divelab/Sys2Bench huggingface dataset:
Question: At a party, 13 guests brought wine and 14 guests brought beer. If exactly 11 guests brought only one of the two types of drinks, how many guests brought both types of drinks?
Options:
A)5
B)6
C)7
D)8
E)14
Rationale: Say x guests brought both drinks.
(13 - x) + (14 - x) = 11 --> x = 8.
Answer: D.
Answer: D
Question: if the price of a book is first decreased by 20% and then increased by 10%, then the net change in the price will be :
Options:
A)10
B)12
C)37
D)29
E)22
Rationale: Explanation:
Let the original price be Rs. 100.
Decreased by 20% = 80
Then increased 10% on Rs 80 = 80 + 8 = 88
Net change in price = 100 - 88 = 12
Answer : B
Answer: B
Question: If |x + 132| = 32 what is the sum of all the values of x.
Options:
A)-264
B)200
C)-64
D)0
E)-328
Rationale: There will be two cases
x+132 = 32 and x+132 = -32
Solve for x => x=32-132=> x=-100 or x= -32 - 132 => x= -164
The sum of both values will be -164 + -100 = -264
Answer is A
Answer: A
Question: 14,24,54,34,44,56,53, ?
Options:
A)44
B)55
C)66
D)77
E)88
Rationale: 14-24...dif -10
54-34..dif -20
44-56..dif-12
53-77...dif-24
ANSWER:D
Answer: D
Question: A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 1/2, and the probability of selecting a blue paper clip is 1/3. What is the probability of selecting a silver paper clip?
Options:
A) 1/6
B) 1/2
C) 7/12
D) 3/4
E) 11/12
Rationale: Prob of Red = 1/2
Prob of Blue = 1/3
Prob of Silver = ?
P(Silver) = 1 - P(Red) - P(Blue) ==> 1-1/2-1/3 = 1/6
Ans: A
Answer: C
Question: Siddharth wants to borrow Rs.10000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
Options:
A)s.21.60
B)s.36.00
C)s.22.29
D)s.21.26
E)s.21.12
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.10,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 10,000{ [1 + 6/100]2 - 1 - 12/100}
= 10,000 {(1.06)2- 1 - 0.12} = 10,000(1.1236 - 1 - 0.12)
= 10,000 (0.0036) = 10 * 3.6 = Rs.36.00
Answer: B
Answer: B
Question: (0.0077)(4.5) / (0.05)(0.1)(0.007)=
Options:
A)99
B)9.9
C)990
D)0.99
E)0.099
Rationale: (0.0077)(4.5) / (0.05)(0.1)(0.007)=0.0077 * 450/5 * (0.1)(0.007)
= 0.077*90/1 * 0.007 = 77*90/7 = 11*90
=990
Answer : C
Answer: C
Question: If 2/a + 3/a + 8/a is an integer, which of the following must also be an integer?
Options:
A)12/a
B)13/a
C)6/a
D)9/a
E)15/a
Rationale: 2/a + 3/a + 8/a
=13/a
Answer B
Answer: B
Question: A trader marked the selling price of an article at 50% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed a discount of :
Options:
A)7.3 %
B)10.5 %
C)11 %
D)12.5 %
E)None
Rationale: Sol.
Let C.P. = Rs. 100. Then, Marked Price = Rs. 110, S.P. = Rs. 99.
∴ Discount % = [11/150 * 100] % = 7.3%
Answer A
Answer: A
Question: The perimeter of a semi circle is 121 cm then the radius is?
Options:
A)17
B)28
C)24
D)26
E)12
Rationale: 36/7 r = 121 => r
= 24
Answer: C
Answer: C
Question: Jake remembers only the last Six letters of his seven-letter Klingon name. If he is sure that the first letter is neither "N" nor "X", and assuming that there are only 12 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
Options:
A)A)8/100
B)B)9/100
C)C)1/10
D)D)4/5
E)E)9/10
Rationale: Total letters 10, out of which the first letter is anything of 10 but N or X...
So there are 10 possible letters for first place..
And only one of them is correct..
So 1/10
Answer: C
Answer: C
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 180. What is their H.C.F.?
Options:
A)15
B)20
C)40
D)60
E)70
Rationale: Let the numbers be 2x, 3x, and 4x.
LCM of 2x, 3x and 4x is 12x.
12x = 180
x = 15
HCF of 2x, 3x and 4x = x = 15
The answer is A.
Answer: A
Question: If the sides of a square are multiplied by 5, the area of the original square is how many times as large as the area of the resultant square?
Options:
A)4%
B)25%
C)50%
D)200%
E)400%
Rationale: Let x be the original length of one side.
Then the original area is x^2.
The new square has sides of length 5x, so the area is 25x^2.
The area of the original square is 1/25 = 4% times the area of the new square.
The answer is A.
Answer: A
Question: The cost of 3 pens and 5 pencils is Rs.340. Also the cost of one pen and one pencil is in the ratio of 4:1 respectively. What is the cost of one dozen pens?
Options:
A)Rs.960
B)Rs.250
C)Rs.300
D)Rs.150
E)None of these
Rationale: Explanation:
Let the cost of one pen is ‘4x’ and pencil is ‘x’
3 X 4x + 5x = Rs.340
12x + 5x = Rs.340
X = 340/17 = 20
:. Cost of 1 pen = 4x = 4 x 20 = 80
:. Cost of 12 pens, i.e. (one dozen) = 80 x 12 = Rs.960
Answer: Option A
Answer: A
Question: In honor of the year 2011, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
Options:
A)18
B)50
C)42
D)36
E)56
Rationale: All options other than 'B' are factors of 2011. Hence, 'B' is the answer
Answer: B
Question: Rohini is standing in a queue in which her position is 21st from either end of the queue.
Can you calculate how many people are standing in the queue?
Options:
A)21 people.
B)31 people.
C)41 people.
D)51 people.
E)61 people.
Rationale: Explanation:
Since Rohini is 21st from either side, there must be 20 people in front of her and 20 people behind her.
20 + 20 + 1 (she herself) = 41
Therefore, the queue consists of 41 people.
Answer C
Answer: C
Question: A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 100$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?
Options:
A)79.55$
B)80.63$
C)81.63$
D)80.27$
E)83.15$
Rationale: let x is the cost of the food
1.07x is the gross bill after including sales tax
1.15* 1.07x=100
x=81.27
Hence, the correct option is D
Answer: D
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his dog?
Options:
A)12
B)24
C)30
D)48
E)120
Rationale: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and M are always together.
Consider F and D to be one unit, then we would have total of four units: {FD}, {C1}, {C2}, {M}. The number of arrangements of these four units is 4!, but F and D within their unit can be arranged in 2 ways: {FD} or {DF}, so total number of arrangements is 4!*2=48.
Answer: D.
Answer: D
Question: If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
Options:
A)z
B)x
C)x/y
D)z/x
E)x/z
Rationale: X people * Y days ----> produce Z jobs ----- (1)
Now,
Y people * X days -----> must produce Z jobs ----- (2)
>>>> Hence, to produce 1 job, divide above equation (2) by Z.
Y people *(X/Z) days -----> 1 job
The answer should be X/Z.
ANSWER:E
Answer: E
Question: A man can row with a speed of 10 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)33
B)15
C)20
D)99
E)71
Rationale: M = 10
S = 5
DS = 10 + 5 = 15
Answer: B
Answer: B
Question: Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.
Options:
A)5113
B)5117
C)5120
D)8119
E)10115
Rationale: Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, D,E The answer to be C
Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.
If x = initial number of trees = 5120
Year 1 = 5/4x
Year 2 = (5/4)(5/4)x
Year 3 = (5/4)(5/4)(5/4)x
Year 4 = (5/4)(5/4)(5/4)(5/4)x
Only for Answer D: (5/4)(5/4)(5/4)(5/4) 5120 = 12500
Hence, correct answer = C
Answer: C
Question: A father's age was 5 times his son's age 5 years ago and will be 3 times son's age after 2 years, the ratio of their present ages is equal to:
Options:
A)10/9
B)10/8
C)10/3
D)10/6
E)10/2
Rationale: Explanation:
Let the Father's age = x, and Son's = y
x - 5 = 5(y – 5)
x + 2 = 3(y + 2)
Solving we get x/y = 10/3
Answer: C
Answer: C
Question: A bank offers 10% interest rate compounded annually. A person deposits Rs. 20,000 every year in his account. If he does not withdraw any amount, then how much balance will his account show after four years?
Options:
A)Rs. 102102
B)Rs. 102220
C)Rs. 104202
D)Rs. 104222
E)Rs. 104233
Rationale: Explanation:
Rs.20000 after 4 years = 20000(1+10/100)4 = 20000(11/10)4 = Rs. 29282
Rs.20000 after 3 years = 20000(1+10/100)3 = 20000(11/10)3 = Rs. 26620
Rs.20000 after 2 years = 20000(1+10/100)2 = 20000(11/10)2 = Rs. 24200
Rs.20000 after 1 year = 20000(1+10/100)1 = 20000(11/10) = Rs. 22000
Total amount after 4 years = 29282 + 26620 + 24200 + 22000 = Rs. 102102
Answer: Option A
Answer: A
Question: In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
Options:
A)90%
B)58%
C)59%
D)50%
E)53%
Rationale: Number of students passed
= 60% of 140 = 60/100 * 140 = 84
Number of students failed
= 140 - 84 = 56.
Required percentage
= 28/56 * 100 = 50%.
Answer:D
Answer: D
Question: The value of 99^(96/99) x 99 is:
Options:
A)9989
B)9896
C)9890
D)9897
E)9810
Rationale: (100 â€“ 3/99) x 99 = 9900 â€“ 3
= 9897.
ANSWER:D
Answer: D
Question: A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability W that all 3 jellybeans removed from the bag are blue?
Options:
A)9/100
B)2/19
C)1/8
D)3/20
E)3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability W= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B
Answer: B
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 2 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
Options:
A)2 hours
B)4 hours
C)5 hours
D)1 hour
E)None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 2 hours, Tank A and B can effectively fill 1⁄12 × 2= 1⁄6 of the tank.
Time taken to fill the remaining 1−(1/6) = 5/6 of the tank = (5/6)/(1/6) = 5 hours. Answer : Option C
Answer: C
Question: A pipe can empty 1/4th of a cistern in 12mins. In 8 mins, what part of the cistern will be empty?
Options:
A)2/3
B)3/7
C)4/9
D)1/6
E)4/7
Rationale: 1/4 ---- 12
? ----- 8 ==> 1/6
D
Answer: D
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 700 grams. Find the profit percent.
Options:
A)100/7%
B)100/23%
C)100/19%
D)100/13%
E)None of these
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 700
100 + g / 100 + 0 = 1000 / 700
100+g = 10/7*100
g = 300/7 %
ANSWER: A
Answer: A
Question: An aeroplane travels distance 2500 km, 1200 km, and 500 km, at the rate of 500 km/h, 400 km/h and 250 km/h respectively. The average speed of the plane is :
Options:
A)420 km/h
B)410 km/h
C)430 km/h
D)415 km/h
E)440 km/h
Rationale: time=distance/speed
time=2500/500+1200/400+500/250
5+3+2=10 hrs
speed=total distance/time
(2500+1200+500)/10
4200/10=420 km/h
ANSWER:A
Answer: A
Question: If (2^32 + 1) is completely divisible by a whole number, which of the following numbers is completely divisible by this number?
Options:
A)(2^96+1)
B)(7 × 223 )
C)(2^16 - 1)
D)(2^15 + 1)
E)(2^17 + 1)
Rationale: Explanation:
Let
2
32
=
x
232=x.
Then
(
2
32
+
1
)
=
(
x
+
1
)
(232+1)=(x+1)
Assume that
(
x
+
1
)
(x+1) is completely divisible by a whole number, N
(
2
96
+
1
)
=
(
2
32
)
3
+
1
=
(
x
3
+
1
)
=
(
x
+
1
)
(
x
2
−
x
+
1
)
(296+1)=(232)3+1=(x3+1)=(x+1)(x2−x+1)
if
(
x
+
1
)
(x+1) is completely divisible by N,
(
x
+
1
)
(
x
2
−
x
+
1
)
(x+1)(x2−x+1) will also be divisible by N
Hence
(
2
96
+
1
)
(2^96+1) is completely divisible N
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)38
B)40
C)42
D)44
E)45
Rationale: Explanation:
x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
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 10 as remainder
Options:
A)1636
B)1346
C)1378
D)1635
E)1489
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 10
5x = 1355
x = 271
Large number = 271+1365 = 1636
A
Answer: A
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 52 years now, the son's age five years back was:
Options:
A)A)14
B)B)67
C)C)56
D)D)21
E)E)34
Rationale: Let the son's present age be x years. Then, (52 - x) = x
2x = 52.
x = 26.
Son's age 5 years back (26 - 5) = 21 years.
Answer:D
Answer: D
Question: A group of 8 friends want to play doubles tennis. How many different ways can the group be divided into 4 teams of 2 people?
Options:
A)420
B)2520
C)168
D)90
E)105
Rationale: C28∗C26∗C24∗C22/4!=105 , we are dividing by 4! (factorial of the # of teams) as the order of the teams does not matter. If 8 people are - 1, 2, 3, 4, 5, 6, 7, 8, then (1,2)(3,4)(5,6)(7,8) would be the same 4 teams as (5,6)(7,8)(1,2)(3,4), as we don't have team #1, team #2, ...
You can think about this in another way.
For the first person we can pick a pair in 7 ways;
For the second one in 5 ways (as two are already chosen);
For the third one in 3 ways (as 4 people are already chosen);
For the fourth one there is only one left.
So we have 7*5*3*1=105
ANSWER:E
Answer: E
Question: Mandrake has to choose from 4 from 22 people. There are 3 girls, 5 boys , 14 children. What is total probability that he will choose 1G , 2B , 1C?
Options:
A)1/7
B)2/7
C)3/61
D)4/7
E)5/7
Rationale: (3C1 * 5C2 * 14C1)/ 22C4 = 3*10*14/7315= 360/7315=3/61
ANSWER:C
Answer: C
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
Options:
A)2
B)4
C)6
D)8
E)9
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: D
Question: A 180 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options:
A)320 meter
B)225 meter
C)230 meter
D)235 meter
E)None of these
Rationale: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+180 /9=500 /9
=>x+180=500
=>x=320
So the length of the train is 320 meters
Option A
Answer: A
Question: A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price e of the machine?
Options:
A)	81
B)	100
C)	120
D)	135
E)	160
Rationale: Since the wholesale price was $90 and the profit was 20% of the wholesale price ([.2][90] = $18), the retail price would have to be above $108, but not that much greater than that.
Let's start by TESTing Answer C: $120....
If.....
Retail Price e= $120
10% discount off = $120 - (.1)(120) = 120 - 12 = 108
20% profit on wholesale price = 90 + (.2)(90) = 90 + 18 = 108
These two numbers MATCH, so this MUST be the answer!
Final Answer:
[Reveal]Spoiler:
C
Answer: C
Question: A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
Options:
A)400
B)991
C)881
D)771
E)551
Rationale: 2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer: A
Answer: A
Question: 6/7 of a certain number is 96. Find quarter of that number.
Options:
A)28
B)29
C)26
D)281
E)17
Rationale: Explanation:
6/7x = 96
x = 112
y = x/4 = 112/4 = 28
ANSWER:A
Answer: A
Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?
Options:
A)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
B)Ram = Rs.2500, Shyam = Rs.500, Mohan = Rs.250
C)Ram = Rs.1200, Shyam = Rs.1300, Mohan = Rs.750
D)Ram = Rs.1600, Shyam = Rs.1350, Mohan = Rs.760
E)None
Rationale: Explanation:
1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
ANSWER IS A
Answer: A
Question: Find the volume & curved surface area of a cylinder with diameter of base 14 cm and height 60 cm.
Options:
A)260 cm2
B)2610 cm2
C)2600 cm2
D)2640 cm2
E)264 cm2
Rationale: Volume = pieR2H= pie x 72 x 60 = 9240	cm3
Curved surface area = 2pieRH = (2 x3.14 x 7 x 60) cm2 =2640 cm2
answer:D
Answer: D
Question: Today is Monday. After 61 days, it will be:
Options:
A)Monday
B)Tuesday
C)Friday
D)Sunday
E)saturday
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer: Option E
Answer: E
Question: A circular mat with diameter 28 inches is placed on a square tabletop, each of whose sides is 36 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Options:
A)2/2
B)1/2
C)3/2
D)3/5
E)6/5
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (22/7)(14)(14)
Area of the Table = (36)(36)
So the quick way to estimate is looking at the fraction like this:616/1296=308/648=154/324=77/162 nearest to 1/2
Answer: B
Answer: B
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
Options:
A)3
B)4
C)5
D)7
E)8
Rationale: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do,. 3
A
Answer: A
Question: Can you find out what day of the week was January 12, 1979?
Options:
A)Friday.
B)saturday
C)sunday
D)monday
E)wednesday
Rationale: 1979 = 1900yrs + 78yrs + (period from 1st Jan to 12th Jan 1979)
1900 yrs have 1 odd day(calculated as 1600yrs have 0 odd days, n 300yrs have 15 odd days i.e.15/7= 2 weeks+1 odd day.so,for 300yrs, it's 1 odd day.totally it's 0+1=1odd day for 1900yrs).
78yrs = 19leap yrs +59 ordinary yrs
= 19 *2 +59 *1
= 97days = 13weeks +6 odd days = 6 odd days
period from 1st Jan to 12th Jan 1979 =12 days = 1week + 5odd days = 5 odd days
Therefore,
12th Jan 1979 = 1+6+5 = 12days =1 week +5 odd days =5 odd days
Therefore, 12th Jan 1979 was a Friday.
(Since,Sunday->0,Monday->1,...,Fri->5,sat->6)
ANSWER:A
Answer: A
Question: If f(x) = x^4 – x^2 + ax^6 – 3, then f(b) – f(-b) will equal:
Options:
A)0
B)2ab
C)2ab^4
D)8b^6 + 6
E)– 2b^2
Rationale: f(x)=x^4 – x^2 + ax^6 – 3
f(b) = b^4 – b^2 + ab^6 – 3
f(-b) = b^4 – b^2 + ab^6 – 3
f(b) - f(-b) = b^4 – b^2 + ab^6 – 3 - b^4 + b^2 - ab^6 + 3
=0
Answer A
Answer: A
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)48
B)36
C)7
D)67
E)15
Rationale: :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.4 = 1.5 km = 1500 m.
Required time = 1500 * 3/125
= 36 sec.
Answer: B
Answer: B
Question: Sunil deposited $6,000 to open a new savings account that earned 4 percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Sunil account one year after the account was opened?
Options:
A) $6,200
B) $6,255
C) $6,200
D) $6,205
E) $6,244
Rationale: Approach #1:
4 percent annual interest compounded semi-annually --> 2% in 6 moths.
For the first 6 moths interest was 2% of $6,000, so $120;
For the next 6 moths interest was 2% of $6,000,plus2% earned on previous interest of $120, so $120+$4=$124;
Total interest for one year was $120+$124=$244, hence balance after one year was $6,000+ $244=$6,244.
Answer: E.
Answer: E
Question: The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is
Options:
A)210
B)212
C)214
D)216
E)None of these
Rationale: Solution
P.W	= Rs.(1080 - 180)
= Rs. 900
S.I on Rs. 1080	=Rs.(180/900 x 1080)
= Rs. 216.
Answer D
Answer: D
Question: If 20 men can build a wall 66 metres long in 6 days, what length of a similar can be built by 86 men in 8 days?
Options:
A)53 m
B)46 m
C)94 m
D)49 m
E)64 m
Rationale: Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Answer is D
Answer: D
Question: A man can row a boat at 30 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/18
B)30/29
C)30/12
D)30/13
E)30/82
Rationale: Speed downstream = 30 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/36
= 30/18 hours.
Answer:A
Answer: A
Question: In what time will a train 100 m long cross an electric pole, it its speed be 136 km/hr?
Options:
A)2.6 sec
B)1.9 sec
C)8.9 sec
D)6.9 sec
E)2.9 sec
Rationale: Speed = 136 * 5/18
= 37.8 m/sec
Time taken = 100/37.8
= 2.6 sec.
Answer: A
Answer: A
Question: the government was giving out 10500 after 6 years of living in the United States and 15500 after 12 years of living in the United Sates. how much is the interest per year.
Options:
A)12%
B)20%
C)15%
D)10%
E)5%
Rationale: for 6 years = (15500 - 10500) = 5000.
for 12 years = (5000x6)/6= 5000
Principal = (10500 - 5000) = 5500.
Hence, rate = (100 x 5000)/(5500x6)	% = 15% ANSWER :C
Answer: C