divelab/Sys2Bench huggingface dataset:
Question: An association of mathematics teachers has 1,260 members. Only 640 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
Options:
A)30.47%
B)58%
C)42%
D)34%
E)25%
Rationale: Total Number of members = 1260
Number of members that cast votes = 640
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*640 = 384
Percent of total membership that voted for winning candidate = (384/1260)*100 = 30.47%
Answer A
Answer: A
Question: John purchased a fridge and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
Options:
A)Rs. 100
B)Rs. 120
C)Rs. 200
D)Rs. 240
E)Rs. 250
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Answer: C
Question: If m is an integer such that (-2)^2m=2^(15-m) then m=?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: (-2)^(2m) = 4^m
and
2^(15-m) = 4^((15-m)/2)
Therefore,
m = (15-m)/2
2m = 15 - m
m = 5
Answer D
Answer: D
Question: Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination.
Options:
A)1
B)159/160
C)157/160
D)0.875
E)0.975
Rationale: If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975.
answer is E
Answer: E
Question: Two goods trains each 1250 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)228
B)278
C)48
D)27
E)120
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 1250 + 1250 = 2500 m.
Required time = 2500 * 6/125 = 120 sec.
Answer:E
Answer: E
Question: A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
Options:
A)8
B)6
C)1
D)5
E)4
Rationale: The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers.
cannot be correct because 4 would not be the longest side.(sides 4, 5, and 4)
could be correct because the other two sides would be 3 and 4.
cannot be correct because this third side would be greater than the sum of the other two sides.
Answer: B
Answer: B
Question: An athlete runs 100 meters race in 12sec. His speed is?
Options:
A)30km/hr
B)15km/hr
C)25km/hr
D)20km/hr
E)32km/hr
Rationale: speed = 100/12 = 25/3 m/sec
= 25/3 * 18/3 km/hr = 30km/hr
Answer is A
Answer: A
Question: If A : B = 4 : 7 and B : C = 5 : 8 then A : B : C is :
Options:
A)20 : 35 : 56
B)35 : 36 : 63
C)30 : 35 : 65
D)25 :34: 68
E)None of these
Rationale: Expl : A : B = 4 : 7
B : C = 5 :8 = 5*7/5 : 8 *7/5 = 7 : 56/5
A : B : C = 4 : 7 : 56/5 = 20 : 35 : 56
Answer: A
Answer: A
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
Options:
A)1/15
B)1/20
C)1/21
D)3/14
E)2/7
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
B
Answer: B
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different E arrangements of plays can be run, if the same play can’t be run more than once?
Options:
A)24
B)125
C)243
D)504
E)729
Rationale: Number of E ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Answer: D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)283
B)240
C)883
D)379
E)123
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x
= 240 m.
Answer: B
Answer: B
Question: Because of the economic slowdown, a multinational company curtailed some of the allowances of its employees. John, the marketing manager of the company whose monthly salary has been reduced to Rs.42,000 is unable to cut more on his expenditure. He finds that there is a deficit of Rs.2,000 between his earning and expenses in the first month. This deficit, because of inflationary pressure, will keep on increasing by Rs.500 every month. John has a saving of Rs 60,000 which will be used to fill the deficit. After his savings get exhausted, John would start borrowing from his friends. How soon will he start borrowing?
Options:
A)12th months
B)11th months
C)10th months
D)8th months
E)13th months
Rationale: Let the Rashid 's savings will last till 'nn' months.
⇒n2[2×2000+(n−1)500]=60,000⇒n2[2×2000+(n−1)500]=60,000
[Expenditure every month increases by 500 rupees]
⇒n2+7n−200=0⇒n2+7n−200=0
n=12.38n=12.38
⇒ Rashid after Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins.
Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the same number of 1 Rupee coins.
Next he goes to the dairy shop to buy milk and butter and gives all 2 Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by 75% more than the original number.
If the number of 1 rupee coins now is 50, the number of 1 rupee and 5 rupee coins originally were will start borrowing money from his friends.
E
Answer: E
Question: What value will come in place of question mark in the following equation? 0.006 +? = 0.6
Options:
A)0.01
B)0.05
C)0.03
D)0.07
E)0.02
Rationale: Let 0.006 / x = 0.6, Then, x = (0.006 / 0.6) = (0.006*10) / (0.6*10) = 0.06/6 = 0.01
Answer is A.
Answer: A
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)22
B)30
C)99
D)77
E)62
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer:B
Answer: B
Question: Find the positive number which when increased by 17 is equal to 60 times the reciprocal of the number
Options:
A)4
B)3
C)2
D)9
E)7
Rationale: Let the number be x
x+17=60/x
x^2+17x-60=0
(x+20)(x-3)=0
x=3
correct answer B
Answer: B
Question: If after 400 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
Options:
A)180 grams
B)220 grams
C)250 grams
D)350 grams
E)800 grams
Rationale: I too think 800 grams should be the answer.
My reasoning is
The h20 content in 200 gms of water is 1
h20 content in 24% solution is 0.76
Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84
Let amount of solution be X
Then the equation can be set up
400*1 + 0.76X = 0.84 (X+400)
0.08X = 64
8X = 6400
X = 800 (ANS E)
Answer: E
Question: a is an integer greater than 19 but less than 32, b is an integer greater than 29 but less than 42, what is the range of a/b?
Options:
A)1/4
B)1/2
C)3/4
D)1
E)5/4
Rationale: min value of a/b will be when b is highest and a is lowest ---> a=20 and b=40
So, a/b = 1/2
max value of a/b will be when b is lowest and a is highest ---> a=30 and b=30
So, a/b = 1
Range is 1-(1/2) = 1/2.
Answer should be B
Answer: B
Question: If A is 25 kms east of B, which is 12 kms south of C, which is 9 kms west of D. A person starts walking at 3 kms/hr from A towards D. Calculate the distance of the point from A where he is going to meet a person from D walking towards A at 2 kms / hr.
Options:
A)20
B)12
C)8
D)20 sqrt (12*8)
E)none
Rationale: 2,3=common factor
hence 20
ANSWER:A
Answer: A
Question: 10 years ago Neha's mother was 4 times older than Neha. After 10 years Neha's mother will be twice Neha's age. How old is Neha now?
Options:
A)10 years
B)15 years
C)17 years
D)20 years
E)23 years
Rationale: Let us assume m = mother and n = neha
m-10 = 4(n-10) => 4n-m = 30 this is equation 1
m+10 = 2(n+10 => -2n+m = 10 this is equation 2
By equations 1 and 2
n=20
n means Neha age = 20 years
ANSWER:D
Answer: D
Question: Find the compound ratio of (2:3), (6:11) and (11:2) is
Options:
A)3:2
B)2:1
C)1:2
D)4:5
E)2:3
Rationale: Required ratio = 2/3 * 6/11 * 11/2 = 2/1 = 2:1
Answer is B
Answer: B
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 13 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 51 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
Options:
A)A)11
B)B)18
C)C)24
D)D)25
E)D)36
Rationale: lets solve by creating equation..
W = 31..
Total = 52..
Not W = 52 -31= 21..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=21 or x=9..
so who won Nobel but not Wolf = x+3 = 12..
But people who won BOTH W and N = 13..
so total who won N = 12+13 = 25..
D
Answer: D
Question: there is one designed bedsheets having length 6m and breadth 4m.in the middle there is square shape design with 3m side.calculate the % of bedsheet which do not have any design.
Options:
A)62
B)60
C)75
D)62.5
E)65
Rationale: area of bedsheet=24m2.
area of square shape design=9m2.
undesigned area=24-9=15m2.
%of undesigned area=15/24*100=62.5%
answer D
Answer: D
Question: There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)288
B)267
C)261
D)211
E)380
Rationale: The total number of stations = 20
From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.
²⁰P₂ = 20 * 19 = 380.
Answer: E
Answer: E
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 3 carpenters build in 4 hours?
Options:
A)2.4.
B)4.8.
C)4.2.
D)5.5.
E)6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 3 carpenters in 4 hrs = 3 × rate of each carpenter x time = 3× 2/5 × 4 = 4.8 desks
B is the correct answer.
Answer: B
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Options:
A)39
B)35
C)42
D)40.5
E)41
Rationale: Explanation:
Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 87 = Total runs scored in 17 innings
=> 16(x-3) + 87 = 17x
=> 16x - 48 + 87 = 17x
=> x = 39
Answer: Option A
Answer: A
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12300 after a year?
Options:
A)3630
B)3690
C)2887
D)9977
E)2212
Rationale: 6300:4200:10500
3:2:5
3/10 * 12300 = 3690.Answer: B
Answer: B
Question: If the length of the sides of two cubes are in the ratio 2:1, what is the ratio of their total surface area?
Options:
A)2:1
B)3:1
C)4:1
D)6:1
E)8:1
Rationale: Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(2x)^2=24x^2.
The ratio of surface areas is 4:1.
The answer is C.
Answer: C
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)6m
B)9m
C)3m
D)2m
E)1m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:D
Answer: D
Question: If n is a negative integer and p is a positive integer, which of the options below must be positive?
Options:
A)(n + p)^2
B)np
C)n/p
D)p/n
E)none of the above
Rationale: A.(n + p)^2
will be positive irrespective of the absolute values of x and y
will be positive always
B. np
-ve*+ve=-ve
will be negative
C. n/p
-ve*/ve=-ve
D.+ve/-ve=-ve
+ve/-ve=-ve
Answer A
Answer: A
Question: A 75-liter solution of cool-drink is made from 8% jasmine water. If 3 liters of jasmine and 12 liters of water were added to the solution, what percent of the solution is jasmine?
Options:
A)10.3%
B)11.5%.
C)10%.
D)12.2%
E)12%.
Rationale: Denominator
75+3+12
90
Numerator
75*0.08=6--->Jasmine water
6+3=9--->New content of Jasmine water in new solution
Ratio
9/90
Answer: C
Answer: C
Question: A train 100 m long crosses a platform 125 m long in 30 sec; find the speed of the train?
Options:
A)36
B)77
C)27
D)33
E)99
Rationale: D = 100 + 125 = 225
T = 30
S = 225/30 * 18/5 = 27 kmph
Answer: C
Answer: C
Question: A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction?
Options:
A)1/20
B)1/25
C)1/30
D)1/35
E)1/40
Rationale: x / (1/18) = (2/5) / (7/9)
x = 2*9*1 / 18*5*7 = 1/35
The answer is D.
Answer: D
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)9
B)7
C)8
D)12
E)10
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
ANSWER C
Answer: C
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 110. If legs are counted, there are 580. The number of hares in the zoo is?
Options:
A)120
B)182
C)190
D)137
E)180
Rationale: 110*2 = 220
580
-----
360
1----2
?----360 = 180
Answer:E
Answer: E
Question: A certain city with a population of 120,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
Options:
A)a) 10,700
B)b) 10,000
C)c) 10,900
D)d) 11,000
E)e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 120k
x = 10,000
Answer : B
Answer: B
Question: The length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)239
B)277
C)255
D)88
E)232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30
= 25/2 ==> 2(120 + X) = 750 ==> X = 255 m.
Answer: C
Answer: C
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
A)9
B)8!
C)2
D)7
E)5
Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is 8P8
= 8!.
Answer: B
Answer: B
Question: If 10,000 microns = 1 decimeter, and 10,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
Options:
A)0.01
B)1,000,000
C)0.001
D)1,000
E)1.0e-05
Rationale: Given that 10,000 microns = 1 decimeter =10,000,000,000 angstroms
So, 1 micron = 10,000,000,000/10,000
=1,000,000
Answer : B
Answer: B
Question: At a florist shop on a certain day, all corsages sold for either $20 or $30. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 35 percent. What was the store's actual revenue from corsages that day?
Options:
A)$320
B)$400
C)$600
D)$800
E)$1000
Rationale: I am doing it elaborately, hope it will help you.
Let, No. of corsages @ $20 = x, no. of corsages @ $30 = y and revenue= r
so, 20x+30y=r.........(1)
Now,
Given the situation, 20(x+8) + 30(y-8)= r-.25r
=> 20x+160+30y-240 = .75r
=> 20x+30y = .75r+80............(2)
so, r = .75r+80
=> r = 320
The answer is A.
Answer: A
Question: A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate.If 70% of the males are literate, the number of literate females is :
Options:
A)20,000
B)24,000
C)30,000
D)34,000
E)44,000
Rationale: population - 3,00,000, males -1,80,000, females-1,20,000
50%of 3,00,000 literate - so 1,50,000 literate
70% of 1,80,000 literate -so 1,26,000 male literates , so rest s
1,50,000 - 1,26,000 = 24,000
ANSWER:B
Answer: B
Question: 50% of the population of a village is 23040. The total population of the village is ?
Options:
A)32256
B)24000
C)44936
D)46080
E)None
Rationale: Answer
∵ 50% of P = 23040
∴ P = (23040 x 100) / 50 = 46080
Correct Option: D
Answer: D
Question: If each side of a square is increased by 25%, find the percentage change in its area?
Options:
A)65.25
B)56.25
C)65
D)56
E)46
Rationale: Explanation:
let each side of the square be a , then area = a x a
New side = 125a / 100 = 5a / 4
New area =(5a x 5a) / (4 x 4) = (25a²/16)
increased area== (25a²/16) - a²
Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25% Answer: B
Answer: B
Question: Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 20 phone numbers by using the readable digits followed by 20 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
Options:
A)1/9
B)10/243
C)2/27
D)10/271
E)1/1000000
Rationale: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 20/(9*9*3+9*3) = 2/27.
Answer: C.
Answer: C
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 9.9. The difference between the unit digit and hundreds digit of that number is :
Options:
A)a) 4
B)b) 3
C)c) 2
D)d) 1
E)e) 0
Rationale: Since the average increased by 9.9 and there were a total of 10 numbers, it means the incorrect number was 99 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 99
99c - 99a = 99(c - a) = 99
99 = 99*1 = 99(c - a)
So c - a = 1
Answer (D)
Answer: D
Question: Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 16 years?
Options:
A)30
B)35
C)40
D)36
E)60
Rationale: Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 16 years = (20 + 16) years =36 years.
Answer : D
Answer: D
Question: Two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction. What time will they take to be 32 km apart?
Options:
A)18
B)16
C)19
D)15
E)34
Rationale: Explanation:
Relative speed = 7.5 - 5.5 = 2 kmph (because they walk in the same direction)
distance = 32 km
time = distance / speed=32/2=16 hr
Answer :B
Answer: B
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
Options:
A)6620
B)2888
C)2776
D)2997
E)2718
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620.Answer: A
Answer: A
Question: Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -10). What is the slope of line m ?
Options:
A)-3
B)1
C)-1/3
D)0
E)Undefined
Rationale: Ans: B
Solution: line m goes through midpoint of (2, 4) and (6, -10). midpoint is (4,-3)
as we can see that the y axis of intercept point is (0,-2) means line m is parallel to x axis
slope M= 1
Ans: B
Answer: B
Question: A 140 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)35
B)20
C)47
D)36
E)40
Rationale: 1: 2/5 = 5: 2
2/7 * 140 =40
Answer:E
Answer: E
Question: For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score E for the exam?
Options:
A)74
B)76
C)78
D)80
E)82
Rationale: A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d
A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d
Solving above for Mean E= 74.
Answer: A.
Answer: A
Question: A new savings account offers 5 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?
Options:
A)$80.00
B)$84.40
C)$360.00
D)$6,303.75
E)$6,365.40
Rationale: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.05) (1/2) = $150. (Note: the 6 months are “1/2” in the equation since 5% s a yearly rate, not a bi-yearly one).
Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,150. The interest earned during the final 6 months of the year is $6,150(.05)(1/2) = $153.75. Therefore, the total balance is the original amount ($6000) + $150 + $153.75= $6,303.75.
The correct answer is E.
Answer: E
Question: How many possible cases are there such that 2 stocks are selected at random from 10 stocks?
Options:
A)35
B)40
C)45
D)50
E)55
Rationale: Number of possible cases = 10c2
=10!/(8!*2!)
=10*9/2
=45
Answer C
Answer: C
Question: How many seconds will a 400 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)287
B)288
C)900
D)277
E)121
Rationale: Let length of tunnel is x meter
Distance = 400+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
400+x = (65/3) * 60
400+x = 20 * 65 = 1300
x = 1300 - 400 = 900 meters
Answer: C
Answer: C
Question: The product of two numbers is 120. The sum of their squares is 289. The sum of the two numbers is :
Options:
A)20
B)23
C)169
D)172
E)198
Rationale: Explanation:
Let the number be x and y . We know that,
(x+y)2=(x2+y2)+2xy=289+2×120
=289+240=529⇒x+y=√529=23
Correct Option: B
Answer: B
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, x
Options:
A)23
B)25
C)29
D)35
E)39
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 30 + 5 = 35.
Answer: D