divelab/Sys2Bench huggingface dataset:
Question: If a is a positive integer then 2^(2a) + (16^a)/(2^(2a)) =
Options:
A)4^a
B)8^a
C)10^a
D)2/4^a
E)2 × 4^a
Rationale: 2^(2a) + 16^a/ 2^(2a) = 4^a + 16^a/4^a = 4^a + (16/4)^a = 4^a + 4^a = 2 × 4^a
Answer : E
Answer: E
Question: A man can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 km/h and the rest at 5km/h. The total distance is
Options:
A)5km
B)6km
C)7km
D)8km
E)9km
Rationale: Distance = 2/3S
distance=1-2/3S=1/3S
21/15 hr=2/3 S/4 + 1/3s /5
84=14/3S * 3
S= 6km
Answer : B
Answer: B
Question: A certain quantity is measured on two different scales, the A-scale and the S-scale, that are related linearly. Measurements on the A-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the A-scale corresponds to a measurement of 100 on the S-scale?
Options:
A) 20
B) 36
C) 48
D) 60
E) 84
Rationale: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that A increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, A will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Answer: C
Question: Find the compound interest on $10000 in 2years at 4% per annum, the interest being compounded half-yearly?
Options:
A)$645.56
B)$824.32
C)$954.26
D)$745.69
E)$1020.45
Rationale: Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 10000*(1 + 2/100)^4 = 10000 * 51/50 * 51/50 * 51/50 * 51/50
= $10824.32
C.I. = 10824.32-10000 = $824.32
Answer is B
Answer: B
Question: The speed at which a woman can row a boat in still water is 30 kmph. If he rows downstream, where the speed of current is 6 kmph, what time will he take to cover 100 metres?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Speed of the boat downstream = 30 + 6 = 36 kmph
= 36 * 5/18 = 10 m/s
Hence time taken to cover 100 m = 100/10 = 10 seconds. Answer: C
Answer: C
Question: In the faculty of Reverse-Engineering, 250 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?
Options:
A)515.
B)545.
C)618.
D)674.
E)666.
Rationale: Answer is D :674
Solution : Total number of students studying both are 423 + 250 - 134 = 539 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 539, so 100% is approx. 674.
Answer: D
Question: 8597-?=7429-4358
Options:
A)5426
B)5706
C)5526
D)5476
E)None of them
Rationale: Let 8597-x=3071
Then x = 8597-3071
=5526
Answer is C
Answer: C
Question: On dividing a number by 7, we get 5 as quotient and 0 as remainder. On dividing the same number by 11, what will be the remainder?
Options:
A)2
B)5
C)8
D)1
E)3
Rationale: Number = 7 * 5+ 0 = 35
11) 35 (3
33
--------
2
Required number = 2.
ANSWER:A
Answer: A
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many R ways can the assembly line be arranged?
Options:
A)120
B)240
C)360
D)480
E)720
Rationale: C) 360
short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want R=6C!/2 -> 720/2 = 360
Answer: C
Question: The average age of a group of persons going for picnic is years. Sixteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
Options:
A)5
B)10
C)16
D)45
E)52
Rationale: Solution
Let the initial number of persons be x. Then
16x + 16 x 15 = 15.5(x+20)
= 0.5x = 8
x = 16
Answer C
Answer: C
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 8 ounces of corn syrup, how many ounces of water does it contain?
Options:
A)45
B)50
C)55
D)60
E)120
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 8*180/12 = 120 ounces of water
E
Answer: E
Question: P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
Options:
A)1/15
B)2/13
C)8/15
D)7/15
E)5/13
Rationale: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
C
Answer: C
Question: If the height of a right cone C is 3 and the diameter of the base of C is 8, what is the distance from the apex of C to any point on the circumference of the base of C?
Options:
A)3√2
B)5
C)5√2
D)√(67)
E)√(73)
Rationale: height of cone=3
radius of base=4
so the distance from the apex of C to any point on the circumference of the base of C will be a right angled triangle
Hence the distance is sqrt(3^2+4^2)= 5
ANSWER:B
Answer: B
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
Options:
A)4 hrs
B)4 hrs 24 min
C)4 hrs 26 min
D)4 hrs 04 min
E)4 hrs 22 min
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Answer: B
Question: What is 25% of 25% equal to
Options:
A)0.625
B)0.0625
C)6.25
D)0.00625
E)None
Rationale: Solution
25% of 25% = 25 / 100 x 25 / 100
= 1 / 16
= 0.0625
Answer D
Answer: D
Question: There are six cards in which it has two king cards. all cards are turned down and two cards are opened :
a) what is the possibility to get at least one king.
b) what is the possibility to get two kings.
Options:
A)a = 1/15 , b = 3/5
B)a = 3/5 , b = 1/15
C)a = 2/15 , b = 4/5
D)a = 6/15 , b = 3/5
E)a = 6/15 , b = 7/5
Rationale: Explanation :
a)
POSSIBILITY TO GET AT LEAST ONE KING IS :
=> = 2C1* 4C1/6C2 + 2C2/6C2
=> = 8/15+1/15
=> = 3/5
b)
P0SSIBLITY TO GET TWO KINGS IS :
=> =2C2/6C2
=> =1/15
Hence (B) is the correct answer.
Answer : B
Answer: B
Question: A and B start a business, with A investing the total capital of Rs.10000, 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.1000 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)A)59000
B)B)37000
C)C)48000
D)D)59000
E)E)67000
Rationale: Interest received by A from B = 10% of half of Rs.10000 = 10% * 5000 = 500.
Amount received by A per annum for being a working partner = 1000 * 12 = Rs.12000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (500 + 12000 + 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
(500 + 12000 + P) = 2(P)
P = 12500
Total profit = 2P + 12000
= 2*12500 + 12000 = 37000
Answer:B
Answer: B
Question: The diagonals of a rhombus are 20 cm and 25 cm. Find its area?
Options:
A)158
B)129
C)250
D)123
E)117
Rationale: 1/2 * 20 * 25 = 250
Answer:C
Answer: C
Question: What missing numberin the Sequence 5 15 5 18 5 ? 14 20 5
Options:
A)23
B)76
C)12
D)55
E)24
Rationale: E
24
write the numbers in ascending order in words as
onE (Position of 'E' in alphabet is 5)
twO (Position of 'O' in alphabet is 15)
threE (Position of 'E' in alphabet is 5)
fouR (Position of 'R' in alphabet is 18)
and so one
Answer: E
Question: A trader lists his articles at 30% above cost price and allows a discount of 10% on cash payment. Find his gain percentage
Options:
A)117% Gain
B)100% Gain
C)17% Profit
D)17% Loss
E)None of these
Rationale: Explanation:
(130 * 90)/100 = Rs.117/-
profit = 17 % profit
Answer: Option C
Answer: C
Question: "A dress is marked up by 16 2/3% to make the final price of $ 140"?
Options:
A)140
B)130
C)120
D)160
E)150
Rationale: let x be original price
% increase is = 16 2/3% of x = 50/3% of x
final price = $ 140
==> x + 50/3 * x% = 140
==> x + 50/300 * x = 140
==> x + x/6 = 140
==> 7x/6 = 140
==> x = 120
ANSWER:C
Answer: C
Question: On a certain Monday, Carlos drove to work at an average speed of 50 miles per hour and home from work along exactly the same route at an average speed of 40 miles per hour. Which of the following is closest to his average speed for both trips combined?
Options:
A)40
B)44.44
C)42
D)46
E)48
Rationale: To solve the average speed questions, we need to know the total distance and the total time.
Let us assume that the distance from work = D
This will also be the distance from work to home
Hence total distance travelled = 2D
Time in going to work = D/50,
Time in coming back from work = D/40
Hence average speed of both the trips = 2D/ (D/50 + D/40)
= 2*200/12 = 44.44
B
Answer: B
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 9 minutes, then the area of the park (in sq. m) is
Options:
A)153200
B)153400
C)153600
D)194400
E)154200
Rationale: Perimeter = Distance covered in 9 min. = 12000 x 9 m = 1800 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1800 or x = 180.
Length = 540 m and Breadth = 360 m.
Area = (540 x 360) m2 = 194400 m2.
D
Answer: D
Question: Find the smallest number which when divided by 13 and 17 leaves respective remainders of 3 and 7.
Options:
A)187
B)211
C)207
D)219
E)227
Rationale: Let 'N' is the smallest number which divided by 13 and 17 leaves respective remainders of 3 and 7.
Required number = (LCM of 13 and 17) - (common difference of divisors and remainders) = (221) - (10) = 211.
ANSWER:B
Answer: B
Question: If x^2 – 13x + 40 = q, and x is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?
Options:
A)1/5
B)1/10
C)2/5
D)3/5
E)3/10
Rationale: (x-5)(x-8) = q
x = 6 or 7 for this to be true, so
2/10 = 1/5
Ans :A
Answer: A
Question: Without stoppages a train travels a certain distance with an average speed of 180 kmph and with stoppages it covers the same distance with an average speed of 90 kmph. What is the time in minutes per hour for which train stops?
Options:
A)10 min/hr
B)20 min/hr
C)25 min/hr
D)30 min/hr
E)35 min/hr
Rationale: Pick a smart number for the distance. lets say LCM 180
Without = 180/180 = 1 hours
With = 180/90= 2 hours
So in a trip of 2 hours, 1 hour is spent in stoppages
Hence, 60/2 = 30 min/hr on stoppages
Answer : D
Answer: D
Question: Find large number from below question The difference of two numbers is 1370. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1245
B)1345
C)1455
D)1577
E)1641
Rationale: Let the smaller number be x. Then larger number = (x + 1370).
x + 1370 = 6x + 15
5x = 1355
x = 271
Large number = 271+1370 = 1641
E
Answer: E
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)382
B)782
C)278
D)270
E)881
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: D
Question: five friends A, B,C,D and E decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share 2 time, no apples were left.How many apples were there?
Options:
A)1023
B)1024
C)1026
D)1029
E)1020
Rationale: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 10 times. So answer is (2^10)-1=1023
Answer A
Answer: A
Question: The combined salaries of three brothers is $225,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?
Options:
A) 35,000
B) 55,000
C) 50,000
D) 30,000
E) 40,000
Rationale: Mr. Small = x;
Mr. Middle = 3/2*x;
Mr. Big = 2x.
x + 3/2*x + 2x = 225 --> x=50
Answer: C
Answer: C
Question: A car going at 30 miles per hour set out on an 80-mile trip at 9:00 A.M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A.M.?
Options:
A) 45
B) 50
C) 53
D) 55
E) 60
Rationale: Let Car A = car that starts at 9 AM
Car B = car that starts at 9:10 AM
Time for which car A travels at speed of 30 m per hour = 1.5 hours
Distance travelled by Car A =30 *1.5 = 45 miles
Since Car B catches up Car A at 10:30 , time = 80 mins = 4/3 hour
Speed of Car B = 45/(4/3) = 60 miles per hour
Answer E
Answer: E
Question: At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 30 of which were white and 5 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?
Options:
A)20%
B)25%
C)50%
D)75%
E)80%
Rationale: R + W + P = 120
S + L = 120
1/3 * 120 = 40
Short-Stemmed White = 30
Short-Stemmed Pink = 5
=> Short-Stemmed Red = 5
5/P = 5/R
=> R = P
So Total Long Stemmed = 80
And Long Stemmed Red + Long Stemmed Pink = 80
So Long Stemmed Red/Long Stemmed = ?
Total White = 30 (As no Long stemmed white)
=> R + R + 30 = 120
=> 2R =90 and R = 45
Long Stemmed R = 45 - 5 = 40
So Long Stemmed Red/R = 40/80 = 50%
Answer - E
Answer: E
Question: Find the area of trapezium whose parallel sides are 28 cm and 20 cm long, and the distance between them is 21 cm?
Options:
A)288 cm2
B)277 cm2
C)504 cm2
D)510 cm2
E)287 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (28 + 20) * (21)
= 504 cm2
Answer: C
Answer: C
Question: A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get profit of 15%?
Options:
A)Rs 25300
B)Rs 22300
C)Rs 24300
D)Rs 21300
E)None of these
Rationale: Explanation :
This type of question can be easily and quickly solved as following:Let at Rs x it can earn 15% profit
85:18700 = 115:x [as, loss = 100 -15, Profit = 100 +15]x = (18700 X 115)/85
= Rs.25300
Answer : A
Answer: A
Question: In how many years will a sum of money doubles itself at 18% per annum on simple interest?
Options:
A)5.9%
B)5.5%
C)6%
D)6.4%
E)7.5%
Rationale: P = (P*18*R)/100
R = 5.5%
Answer:B
Answer: B
Question: If the height of a pole is 2√3 metres and the length of its shadow is 2 metres, find the angle of elevation of the sun.
Options:
A)30°
B)45°
C)60°
D)90°
E)None of these
Rationale: Solution
Let AB be the pole and AC be its shadow.
Then, < ACB	= θ.
Then, AB= 2 √3 m, AC = 2m,
tanθ= AB/AC=2√3/2
= √3
θ=60°
Answer C
Answer: C
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)288
B)268
C)375
D)166
E)131
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: C
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
Options:
A)(n/m)%
B)(m × n)%
C)(100 / [m × n]) %
D)(100 × m/n)%
E)(100 × n/m)%
Rationale: x is n% of y: x=n/100∗y
z is m% of y: z=m100∗y
What percentage must x be of z: xz∗100=n/m∗100
Answer: E.
Answer: E
Question: Three people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?
Options:
A)2.
B)4.
C)6.
D)8.
E)10.
Rationale: Possible combinations can be
1. Erik Joe X
2. X Erik Joe
3. Joe Erik X
4. X Joe Erik
Hence, answer is B.
Answer: B
Question: What will be the output of the following code statements?
Integer a = 25, b = 40, c = 10 print (a × b / c) – c
Options:
A)65
B)26
C)29
D)26
E)90
Rationale: Explanation:
Apply BODMAS rule
25 × 40 = 1000/10-10 =100 –10 =90
Answer:E
Answer: E
Question: Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 40hr. If all pipes are opened simultaneously, then the cistern will be filled in
Options:
A)6.32 hr
B)8 hr
C)8.5 hr
D)10 hr
E)None of these
Rationale: Solution:
Work done by all the tanks working together in 1 hour.
1/10+1/12−1/40=3/19
Hence, tank will be filled in 19/3=6.32 hour
Option(A)
Answer: A
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:2. The ratio of economy cars to sport utility vehicles is 5:4. What is the ratio of luxury cars to sport utility vehicles?
Options:
A)9:8
B)8:9
C)3:2
D)10:12
E)1:2
Rationale: The ratio of economy to luxury cars is 3:2 --> E:L = 3:2 = 15:10.
The ratio of economy cars to sport utility vehicles is 5:4 --> E:S = 5:4 = 15:12.
Thus, L:S = 10:12.
Answer: D.
Answer: D
Question: The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 70 black cars in the lot, how many red cars are there in the lot?
Options:
A)11
B)26
C)24
D)27
E)32
Rationale: B is correct
R/B = 3/8 and B =70
R = 70*3/8 = 26
Answer: B
Question: A train 70 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)140 sec
B)160 sec
C)176 sec
D)150 sec
E)170 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 70 * 2/35 = 140 sec
Answer:A
Answer: A
Question: Find the middle one when The sum of three consecutive even numbers is 36?
Options:
A)10
B)12
C)14
D)18
E)22
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: B
Question: BIRLA company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Options:
A) 16
B) 64
C) 256
D) 576
E) 4096
Rationale: MAGOOSHOFFICIAL SOLUTION:
BIRLA company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: C
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1235
B)1345
C)1450
D)1567
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that y > x or x > 0?
Options:
A)7/8
B)5/6
C)3/8
D)1/2
E)3/4
Rationale: The line y=x divides the circle into two equal areas.
All the points above the line y=x satisfy the condition that y > x.
All the points to the right of the y-axis satisfy the condition that x > 0.
The union of these two areas is 7/8 of the circle.
The answer is A.
Answer: A
Question: 11 is subtracted from 40% of a number and results is 23. What is the number?
Options:
A)160
B)92
C)88
D)85
E)34
Rationale: (40/100) * X â€“ 11 = 23
4X = 340
X = 85
Answer:D
Answer: D
Question: 22
a2
+ 3b
____
80
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 2b ?
Options:
A)2
B)7
C)9
D)11
E)14
Rationale: Adding the digits in unit's place , 2+ 2 + b = 10 (Since a and b are positive single digits )
=> b = 6
Now adding the digits in ten's place , 2+a + 3 + 1= 8 (1 has been carried over from unit's place addition)
=> a= 2
a+2b = 2+2*6
=14
Answer E
Answer: E
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
Options:
A)24
B)26
C)27
D)29
E)30
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
C
Answer: C
Question: 20.05 + 35.603- …… =43.087
Options:
A)10.263
B)12.566
C)15.426
D)13.286
E)14.286
Rationale: 20.05 + 35.603- 43.087 = 55.653- 43.087
= 12.566
ANSWER:B
Answer: B
Question: Four people need to cross a dark river at night.
* They have only one torch and the river is too risky to cross without the torch.
* If all people cross simultaneously then torch light wont be sufficient.
* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.
What is the shortest time needed for all four of them to cross the river ?
Options:
A)17 minutes
B)18 minutes
C)19 minutes
D)20 minutes
E)21 minutes
Rationale: Solution:
17 min
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.
Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.
1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)
Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes
Answer A
Answer: A
Question: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Options:
A)42
B)56
C)74
D)36
E)55
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
ANSWER A
Answer: A
Question: A sum of Rs.5000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)2888
B)3120
C)2877
D)2999
E)3250
Rationale: Let A be the amount received at the end of the three years.
A = 5000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (5000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.8250
So the interest = 8250 - 5000 = Rs.3250
Answer: E
Answer: E