B)16.7 %
C)66.7 %
D)77 %
E)None of these
Rationale: Explanation :
Geometry Book percentage = (120/360 x 100)%
= 33.3 %
Answer : A
Answer: A
Question: Rick deposited $650 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?
Options:
A)5.
B)25.
C)50.
D)35.
E)65.
Rationale: 5x+15y=650 --1
x+y=60 ---2
multiply eq 2 with 5 and subtract from eq 1
5x+15y=650
5x+5y=300
10y= 350
y=35 and x = 25
therefore $15 bills = 35
Answer D
Answer: D