divelab/Sys2Bench huggingface dataset:
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/3 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
Options:
A)0
B)1/15
C)2/15
D)1/6
E)2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/3) = L
CX = 3L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 3L
= 1/6
Answer will be D
Answer: D
Question: How many integers n greater than and less than 100 are there such that,if the digits of n are reversed, the resulting integer is n+9 ?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: (10x+y)=(10y+x)+9
=> 9x-9y=9
=> x-y=1
and only 8 numbers satisfy this condition and the numbers are 21,32,43,54,65,76,87,98
ANSWER:D
Answer: D
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o’clock in the afternoon?
Options:
A)120°
B)90°
C)180°
D)320°
E)None of these
Rationale: Sol.
Angle traced by the hour hand in 4 hours = [360/12 * 4]° = 120°
Answer A
Answer: A
Question: Which of the following could be the value of x, if |3x – 9| = 0?
Options:
A)–3
B)1/9
C)1/3
D)-1/3
E)3
Rationale: |3x – 9| = 0
=> 3x - 9 = 0
or -(3x - 9) = 0
=> 3x = 9 or -3x = -9
=> x = 3 or x = 3
Answer E
Answer: E
Question: I. a^2 - 9a + 20 = 0,
II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?
Options:
A)If a < b
B)If a ≤ b
C)If the relationship between a and b cannot be established
D)If a > b
E)If a ≥ b
Rationale: I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b
Option E
Answer: E
Question: How many ways are there to select a subcommittee of 11 members from among a committee of 17?
Options:
A)12376
B)19448
C)28791
D)27711
E)12111
Rationale: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,11)= 12,376
Answer: A
Answer: A
Question: What least number should be added to 1053, so that the sum is completely divisible by 23
Options:
A)A)4
B)B)1
C)C)2
D)D)3
E)E)5
Rationale: Explanation:
(1053 / 23) gives remainder 18
18 + 5 = 23, So we need to add 5
Answer: Option E
Answer: E
Question: The sum of three consecutive even numbers is 93. Find the middle number of the three?
Options:
A)14
B)35
C)39
D)31
E)12
Rationale: Middle value =93/3
=31
Ans D
Answer: D
Question: A boy has 9 trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)100
B)140
C)104
D)135
E)125
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 15 = 135 ways.
D
Answer: D
Question: The average age of husband, wife and their child 3 years ago was 25 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A)22
B)40
C)34
D)21
E)11
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 84 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (84 - 50) years = 34 years.
Answer: C
Answer: C
Question: The effective annual rate of interest corresponding to a nominal rate of 14% per annum payable half-yearly is?
Options:
A)16.06%
B)16.07%
C)16.08%
D)14.49%
E)16.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 7/100)2] = Rs. 14.49 Effective rate = (114.49 - 100) = 14.49%
ANSWER:D
Answer: D
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)1877 sq m
B)1976 sq m
C)4312 sq m
D)1987 sq m
E)1678 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer:C
Answer: C
Question: In a certain province in France there are 13 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
Options:
A)76
B)78
C)75
D)98
E)72
Rationale: 1 city needs 12 roads to connect directly to the rest => 13 city needs 13*12 roads.
One road is counted twice => the number of road needed is 13*12/2 = 78
Answer B
Answer: B
Question: At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:40 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
Options:
A)0.5 + (p - 0.5s)/(r + s)
B)(p - 0.5s)/(r + s)
C)0.5 + (p - 0.5r)/r
D)(p - 0.5r)/(r + s)
E)0.5 + (p - 0.5r)/(r + s)
Rationale: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]
ans is D
Answer: D
Question: The cost price of 30 articles is the same as the selling price of x articles. If the profit is 20%, what is x?
Options:
A)20
B)21
C)23
D)25
E)27
Rationale: Let the cost price = y
The cost price of 30 articles = 30y
The selling price of x articles = 1.20y*x
1.20y*x = 30y
x = 30 / 1.2 = 25
The answer is D.
Answer: D
Question: A certain psychologist charges $20 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $300, what is the total charge to a patient who receives only 3 hours of therapy ?
Options:
A) $120
B) $135
C) $150
D) $165
E) $188
Rationale: Let the charge for first hour = x+20
then charge for each additional hour = x
x+20 + 4x = 300
=> 5x = 280
=> x = 56
Total charge for patient for 3 hours of therapy = x+20 + 2x = 3x+20
= 188 $
Answer E
Answer: E
Question: A man can row 5 kmph in still water. When the river is running at 2.3 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)2.91
B)3.48
C)2.98
D)3.78
E)4.21
Rationale: M = 5
S = 2.3
DS = 6.3
US = 2.7
x/6.3 + x/2.7 = 1
x = 1.89
D = 1.89* 2 = 3.78
Answer: D
Answer: D
Question: D is the set of all the multiples of 3 between 30 and 100. E is the set of all the factors of 400. Set D and Set E have how many numbers in common?
Options:
A)1
B)0
C)3
D)5
E)12
Rationale: D is a set of multiples of 3.
400 is NOT a multiple of 3, hence none of its factors is a multiple of 3.
Therefore, those two sets won't have any overlap.
Answer: B
Answer: B
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
Options:
A)267 m
B)420 m
C)167 m
D)287 m
E)265 m
Rationale: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer:B
Answer: B
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
Options:
A)4 1/8 km
B)5 4/8 km
C)6 1/8 km
D)4 3/8 km
E)3 2/8 km
Rationale: D
4 3/8 km
RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8 = 4 3/8 km
Answer: D
Question: Rasik walked 20 m towards north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which direction and how many metres is he from the starting position?
Options:
A)23
B)38
C)37
D)45
E)92
Rationale: 45 m East
Answer: D
Answer: D
Question: If 10^(b-1)< 0.000125 <10^b, what is the value of an integer b?
Options:
A)-4
B)-3
C)-2
D)3
E)4
Rationale: -> Multiply 10^6- > (10^6){10^(b-1)}<125<(10^6)(10^b) -> 125 is bigger than 100
-> (10^6)(10^(b-1))=100 -> 10^(6+b-1)=10^2, b+5=2 -> b=-3
Thus, the answer is B
Answer: B
Question: A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage?
Options:
A)10% Loss
B)20% Loss
C)30% Loss
D)40% Loss
E)50% Loss
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (810 ~ 900)/900 = 10% Loss
A)
Answer: A
Question: At 1:00, Annie starts to bicycle along a 84 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?
Options:
A)2:30
B)3:00
C)4:00
D)5:00
E)6:00
Rationale: In the first 30 minutes, Scott can travel 6 miles, so there are 78 miles left.
Together Annie and Scott can complete 26 miles.
78/26 = 3, so they will meet 3 hours after 1:00.
The answer is C.
Answer: C
Question: How many integers from 20 to 150, inclusive, are divisible by 3 but not divisible by 7?
Options:
A)37
B)40
C)42
D)45
E)55
Rationale: We should find # of integers divisible by 3 but not by 3*7=21.
# of multiples of 21 in the range from 20 to 150, inclusive is (147-21)/21+1=7;
44-7=37.
Answer: A.
Answer: A
Question: The product of all the prime numbers less than 12 is closest to which of the following powers of 10 ?
Options:
A)10^7
B)10^4
C)10^8
D)10^5
E)10^9
Rationale: Product of Prime numbers less than 12 is 2*3*5*7*11
2*5=10 .
10*11*3*7 = 10*10*3*10 (approximately) ~ Product will be >10^3 <10^5 i.e. 10^4
B is the answer
Answer: B
Question: A restaurant meal cost $40 and there was no tax. If the tip was more than 5 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
Options:
A)$40 and $42
B)$41 and $46
C)$41 and 45
D)$43 and $46
E)$41 and $47
Rationale: let tip=t
meal cost=40
range of tip = from 5% of 40 to 15% of 40 = 2 to 6
hence range of amount paid= 40+T= 42 to 46 i.e. E
Answer: E
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is?
Options:
A)Rs. 112.75
B)Rs. 121.75
C)Rs. 124.75
D)Rs. 118.75
E)Rs. 234.75
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: C
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
Options:
A)$20000
B)$15000
C)$12000
D)$10000
E)$9000
Rationale: Since investment doubles in 70/r years, then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).
Answer: A.
Answer: A
Question: In an intercollegiate competition that lasted for 3 days, 115 students took part on day 1, 80 on day 2 and 100 on day 3. If 50 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 40 took part on all three days, how many students took part only on day 3?
Options:
A)20
B)35
C)40
D)55
E)60
Rationale: Day 1&2 = 50; Only Day 1&2 (50-40) = 10,
Day 2&3 = 70; Only Day 2&3 (70-40) = 30,
Only Day 3 = 100 - (10+30+40) = 20
Answer:A
Answer: A
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)227
B)177
C)120
D)288
E)271
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.Answer:C
Answer: C
Question: If d is a positive integer, and if the units' digit of d^2 is 4 and the units' digit of (d + 1)^2 is 1, what is the units' digit of (d + 2)^2 ?
Options:
A)	0
B)	2
C)	4
D)	6
E)	8
Rationale: A for me.
_1² = _1
_2² = _4
_3² = _9
_4² = _6
_5² = _5
_6² = _6
_7² = _9
_8² = _4
_9² = _1
_0² = _0
On the list, the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _8.
So, d = _8, that has square 4. The next square is 1 andnext nextsquare is 0.
Answer: A
Question: Find the number of square tiles to cover the floor of a room measuring 10.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Options:
A)422
B)476
C)1440
D)428
E)413
Rationale: Floor area to be covered by tiles = 10 * 9 = 90
tiles area = 0.25 * 0.25 =0.0625
No. of tiles = 90/0.0625 = 1440
Answer : C
Answer: C
Question: If p=25*343*9/1575, how many digits are in p?
Options:
A)7
B)2
C)1
D)4
E)3
Rationale: p = 25 * 343 * 9 / 1575
p = 5^2 * 7^3 * 3^2 / (5^2 * 3^2 * 7)
p = 7 ^ 2
p = 49
Ans: B
Answer: B
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)8
B)7
C)6
D)5
E)1
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) = 42 years.
Required difference = (42 - 36) = 6 years.
Answer: C
Answer: C
Question: How many four digit even numbers do not use any digit more than once
Options:
A)1720
B)2160
C)None of these
D)2460
E)2520
Rationale: The Way i solved it is
A B C D ( thousand , hundreds, tens, units)
D can be 0 2 4 6 8 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
C can be anything execpt A and B so 8 possibilities
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 8 * 7 * 8 * 5 = 2240
Ans : C
Answer: C
Question: Given that 0 < a < b < c < d, which of the following the largest ?
Options:
A)(c+d) / (a+b)
B)(a+d) / (b+c)
C)(b+c) / (a+d)
D)(b+d) / (a+c)
E)None of these
Rationale: Explanation :
For the fraction to be largest, denominator should be minimum and numerator should be maximium.
Here a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.
Hence 1.) (c+d) / (a+b
Answer : A
Answer: A
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
Options:
A)1979
B)1456
C)1699
D)1485
E)1689
Rationale: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15
=1485
Answer:D
Answer: D
Question: If a new town has 350 residents, and the population doubles every 10 years, what will be its population after 75 years?
Options:
A)63357 residents
B)9051 residents
C)12068 residents
D)15075 residents
E)18102 residents
Rationale: 350*2^(75/10)=350*2^7.5=100*181.02=63357
The answer is A.
Answer: A
Question: If 4f^4 − 41f^2 + 100 = 0, then what is the sum of the two greatest possible values of f ?
Options:
A)4
B)9/2
C)7
D)41/4
E)25
Rationale: just forget about the value of f^4 for the moment and let f^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so f^2 = 4 and 25/4
so f= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Answer: B
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Options:
A)45%
B)54%
C)57%
D)60%
E)65%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: C
Question: If X and Y are consecutive integers (Y>X), which of the following statements could be false?
1. The multiplication XY is an even number.
2. (Y/X) > 1.
3. (X + Y) is always an odd number.
Options:
A)1 only
B)2 only.
C)1 and 2 only.
D)1 and 3 only.
E)1, 2 and 3
Rationale: Consecutive numbers means that one will be even and one will be odd.
1. The multiplication XY is an even number. Odd*even= even. True
2. (Y/X) > 1.
If Y= 1 and X=0
Y/X= Undefined
Or if Y =-1 and X=-2
Y/X= 1/2 <1
Could be False
3. (X + Y) is always an odd number.
Even+ Odd= Odd. True
B is the answer
Answer: B
Question: Of the 100 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
Options:
A)20
B)30
C)50
D)80
E)100
Rationale: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 20
Answer: Option A
Answer: A
Question: An alloy weighing 26 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?
Options:
A)6
B)9
C)12
D)34
E)48
Rationale: In 24 ounces, gold is 26 * (70/100) = 18.2 ounces. Now we add x ounces of pure gold to make it 90% gold.
So 18.2 + x = (24 + x)* 90/100 => x =34.
Answer is D.
Answer: D
Question: By approximately what percent is x greater than 1/3 if (2/3)(x) = 1?
Options:
A)173%
B)516%
C)461%
D)350%
E)290%
Rationale: what percent is x greater than 1/3 if (2/3)(x) = 1?
=> x = 3/2
% change =[(3/2 -1/3) /(1/3) ] * 100
= 350
Ans D, 350%
Answer: D
Question: By travelling at 50 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Options:
A)23 kmph
B)24 kmph
C)25 kmph
D)26 kmph
E)27 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance = 50 * 3x = 150x km
He covered 2/3 * 150x = 100x km in 1/3 * 3x = x hours So, the remaining 50x km, he has to cover in 2x hours. Required speed = 50x/2x
=25 kmph.
Answer: C
Answer: C
Question: If e = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
Options:
A)-2
B)-1
C)0
D)2
E)None of the above
Rationale: Let us transform the formula:
e = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Answer: D
Question: Three times the first of three consecutive odd integers is 4 more than twice the third. The third integer is:
Options:
A)9
B)11
C)13
D)16
E)17
Rationale: Let the three integers be x, x + 2 and x+ 4.
Then,
3x = 2(x + 4) + 4
x = 12
Third integer = x + 4 = 16.
ANSWER:D
Answer: D
Question: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
Options:
A)5.15 kmph
B)4.14 kmph
C)4.25 kmph
D)4.4 kmph
E)4.8 kmph
Rationale: in 100 m race
A's speed is 5kmph so in m/s it is 5*5/18
time taken by A=D/S=100*18/25=72 sec
Now
B would take 72+8=80 seconds
Speed of B is=(100-8)=(92/80)*18/5= 4.14kmph
ANSWER:B
Answer: B
Question: John and Jacob set out together on bicycle traveling at 15 and 10 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
Options:
A)1 1/2
B)3 1/3
C)3 1/2
D)4
E)4 1/2
Rationale: John's speed - 15 miles/hr
Jacob's speed - 10 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 10x5/3 = 16.7 miles.
Now, when John starts riding back, the distance between them is 6.7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-10 = 5 miles/hr.
Thus, to cover 6.7 miles at 5 miles/hr, John will take 6.7/5 = 1.34 hours
Answer A
Answer: A
Question: A fruit seller had some mangoes. He sells 30% mangoes and still has 280 mangoes. Find the number of mangoes he had.
Options:
A)228 mangoes
B)400 mangoes
C)287 mangoes
D)408 mangoes
E)289 mangoes
Rationale: Explanation:
Suppose originally he had X mangoes.
Then, (100 – 30)% of X = 280
70/100 * X = 280
X = (280 * 100) / 70 = 400
ANSWER: B
Answer: B
Question: A certain sum of money at simple interest amounted Rs.860 in 10 years at 3% per annum, find the sum?
Options:
A)661.54
B)662.54
C)663.54
D)664.54
E)665.54
Rationale: 860 = P [1 + (10*3)/100]
P = 661.54
Answer: A
Answer: A
Question: A boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream,it takes 4 hours.What is the speed of the boat in still water ?
Options:
A)4.5 km/hr
B)6 km/hr
C)8 km/hr
D)Data inadequate
E)None of these
Rationale: Solution
Rate downstream =(12/2) kmph = 6 kmph, Rate upstream =(12/4) = 3 kmph.
∴ Speed in still water =1/2(6+3) kmph = 4.5 kmph.
Answer A
Answer: A
Question: A sum of money was invested in a bank at 8% simple interest p.a. for 3 years. Instead had it been invested in mutual fund at 8.5% p.a. simple interest for 4 years, the earning would have been Rs.500 more. What is the sum invested?
Options:
A)Rs.4500
B)Rs.5000
C)Rs.3500
D)Rs. 5500
E)Rs. 6500
Rationale: Let the sum be Rs.x
S.I from the bank = x*8*3/100 = 34x/100Earnings in the form of interest from mutual fund = (x * 8.5
*4)/100 = 34x/100
Given that 34x/100 - 34x/100 = Rs.500 ; x = 5000
: . The sum invested = 5000
ANSWER:B
Answer: B
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 6 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
Options:
A)30
B)45
C)60
D)90
E)120
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/5x + 2/3x + 6
x - 13/15x = 6
2/15x = 6 => so x = (15/2)*6 = 45Km
Answer B
Answer: B
Question: The population of a bacteria colony doubles every day. If it was started 8 days ago with 3 bacteria and each bacteria lives for 12 days, how large is the colony today?
Options:
A)512
B)768
C)13122
D)2048
E)4096
Rationale: 3^8*(2) = 13122
The answer is C
Answer: C
Question: There are 20 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12th pole . How much time will it take to reach the last pole?
Options:
A)25.25 s
B)17.45 s
C)35.75 s
D)41.45 s
E)None of these
Rationale: Let the distance between each pole be x m.
Then, the distance up to 12th pole = 11 xm
Speed = 11x⁄24 m/s
Time taken to covers the total distance of 19x
= 19x×24/11x=41.45s
Answer D
Answer: D
Question: A train 175 m long running at 36 kmph crosses a platform in 40 sec. What is the length of the platform?
Options:
A)271
B)266
C)225
D)277
E)232
Rationale: Length of the platform = 36 * 5/18 * 40 = 400 – 175
= 225
Answer:C
Answer: C