divelab/Sys2Bench huggingface dataset:
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Options:
A)200 m
B)876 m
C)868 m
D)100 m
E)862 m
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: D
Question: If 2/3rd of the contents of a container evaporated on the 1st day. And 1/4th of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day?
Options:
A)1/4
B)1/12
C)1/18
D)1/6
E)1/2
Rationale: After first day, 1/3 of the contents remain.
After second day,
(1/3) - (1/4(2/3)) = (1/3) - (1/6) = 1/6 of the contents remain
ANSWER:D
Answer: D
Question: A sum fetched a total simple interest of 4052.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
Options:
A)9005
B)8925
C)2345
D)6474
E)8723
Rationale: Principal = (100 x 4052.25)/(9 x 5)
= 405225/45
= 9005.
ANSWER A
Answer: A
Question: Every day a certain bank calculates its average daily deposit for that calendar month up to and including that day. If on a randomly chosen day in June the sum of all deposits up to and including that day is a prime integer greater than 100, what is the probability that the average daily deposit up to and including that day contains fewer than 5 decimal places?
(A)
(B)
(C)
(D)
(E)
Options:
A)1/10
B)2/15
C)4/15
D)3/10
E)11/30
Rationale: average=p/d has less than 5 decimal places? Where p=prime>100 and d is the chosen day.
If the chosen day, d, is NOT of a type 2^n5^m (where n and m are nonnegative integers) then average=p/d will not be a terminating decimal and thus will have more than 5 decimal places.
How many such days are there of a type 2n5m: 1, 2, 4, 5, 8, 10, 16, 20, 25 (1=2^0∗5^0, 2=2^2, 4=2^2, 5, 8=2^3, 10=2∗5, 16=2^4, 20=22∗5, 2^5=52), total of 9 such days (1st of June, 4th of June, ...).
Now, does p divided by any of these d′s have fewer than 5 decimal places? Yes, as p/d∗10,000=integer for any such d (10,000 is divisible by all these numbers: 1, 2, 4, 5, 8, 10, 16, 20, 25).
So, there are 9 such days out of 30 in June: P=9/30=3/10 .
Answer: D.
Answer: D
Question: (3 x 10^4) + (2 x 10^3) + (4 x 10^2) =
Options:
A)302400
B)32400
C)30240
D)3240
E)324
Rationale: When you multiply a number by 10 you just add a zero
=> 3 x 10^4 => add 4 zeros => 3 x 10^4 = 30000
=>2 x 10^3 = 2000
=> 4 x 10^2 = 400
=>3 x 10^4 + 2 x 10^3 + 4 x 10^2 = 30000 + 2000 + 400 = 32400
=> answer is B ( 32400)
Answer: B
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
Options:
A)22%
B)31%
C)25%
D)30%
E)29%
Rationale: C
25%
Let C.P. = $ 4x. Then, S.P. = $ 5x
Gain = (5x - 4x) = $ x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 6 years ago was 20 years. The present age of the husband is:
Options:
A)20 years
B)30 years
C)60 years
D)38 years
E)35 years
Rationale: D
38 years
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 6 x 2) years = 52 years.
Husband's present age = (90 - 52) years = 38 years.
Answer: D
Question: A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone can finish the job?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Explanation:
(A+B)'s 15 days work = (1/20 × 15) = ¾
Remaining work = (1 - ¾) = ¼
Now, ¼ work is done by A in 10 days.
Whole work will bedone by A in (10 × 4 = 40) days.
Answer: B
Answer: B
Question: If n and k are integers whose product is 400, which of the following statements must be true?
Options:
A)n + k > 0
B)n is not equal to k.
C)Either n or k is a multiple of 10.
D)If n is even, then k is odd.
E)If n is odd, then k is even.
Rationale: For the product of two integers to be even at least one integer must be even.
A. n+k>0 --> not necessarily true: nk=(−20)∗(−20)=400
B. n does not equal k --> not necessarily true: nk=20∗20=400
C. Either n or k is a multiple of 10 --> not necessarily true: nk=16∗25=400
D. If n is even, then k is odd --> not necessarily true, nn can be even and kk be even too --> nk=20∗20=400
E. If n is odd, then k is even --> this must be true, if one of the factors is odd (nn) the second one (kk) must be even for their product to be even.
Answer: E.
Answer: E
Question: In a camp,there is a meal for 140 men or 200 children.If 150 children have taken the meal,how many men will be catered to with the remaining meal ?
Options:
A)35
B)30
C)40
D)50
E)60
Rationale: Solution
There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 140 men
50 children =( 140/200x50)men= 35 men. Answer A
Answer: A
Question: The average of 65 numbers is 40. If two numbers, 40 and 60 are discarded, then the average of the remaining numbers is nearly
Options:
A)28.32
B)39
C)38.78
D)39.68
E)30
Rationale: Explanation :
Total sum of 63 numbers = (65 * 40) - (40+60) = 2600 - 100 = 2500
Average = 2457/63 = 39.68
Answer : D
Answer: D
Question: If you roll one fair six-sided die, what is the probability that the number is odd or greater than 3?
Options:
A)1/2
B)2/3
C)3/4
D)4/5
E)5/6
Rationale: The numbers which satisfy the conditions are 1, 3, 4, 5, and 6.
The probability is 5/6
The answer is E.
Answer: E
Question: If a man buys 10 lollipops for $80 and sold them for $5 dollars determine his loss.
Options:
A)50
B)60
C)70
D)80
E)30
Rationale: Cost of 10 lollipops = $80
Sold each lollipop for $5
So he sold 10 lollipops for $(10 × 5) = $50
Loss = $(80 – 50) = $30
answer :E
Therefore, loss = $ 30.
Answer: E
Question: Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer W represents the product of all elements in set X and if 11W is an even number, what is the range of set X?
Options:
A) 14
B) 16
C) 17
D) 20
E) 26
Rationale: Since 11W = Even therefore W has to beEVENsince 11 is a odd integer (Even * Odd = Even)
Similarly, W is the product of all integers in set X But all integers in Set X are odd except the unknown K and since X contains only prime numbers, K has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)
Since you know value of K you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =17
Answer is C
Answer: C
Question: If D is the least common multiple of 90,196, and 300, which of the following is NOT a factor of D?
Options:
A)600
B)700
C)900
D)2,100
E)4,900
Rationale: IF D is the least common multiple of 90,196 and 300, which of the following is NOT a factor of D?
A- 600
B- 700
C- 900
D- 2100
E- 4900
90 = 2 * 3 * 3 * 5
196 = 2 * 2 * 7 * 7
300 = 2 * 2 * 3 * 5 * 5
LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7
(TWO 2, TWO 3, TWO 5, TWO 7)
600 = 2 * 2 * 2 * 3 * 5 * 5
700 = 2 * 2 * 5 * 5 * 7
900 = 2 * 2 * 3 * 3 * 5 * 5
2100 = 2 * 2 * 3 * 5 * 5 * 7
4900 = 2 * 2 * 5 * 5 * 7 * 7=A
Answer: A
Question: A train 330 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)18 sec
B)15 sec
C)4 sec
D)16 sec
E)12 sec
Rationale: Speed of train relative to man
= (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
= [55/3] m/sec.
Time taken to pass the man
= [330 * 3/55] sec
= 18 sec
Answer:A
Answer: A
Question: The cost of 20 kgs. of sugar is Rs.400. What is the cost of 12.5 kgs. of sugar?
Options:
A)Rs.200
B)Rs.150
C)Rs.250
D)Rs.125
E)Rs.225
Rationale: Explanation:
The cost of .153 kgs. of sugar = 400x 12.5/20 = Rs.250
Answer: Option C
Answer: C
Question: If a(a - 4) = 5 and b(b -4) = 5, where a ≠ b, then a + b =
Options:
A)−48
B)−4
C)4
D)9
E)48
Rationale: i.e. if a = -1 then b =5
or if a = 5 then b = -1
But in each case a+b = -1+5 = 4
Answer: option C
Answer: C
Question: A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1660 are infected, how manyworkersinhabit the colony?
Options:
A)1500
B)2500
C)2750
D)3000
E)3250
Rationale: From two question we get wo equations:
(1) 0,3s + 0,14w = 1660
(2) s + w = 7000
From (2) we get w=7000-s
In (1) 0,3s + 980-0,14s= 1660
0,16s=680
68000:16= 4250 =s
In (2) 4250 + w = 7000
w= 2750 C
Answer: C
Question: What is the unit digit in 7^105
Options:
A)7
B)0
C)2
D)3
E)5
Rationale: Explanation:
Unit digit in 7^105 = Unit digit in [ (7^4)26 x 7 ]
But, unit digit in (7^4)26 = 1
Unit digit in 7105 = (1 x 7) = 7
A
Answer: A
Question: How many factors does 34^2 have?
Options:
A)2
B)8
C)20
D)25
E)26
Rationale: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 5*4 = 20
Answer C.
Answer: C
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options:
A)456
B)124
C)145
D)116
E)209
Rationale: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
= 209.
Ans: E
Answer: E
Question: The factorial expression 10!/2! is not divisible by which of the following integers?
Options:
A)3
B)5
C)6
D)7
E)None of these
Rationale: 10!/2! => 10 x 9 x 8 x7 x 6 x 5 x 4x3
(A) 3 Can divide 12 or 9
(B) 5 Can divide 10
(C) 6 Can divide 12
(D) 7 can divide 7,21,28
Hence answer will be (E)
Answer: E
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2013) = ?
Options:
A)2014
B)2088
C)270
D)1881
E)1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2013) = 2014
Ans: A
Answer: A
Question: An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 5, in how many ways can she choose and rank her top 4 picks?
Options:
A)210
B)350
C)110
D)120
E)840
Rationale: Number of ways of ch0osing 4 stocks = 5C4
Number of ways of ranking the chosen stocks = 4!
Hence total ways of chosing and ranking = 5C4 * 4! = 120
Correct Option: D
Answer: D
Question: The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal	to the average speed, in miles per hour, for the entire trip?
Options:
A)300/(x + y)
B)600/(x + y)
C)150/x + 150/y
D)300/x + 300/y
E)600/x + 600/y
Rationale: Time taken to cover first half i.e 300 miles of a 600 mile trip = x
time taken to cover the second half i.e 300 miles of a 600 mile trip = y
Total time taken = x+y
Average speed for the entire trip =total distance /total time
=600/(x+y)
Answer B
Answer: B
Question: Chris age after 20 years will be 5 times his age 5 years back. what is the present age of Chris?
Options:
A)A)20
B)B)25
C)C)15
D)D)22
E)E)5
Rationale: Chris present age= x
after 20 years = x+20
5 years back = x-5
x+20= 5(x-5)
x=5
Answer is E
Answer: E
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become seven times at the same rate?
Options:
A)12 Â½ years
B)62 Â½ years
C)18 Â½ years
D)72 Â½ years
E)14 Â½ years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
700 ---- 14 Â½ years
Answer:E
Answer: E
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 12 minutes. How long will it take to go 5 km in stationary water?
Options:
A)40 minutes
B)1 hour
C)1 hour 25 min
D)1 hour 30 min
E)1 hour 10 min
Rationale: speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(12/60)= 5 kmhr
speed in still water = 1/2 (2+5) = 3.5 kmhr
time taken in stationary = 5/3.5 = 1 hrs 25 min
ANSWER:C
Answer: C
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/3, 1/4, 1/5 respectively. Find the probability of success of at least two.
Options:
A)1/6
B)2/5
C)3/4
D)3/5
E)4/5
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/3 x 1/4 x 4/5 + 1/4 x 1/5 x 2/3 + 1/3 x 1/5 x 3/4 + 1/3 x 1/4 x 1/5 = 10/60 = 1/6
ANSWER:A
Answer: A
Question: In how many ways can a group of 7 men and 5 women be made out of a total of 10 men and 7 women?
Options:
A)2200
B)2520
C)2689
D)2540
E)2680
Rationale: We need to select 7 men from 10 men and 5 women from 7 women. Number of ways to do this= 10C7 × 7C5=2520B)
Answer: B
Question: A certain barrel, which is a right circular cylinder, is filled to capacity with 40 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?
Options:
A)There is no empty capacity
B)100 gallons
C)280 gallons
D)700 gallons
E)800 gallons
Rationale: Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diameter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=40
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=40 in the second cylinder,volume= pie (r^2)*4*2=40*8=320 gallons
Empty capacity=280 gallons
Answer C
Answer: C
Question: A can give B 100 meters start and C 300 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)110.22 meters
B)111.22 meters
C)222.22 meters
D)333.22 meters
E)None of these
Rationale: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 700 meters.
Therefore, B runs 900 meters while C runs 700 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 700)/900 = 777.77 meters
Thus, B can give C (1000 - 777.77) = 222.22 meters start
Answer: C
Answer: C
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 500km less in time. Find his speed?
Options:
A)120km/hr
B)130km/hr
C)140km/hr
D)150km/hr
E)100km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 500
50x - 45x = 500
5x = 500
x = 100km/hr
Answer is E
Answer: E
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is?
Options:
A)4:5
B)5:3
C)4:4
D)4:8
E)4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √25 : √9
= 5:3
Answer: B
Answer: B
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
Options:
A)20/68
B)20/63
C)20/62
D)20/61
E)20/67
Rationale: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer:B
Answer: B
Question: The cost of the paint is rs.40.00 per kg. if 1kg of paint covers 20sq.ft, how much will it cost to paint outside of a cube having 10 feet each side
Options:
A)Rs.1200
B)Rs.672
C)Rs.546
D)Rs.876
E)None of these
Rationale: Explanation:
surface area of a cube= 6 x 10^2 = 600s q.ft
quantity of paint required=(600/20)=30 kg
cost of painting= 40 x 30 = Rs.1200
Answer: A
Answer: A
Question: When tossed, a certain six-sided die has an equal probability of landing on any of the six sides. If the die is tossed 3 times, what is the probability that it will land on the same side each time?
Options:
A)1/6
B)1/12
C)1/36
D)1/72
E)1/216
Rationale: On the first toss, the die will land on one of the sides.
On the second toss, the probability of landing on the same side is 1/6.
On the third toss, the probability of landing on the same side is 1/6.
P(same side three times)=1/6*1/6=1/36.
The answer is C.
Answer: C
Question: In a certain sequence of 10 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: Non - Negative ( zero to positive infinity )
Solution to the question :
-5,-4,-3,-2,-1,0 , 1,2,3,4
Hence ans is 4 ..option E
Answer: E
Question: A cube of edge 16cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
Options:
A)6cm
B)8.25cm
C)13.65cm
D)15.12cm
E)20.62cm
Rationale: Increase in volume = volume of the cube = 16*16*16 cm^3
Rise in water level = volume / area = 16*16*16/20*15 = 13.65cm
Answer is C
Answer: C
Question: Walking at 8KMPH From Point Q to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point Q to Railway station?
Options:
A)A)9KM
B)B)6.66KM
C)C)7.25KM
D)D)12.40KM
E)E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point Q and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point Q and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: B
Question: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 -5/6=
Options:
A)0
B)2/15
C)2/5
D)9/20
E)5/6
Rationale: We need to determine the result of 1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20
Let’s add the given fractions in two groups. In the group of the first three fractions, notice that1/3 and 1/2 share a common denominator of 6 with 5/6.
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Thus, 5/6 – 5/6 = 0
Looking at the 2nd group of the fractions (1/5, 1/4, and 9/20), notice that1/5 and 1/4 share a common denominator of 20 with 9/20.
1/5 + 1/4 = 4/20 + 5/20 = 9/20
Thus, 9/20 – 9/20 = 0.
Thus, the result of 1/3 + 1/2 – 5/6 + 1/5 + 1/4 – 9/20 is 5/6.
Answer: E
Answer: E
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Options:
A)1/2
B)1/2
C)8/15
D)9/20
E)9/24
Rationale: Explanation :
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20
Answer : D
Answer: D
Question: A box contains nine bulbs out of which 3 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Options:
A)125/167
B)125/186
C)83/84
D)125/186
E)125/128
Rationale: Required probability
= 1 - 1/84
= 83/84
Answer: C
Answer: C
Question: If you roll a fair-sided die twice, what is the probability of getting a (3,3 ) double?
Options:
A)1/2!
B)1/4!
C)1/3!
D)1/5!
E)1/6!
Rationale: total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(3, 3) = 6
Probability= 6/6*6= 1/6=1/3!
C
Answer: C
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions
Options:
A)700
B)704
C)704
D)706
E)707
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m
Answer: Option B
Answer: B
Question: How many times are the hands of a clock at right angle in a day?
Options:
A)22
B)11
C)33
D)55
E)44
Rationale: In 12 hours, hands of a clock are at right angles 22 times.
In 24 hours, hands of a clock are at right angles 44 times.
Answer is E.
Answer: E
Question: Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed)
Options:
A)60
B)75
C)65
D)55
E)45
Rationale: There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and
4 ways respectively. Required number of numbers =3x5x4=60. Ans: A
Answer: A
Question: If the quantity 6^2+ 6^4 + 6^6 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
Options:
A)52
B)15
C)36
D)22
E)25
Rationale: (a+b)(a-b) = a^2 - b^2
6^2+ 6^4 + 6^6 = 6^2 (1+6^2+6^4)
if the above expression is solved even then every term of the expression will remain a multiple of 6^2 which is out of parenthesis
hence, b must be a multiple of 6^2 i.e. 36
Answer: option C
Answer: C
Question: What does RBI regulate through Open Market Operation Transactions?
Options:
A)Flow of Foreign Direct Investment
B)What does RBI regulate through Open Market Operation Transactions?
C)Borrowing powers of the banks
D)Liquidity in economy
E). Inflation
Rationale: Explanation:
Outright purchase and Repurchase agreement are the two traditional type of OMO's used by RBI.
ANSWER: D
Answer: D
Question: A company has 12 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?
Options:
A)475
B)480
C)485
D)490
E)495
Rationale: 12C4=495
The answer is E.
Answer: E
Question: A candidate got 25% of the votes polled and he lost to his rival by 4000 votes. How many votes were cast?
Options:
A)7500
B)2028
C)2775
D)5496
E)8000
Rationale: 25%-----------L
75%-----------W
------------------
50%----------4000
100%---------? => 8000
Answer: E
Answer: E
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 12, 13, 15, 12, 14, 14
II. 32, 32, 32, 32, 32, 32
III. 37, 48, 59, 40, 41, 42
Options:
A)I, II, III
B)I, III, II
C)II, I, III
D)II, III, I
E)III, II, I
Rationale: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.
correct order from least to greatest standard deviation is II, I. III
C
Answer: C
Question: A train 210 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options:
A)28 sec
B)32 sec
C)36 sec
D)38 sec
E)40 sec
Rationale: Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(210×2/15) sec=28 sec
ANSWER :A
Answer: A
Question: A jogger running at 9 km/hr along side a railway track is 150 m ahead of the engine of a 100 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)88
B)27
C)36
D)80
E)25
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 150 + 100 = 250 m.
Time taken = 250/10 = 25 sec.
Answer: E
Answer: E
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)16 : 5
B)14 : 5
C)16 : 7
D)19 : 5
E)24:8
Rationale: Explanation:
Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5
Answer: Option D
Answer: D