divelab/Sys2Bench huggingface dataset:
Question: A can do a piece of work in 4 hours; B and C together can do it in 2 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
A)12
B)9
C)8
D)6
E)4
Rationale: A's 1 hour's work = 1/4 ;
(B + C)'s 1 hour's work = 1/2 ;
(A + C)'s 1 hour's work = 1/2 .
(A + B + C)'s 1 hour's work = ( 1/4+ 1/2) =3/4 .
B's 1 hour's work = ( 3/4 - 1/2 ) = 1/4.
Therefore A alone will take 4 hours to do the work.
E
Answer: E
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)45 km/hr
B)50 km/hr
C)54 km/hr
D)55 km/hr
E)57 km/hr
Rationale: Speed of the train relative to man =125/10 m/sec
=25/2 m/sec.
=25	/2x18/5km/hr
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 x =50 km/hr.
Answer:B
Answer: B
Question: A kindergarten class is going to a play with some teachers. Tickets cost 5 dollars for children and 12 dollars for adults
Number of tickets sold amount to 163 dollars.
How many teachers and children went to the play?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: First, make sure you understand the problem. What the problem is really asking is the following:
How many adult tickets were sold? How many children tickets were sold?
Guess and check!
Pretend that 3 children tickets were sold. Then, 17 adult tickets were sold
Total cost = 3 × 5 + 17 × 12 = 15 + 204 = 219
The total is too high. Pretend that 14 children tickets were sold. Then, 6 adult tickets were sold
Total cost = 14 × 5 + 6 × 12 = 70 + 72 = 142
The total is a little too low now. Pretend that 12 children tickets were sold. Then, 8 adult tickets were sold
Total cost = 12 × 5 + 8 × 12 = 60 + 96 = 156
As you can see, it is going higher again and it is getting closer to 163. May be 11 tickets for children and 9 tickets for adults will work
Total cost = 11 × 5 + 9 × 12 = 55 + 108 = 163
Here we go! 11 children and 9 teachers went to the play
Answer B
Answer: B
Question: How many words can be formed from the letters of the word SIGNATURE so that the vowels always come together?
Options:
A)720
B)1440
C)3600
D)2880
E)None of these
Rationale: The word SIGNATURE consists of nine letters comprising four vowels (A, E, I and U) and five consonants (G, N, R, T and S). When the four vowels are considered as one letter, we have six letters which can be arranged in 6P6 ways i.e 6! ways. Note that the four vowels can be arranged in 4! ways.
Hence required number of words
= 6! × 4! = 720 × 24
= 17280
Answer E
Answer: E
Question: By selling a watch for Rs.480/-, a man loses 20% what is that watch cost price?
Options:
A)s. 600/-
B)s. 700/-
C)s. 800/-
D)s. 850/-
E)s. 900/-
Rationale: 80 % ------> 480 (80 * 6 = 480)
100 % ------>600 (100 * 6 = 600)
Cost price = Rs. 600/-
A)
Answer: A
Question: A CAN FINISH A WORK IN 15 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
Options:
A)5
B)5 1/2
C)6
D)8
E)NONE OF THESE
Rationale: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (15*1/3)=5 DAYS.
CORRECT OPTION:A
Answer: A
Question: Pipe A can fill the tank in 50 minutes and pipe B in 40min and pipe C can empty the tank in 2 hours. How long it will take to fill the tank if three of the pipes are operating together?
Options:
A)22.22
B)27.27
C)29.35
D)31.2
E)35.6
Rationale: Pipe A fills 1/50th of the tank in a minute and pipe B, 1/40th. Pipe C empties in 120min(2 hours)
(1/50)+(1/40)-(1/120)=(1/x)
22/600=1/x => x=600/22 => x=27.27 minutes
Answer: B
Answer: B
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)19
B)50
C)72
D)25
E)28
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Answer: B
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Options:
A)59002
B)59001
C)59008
D)59000
E)59004
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer: D
Answer: D
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y + 2)
II. z>(x − 1)/(y + 2)
III. z>(x + 1)/(y - 2)
Options:
A)I only
B)I and II
C)II and III
D)II only
E)I and III
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y + 2) --> 2/3 > 1/5 --> True
II. z>(x − 1)/(y + 2) --> 2/3 < 1/5 --> True
III. z>(x + 1)/(y - 2) --> 2/3 > 3/1 --> False
Answer: B
Answer: B
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
Options:
A)65
B)44
C)18
D)16
E)14
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer:C
Answer: C
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
Options:
A)90
B)27
C)21 sec
D)92
E)62
Rationale: Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5)
= 90 sec.
Answer: A
Answer: A
Question: Three years ago, Arjun’s age was double of Ajith’s age. Seven years hence, the sum of their united ages will be 83 years. The age of Arjun today is ?
Options:
A)47 years
B)45 years
C)35 years
D)24 years
E)None of these
Rationale: Let us consider Arjun’s age to be X,
X - 3 = 2 (Y - 3) or X - 2Y = - 3 ...(i)
(X + 7) + (Y + 7) = 83 or X + Y = 69 ...(ii)
Therefore, Y= 24, X = 45.
The age of X today = 45 years
ANSWER:B
Answer: B
Question: If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 3)?
Options:
A)3
B)P + 2
C)p – 2
D)3p – 1
E)2p + 1
Rationale: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+3)=pq+3p is (pq+3p-pq)-1=3p-1.
Answer: D.
Answer: D
Question: A river 4m deep and 40 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is?
Options:
A)10666
B)11678
C)12345
D)10678
E)19099
Rationale: (4000 * 4 * 40)/60
= 10666 M3
Answer:A
Answer: A
Question: If D||D', D:2x - y = 1 and D':(a - 1)x + 2y = x - 2, then find the value of a.
Options:
A)-3
B)-2
C)-1
D)0
E)1
Rationale: D:2x−y=1, D’:(a−1)x+2y=x−2
D:2x−y=1, D′:(a−1)x+2y=x−2
D∥D′⇒mD=m′
DD∥D′⇒mD=mD′
2x−y=1→y=2x−1→mD=22x−y=1→y=2x−1→mD=2
(a−1)x+2y=x−2→2y=x(1−a+1)−2→2y=x(2−a)−2→(a−1)x+2y=x−2→2y=x(1−a+1)−2→2y=x(2−a)−2→
y=x×(2−a)2−1→m′D=(2−a)2y=x×(2−a)2−1→mD′=(2−a)2
mD=m′D→(2−a)2=2→2−a=4→a=−2
ANSWER : B -2
Answer: B
Question: How much greater is the value of 3x + 5 than the value of 3x − 7?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Explanation: The easiest way to do this is to pick a number for x. Let’s say x = 3.
3(3) + 5
= 9 + 5
= 14
3(3) − 7
= 9 − 7
= 2
The correct answer is 14 − 2 = 12.
Answer : (C)
Answer: C
Question: Arun bought a computer with 15% discount on the labeled price. He sold the computer for $2880 with 20% profit on the labeled price. At what price did he buy the computer?
Options:
A)$2440
B)$2420
C)$2410
D)$2310
E)$2040
Rationale: SP = 2880
Arun sold the computer with 20% profit on the Labeled Price
⇒2880=(120×Labeled Price) / 100
⇒Labeled Price=(2880×100)/120=28800/12=96004=2400
Arun bought a computer with 15% discount on the labeled price
=> CP = (Labeled Price×85) / 100=(2400×85) / 100=24×85=2040
ANSWER:E
Answer: E
Question: The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is:
Options:
A)30/7
B)30/98
C)60/147
D)50/294
E)52/294
Rationale: Required fraction = L.C.M of 6/7, 5/14, 10/21
= (L.C.M of 6, 5, 10) / (H.C.F of 7, 14, 21) = 30/7
ANSWER:A
Answer: A
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 37.5 miles ahead of Joe?
Options:
A)15
B)60
C)180
D)90
E)105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Joe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +37.5 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 37.5 miles in 150 mins
So answer 30+150= 180 mins. (ANSWER C)
Answer: C
Question: If the area of a circle is 81pi square feet, find its circumference.
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: The area is given by pi * r *r. Hence
pi* r *r = 81 pi
r * r = 81 * hence r = 81 feet
The circumference is given by
2 * pi * r = 2 * pi *9 = 18 pi feet
correct answer D
Answer: D
Question: A person can row at 9 kmph and still water. He takes 3 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?
Options:
A)32
B)28
C)29
D)54
E)16
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 3.5
=> x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x
= 16 km.
Answer:E
Answer: E
Question: Of the c students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
Options:
A) c + w- x- y
B) c - w- x- y
C) z- w - x + y
D) w + x + y- z
E) w - x - y - z
Rationale: {Total} = {French} + {German} - {Both} + {Neither}
c = x + y - w + {Neither}
{Neither} = c + w - x - y.
Answer: A.
Answer: A
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 27. What is the difference between the two digits of that number?
Options:
A)3
B)5
C)6
D)8
E)9
Rationale: Sol.
Let the ten’s digit be x and unit’s digit be y,
Then, (10x + y) - (10y + x) = 27 ⇔ 9 (x - y) = 27
⇔ x - y = 3
Answer A
Answer: A
Question: The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 47 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?
Options:
A)55
B)56
C)57
D)58
E)59
Rationale: 20x + 47 = 21(x – 5)
X=58
ANSWER:D
Answer: D
Question: If it is true that z < 8 and 2z > -4, which of the following must be true?
Options:
A) -8 < z < 4
B) z > 2
C) z > -8
D) z < 4
E) None of the above
Rationale: Two points:
1) z < 8
2) 2z > -4 or z > -2
From 1 and 2: -2 < z < 8
(A) is not true because z could be > 4.
(B) is not true because z could be < 2.
(C) is true because z's value is always > -8.
(D) is not true because z could be >4.
(E) is not true because C is true.
Answer: C
Question: 20% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 3000. Find the number of original inhabitants?
Options:
A)2500
B)3000
C)1500
D)2000
E)5000
Rationale: Let the total number of original inhabitants be x
Then, (100-25)% of (100-20)% of x = 3000
75/100 * 80/100 * x = 3000
x = 5000
Answer is E
Answer: E
Question: Susan finds that she spends her free time during summer vacation between swimming, reading, and hanging out with friends in a ratio of 1:4:10. How many hours did she spend reading if she hung out with her friends for 20 hours?
Options:
A)2
B)4
C)5
D)8
E)10
Rationale: The ratio is 1 hour swimming: 4 hours reading: 10 hours hanging out with friends.
Divide 20 by 10 to find 1 "part" of the ratio.
20/10 = 2
Multiply this by 4 to find the hours spent reading.
2*4 = 8
The answer is D.
Answer: D
Question: 8 ÷ 4 (3 - 2) x 4 + 3 - 7 = ?
Options:
A)- 3
B)- 4
C)4
D)5
E)6
Rationale: Answer
Given expression = 8 ÷ 4 (3 - 2) x 4 + 3 - 7
= 8 x (1/4) x 1 x 4 + 3 - 7
= 8 + 3 - 7
= 4
Option: C
Answer: C
Question: 0.01 x 0.02=?
Options:
A)3.15e-05
B)0.000315
C)0.2
D)0.02
E)0.0002
Rationale: 1 x 2 = 2
Sum of decimal places =4
Therefore, 0.01 x 0.02 = 0.0002
Answer is E.
Answer: E
Question: Jug contains water and orange juice in the ratio 5:7 . another jug contains water and orange juice in ratio 7 : 2 . In what proportion should these 2 liquids be mixed to give a water and orange juice in ratio 3 : 4
Options:
A)4 : 5
B)85 : 3
C)88 : 3
D)2 : 3
E)87 : 7
Rationale: Let x ml of Jug 1 be mixed with y ml of jug 2
5x/12 + 7y/9 = 3/7*(x+y)
7x/12 + 2y/9 = 4/7 *(x+y)
=> (15x + 28y)/36 = 3/7 * (x+y)
=> 105x + 196y = 108x + 108y
=> 88y - 3x = 0
=> x/y = 88/3
Answer - C
Answer: C
Question: If Jamie's income is Rs 20000, calculate his savings given that his income and expenditure are in the ratio 7:5.?
Options:
A)Rs 7500
B)Rs 4000
C)Rs 2000
D)Rs 8000
E)Rs 7000
Rationale: Let the income and the expenditure of the person be Rs.7x and Rs.7x respectively.
Income, 7x = 28000 => x = 4000
Savings = Income - expenditure = 7x - 5x = 2x
So, savings = Rs.8000
Answer: D
Answer: D
Question: If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
Options:
A)0.2
B)0.4
C)0.3
D)-0.4
E)0.1
Rationale: (0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer : D
Answer: D
Question: Find the odd man out
15, 35, 45, 24 ,55, 65, 95
Options:
A)15
B)24
C)55
D)95
E)35
Rationale: In the series, 24 is the number which is not divisible by 5.
ANSWER:B
Answer: B
Question: If the sales tax be reduced from 4 (1/5) % to 3(1/4) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 5400?
Options:
A)Rs. 100.2
B)Rs. 50.2
C)Rs. 20.5
D)Rs. 100
E)None of these
Rationale: Explanation:
Required difference = (4 (1/5) of Rs. 5400) - (3 (1/4) of Rs. 5400)
= (21/5 – 13/4) % of Rs. 5400
= (19/20) x (1/100) x 5400
= Rs. 51.30
ANSWER E
Answer: E
Question: If the a radio is sold for rs 490 and sold for rs 465.50.find loss%.
Options:
A)2%
B)4%
C)3%
D)5%
E)6%
Rationale: sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
ANSWER D
Answer: D
Question: Paul’s salary is reduced by 50% and then reduced salary is increased by 50%. Find ,how many percentage his present salary is less as compared to his previous salary?
Options:
A)20%
B)25%
C)30%
D)15%
E)10%
Rationale: 50*50
-------- = 25%
100
Answer: B
Answer: B
Question: Peter invests a sum of money and gets back an amount of $ 810 in 3 years . David invests an equal amount of money and gets an amount of $854 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
Options:
A)670
B)683
C)698
D)744
E)700
Rationale: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 854 - 810 = 44
Interest earned for 3 years = 44*3 = 132
Amount invested = 815 - 132= 683
Answer: B
Answer: B
Question: Which of the following has a decimal equivalent that is a terminating decimal?
Options:
A)2/3^20
B)3^5/20^3
C)2^3/3^2
D)8^2/7^5
E)3^6/6^3
Rationale: For a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values
Hence,
1. There is a 3 in the denominator, hence it is a non terminating decimal
2. Has both 2 and 5 in the denominator, hence terminating
3. There is a 3 in the denominator, hence it is a non terminating decimal
4. There is a 7 in the denominator, hence it is a non terminating decimal
5. Has both 2 & 3 in the denominator, hence non terminating
Option B
Answer: B
Question: What is theleast number should be added to 410, so the sum of the number is completely divisible by 20?
Options:
A)1
B)2
C)10
D)6
E)8
Rationale: (410 / 20) gives remainder 10
10 + 10 = 20, So we need to add 10
Answer : C
Answer: C
Question: A dishonest DEALER professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
Options:
A)29%
B)25%
C)235%
D)85%
E)22%
Rationale: 800 --- 200
100 --- ? => 25%
Answer: B
Answer: B
Question: Let C be defined as the sum of all prime numbers between 0 and 38. What is C/3
Options:
A)155
B)76.6
C)61
D)47
E)43
Rationale: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23 , 29, 31, 33, 37
Sum,C = 230
C/3 = 76.6
Answer B
Answer: B
Question: If 3g + 1 < 2g < 9 - g, which of the following must be true?
I. -1 < g < 3
II. g < -1
III. g < 3
Options:
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
Rationale: Just try plugging g in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.
So you can immediately cross out any answers with I or III, leaving just (A) II only.
Answer: A
Question: For any positive integer n, n>1, thelengthof n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 60 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
Options:
A)10
B)9
C)8
D)7
E)6
Rationale: you are missing something in your post:
For any positive integer n , n > 1, thelengthof n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)
the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6
but we need n < 1000
using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 8 the length of 512.
the answer is (C)
Answer: C
Question: If a student handwrites her homework it takes her 5 hours to complete it, instead if she types it takes her 8 hours to compete. Since her teacher does not mind, she starts handwriting and after 1 hour, she switches to the computer and continues by typing for 2 hours. Then asking her brother to help, he types another 11 hours and homework is completed. How long would it take to complete the homework, if she had asked her brother for help in the first place.
Options:
A)5 hours
B)10 hours
C)15 hours
D)20 hours
E)25 hours
Rationale: 1/5+2/8 + 3/x = 1x =20 hours. ANSWER =D
Answer: D
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
Options:
A)7
B)9
C)11
D)13
E)14
Rationale: Explanation:
3x + 5x + 7x = 45
x =3
3x = 9
B)
Answer: B
Question: Two trains 200 m and 180 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
Options:
A)72 sec
B)132 sec
C)192 sec
D)273.6 sec
E)None
Rationale: Solution
Relative Speed	= (45 - 40 ) Kmph
= 5 kmph
=(5 x 5 / 18)m/sec
= (25 / 18 ) m/sec
Time taken	= (380 x 18 / 25) sec
= 273.6 sec.
Answer D
Answer: D
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 3 years and that for 15 years?
Options:
A)3 : 2
B)1 : 5
C)2 : 3
D)3 : 1
E)2 : 1
Rationale: Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 3 years/Simple Interest for 15 years
=T1/T2
=3/15
=1/5
=1:5
Answer : Option B
Answer: B
Question: A 90-liter solution of cool-drink is made from 5% jasmine water. If 8 liters of jasmine and 2 liters of water were added to the solution, what percent of the solution is jasmine?
Options:
A)6.5%
B)8.5%
C)10.5%
D)12.5%
E)14.5%
Rationale: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)
(0.05(90) + 8) / 100 = 12.5/100 = 12.5%
The answer is D.
Answer: D
Question: What is the units digit of 17^83 × 13^82 × 11^67?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: To find : the units digit of 17^83 × 13^82 × 11^87
Let's reduce the clutter and simplify the product
(7^83) (3^82) (1^87)
7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4th power
so 7^5 has the same last digit as 7^1, 7^9, 7^13
Thus , 7^83 has the same last digit as 7^3, 7^7, 7^11 i.e.3
3 has a cyclicity of 4 : exactly the same routine as above
Thus , 3^82 has the same last digit as 3^2, 3^6, 3^10 i.e.9
Any power of 1 will result in1as the last digit
So, product of our last digits = 3 x 9 x 1 = 27....last digit is 4
Correct Option : A
Answer: A
Question: ABCD is a square where AB =âˆš6000. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD.
Options:
A)3008
B)2002
C)1008
D)2016
E)3000
Rationale: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is
always
6000/2= 3000 .
correct answer E
Answer: E
Question: The sale price sarees listed for Rs.400 after successive discount is 12% and 5% is?
Options:
A)338
B)277
C)342
D)334.4
E)212
Rationale: 400*(88/100)*(95/100) = 334.4
Answer: D
Answer: D
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Options:
A)5:4
B)4:5
C)2:5
D)5:2
E)None of them
Rationale: Let the third number be x.
Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2
Therefore, Ratio of first two numbers = (6x/5 : 3x/2)
= 12x : 15x = 4 : 5.
Answer is B.
Answer: B
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
Options:
A)2/23
B)3/23
C)4/25
D)5/26
E)8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: E
Question: 45 x ? = 45% of 900
Options:
A)16.2
B)4
C)5
D)9
E)11
Rationale: Answer
Let 45 x A = (25 x 900)/100
∴ A = (45 x 9)/45 = 9
Correct Option: D
Answer: D
Question: A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability E that all 3 jellybeans removed from the bag are blue?
Options:
A)9/100
B)2/19
C)1/8
D)3/20
E)3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability E= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B
Answer: B