divelab/Sys2Bench huggingface dataset:
Question: There are 4 gold chain. 1 has 5links, other has 4 links and the other 2 have 3 links.
goldsmith takes 50 paise to open the link and 1.00/- to attach the link. what is least cost to
bake whole bracelet.
Options:
A)3.50 rupees
B)4.50 rupees
C)4.80 rupees
D)5.50 rupees
E)6.50 rupees
Rationale: Let,the shape of the bracelet is closed circle.[It is supposed to assume]
gold chain with 5 links: A_ _ _ _ _B
gold chain with 4 links: C_ _ _ _D
gold chain with 3 links: E_ _ _F
gold chain with 3 links: G_ _ _H
We,generally hold a common notion that since there are 4 gold chains and since we are to make a closed circular shaped bracelet, so,we have to join the ends namely :(B,C),(D,E),(F,G),(H,A),i.e, total 4 links have to be broken and further joined,i.e, total cost will then be 4(1+.50)= 6 rupees.
But,now we will tackle the problem in a different way.
Let, all the 3 links of GH chain are broken.
Then,
with the help of 1st broken link, B and C ends are joined.
with the help of 2nd broken link, D and E ends are joined.
and,
With the help of the remaining broken link, F and A ends are joined.
So, the above mentioned method explains us that breaking only 3 links and subsequently joining two free ends with each link facilitates us to make a whole closed circular shaped bracelet.
Therefore,the cost in this case : 3*(1+.50) = 3*(1.50)=4.50 rupees;
So,evidently,the least cost to make the whole bracelet :4.50 rupees .
ANSWER:B
Answer: B
Question: Average age of A and B is 24 years and average age of B, C and D is 22 years. The sum of the ages of A, B, C and D is
Options:
A)76 years
B)30 years
C)77 years
D)88 years
E)56 years
Rationale: Let their ages 10 years ago is x, 2x and 3x years.
10 + 2x + 10 + 3x + 10 = 90 hence x= 10
B’s present age = (2x + 10) =30 years
Answer: B
Answer: B
Question: Jake, Lena, and Inna need to drive home from a corporate reception in an SUV that can seat 5 people. If only Inna or Jake can drive, how many seat allocations are possible?
Options:
A)24
B)42
C)120
D)360
E)720
Rationale: 3 people ,5 seats, only 2 can drive
if inna is in one seat remaining, 2 people can be arranged in 2p2 i.e 2! =2 ways
since any one can drive total ways = 2 *2= 4 ways
4 seats can be chosen out of remaining 5 seats in 5c4 ways = 5!/(3!*2!)= 6 ways
4*6=24
A
Answer: A
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)1.8
B)1.5
C)1.9
D)1.2
E)1.1
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: B
Question: In a urban village of india named "owlna" , 80% people have refrigerator , 82% people have television , 70% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury.
Options:
A)3%
B)8%
C)7%
D)10%
E)15%
Rationale: C
7%
100 - [ (100-80)+(100-82)+(100-70) +(100-75)]
=100-(20+18+30+25)
=100-93
Answer: C
Question: If x - 8 = -|x|, then x=?
Options:
A)2
B)-4
C)4
D)3
E)5
Rationale: x - 8 = -|x| ...(given)
x^2 - 16x + 64 = x^2
0*x^2 + 16*x -64 = 0 ....(by solving above eq. we get) , x = 4 ===> Ans - C
Answer: C
Question: In a division, divident is 760, divisior is 36 and quotient is 21. Find the remainder.
Options:
A)A)4
B)B)3
C)C)2
D)D)5
E)E)6
Rationale: Explanation:
760 = 36 x 21 + r
760 = 756 + r
r = 760 - 756 = 4
Answer: Option A
Answer: A
Question: The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?
Options:
A)22
B)77
C)66
D)50
E)88
Rationale: Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years
=> C.I - S.I
=> 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100
=> 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5
=> 16r/100 + 8r2/(100)2 = 20r/100
=> 4r/10 = 8r2/(100)2
=> 8[r/100]2 - 4r/100 = 0
=> r/100 {8r/100 -4} = 0
=> r = 0% of 50%
Since r!= 0%, r =50%
Answer:D
Answer: D
Question: If y = 1296 * 125 * 4096 / 25, How many digits are in y,
Options:
A)4
B)8
C)2
D)6
E)3
Rationale: y = 1296 * 125 * 4096 / 25
y = 8^4 * 5^3 * 6^4 / 5^2
y = 48^4 * 5
y = 26542080
Ans: B
Answer: B
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.64 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
Options:
A)8%
B)10%
C)11%
D)12%
E)14%
Rationale: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.
3(0.22-x)(15) + 2x(18) = 8.64
9.9 - 45x + 36x = 8.64
9x = 1.26
x = 0.14
The answer is E.
Answer: E
Question: Of 100 applicants for a job, 50 had at least 5 years of prior work experience, 40 had advanced degrees, and 10 had at least 5 years of prior work experience and advanced degrees. How many of the applicants had neither 5 years of prior work experience nor advanced degrees?
Options:
A)30
B)15
C)20
D)34
E)22
Rationale: Had advanced degrees and 5 years work experience: 10
Only had 5 years work experience: 50-10 = 40
Only had advanced degrees: 40-10 = 30
100-10-40-30=20
Answer: C
Answer: C
Question: An urn contains g green marbles and b blue marbles. If 3 green marbles and 7 blue marbles are added, and then one marble is selected at random from the urn, what is the probability that a blue marble will be drawn?
Options:
A)b/(b+g)
B)(b+5)/(g+3)
C)(b+5)/(b+g+8)
D)(b+5)/(b+g+3)
E)b+7/(b+g+10)
Rationale: no of fav outcomes i.e. blue MArbles = b+5
Total no of outcomes i.e. total Marbles = (b+7)+(g+3)= b+g+10
probability = (b+7) /(b+g+10)
Answer E
Answer: E
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 12%?
Options:
A)20%
B)25%
C)13 1/30%
D)32%
E)13%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 88
2/3 SP1 = 88
SP1 = 132
100 --- 32 => 32%
ANSWER:D
Answer: D
Question: In a group of 6 male and 4 female, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options:
A)200
B)209
C)207
D)300
E)350
Rationale: req no = 6C1*4C1 + 6C2*4C1 + 6C4
==6C1+4C1 + 6C2+4C2 + 6C3*4C1 + 6C4
(6*4) + (6*5/2*1 * 4*3/2*1) + 6*5*4/3*2*1*4 + 6*5/2*1
==> 209
ANSWER B
Answer: B
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
Options:
A)39:40
B)39:86
C)39:18
D)39:10
E)32:40
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: A
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 0
II. y = 0
III. x = -y
Options:
A)I only
B)II only
C)III only
D)I and III only
E)I, II, and III
Rationale: Re-arrange equation: x^2 - xy = 0 => x*(x-y) = 0
Therefore, either x=0 or x=y. We know that x and y are different, so x must be equal to 0.
ANSWER:A
Answer: A
Question: Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 46?
Options:
A)1/16
B)5/42
C)1/8
D)3/16
E)1/4
Rationale: so the # of factors 230 has 8 (see below);
so out of 8 factors only two are multiples of 46: 46 and 230, itself;
So, the probability is 2/8=1/4.
Answer: E.
Answer: E
Question: A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 1 specified cars. In how many ways cars can be arranged?
Options:
A)1210
B)120
C)1500
D)1640
E)1440
Rationale: we arranged 1 specified cars in 1 slots = 1!
remaining 5 cars in 5 slots = 5!
number of ways = 1!*5! = 120
correct option is B
Answer: B
Question: A class of six students has to split into two indistinguishable teams of three people. Compute
the number of distinct team arrangements that can result.
Options:
A)2 distinct teams.
B)4 distinct teams.
C)10 distinct teams.
D)8 distinct teams.
E)7 distinct teams.
Rationale: Consider one specific person of the six students. There are
(5
2)
to choose the 2
partners on his team. Hence, there are
(5
2)
= 10 distinct teams.
correct answer C
Answer: C
Question: If x is divisible by 2, 14, and 10, which of the following must be the least multiple of x?
Options:
A)308
B)154
C)70
D)44
E)21
Rationale: We are looking for the LCM (which is not 0) of 2, 10 = 2*5, 14 = 2*7:
2 * 5 * 7 = 70
The answer is C.
Answer: C
Question: A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $50000. Find his total income?
Options:
A)A)452000
B)B)562000
C)C)800000
D)D)1000000
E)E)652000
Rationale: 3 children got = 3*20% = 60%
wife got = 30%
orphan house = 5%
total = 60+30+5 = 95%
remaining = 100-95 = 5%
5% = 50000
100% = 50000*100/5 = $1000000
Answer is D
Answer: D
Question: In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ?
Options:
A)B can give C 1 points
B)B can give C 4 points
C)B can give C 2 points
D)B can give C 6 points
E)B can give C 8 points
Rationale: A: B = 80 : 75, A : C = 80 : 65.
B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5
Therfore ,In a game of 60, B can give C 8 points.
Answer is E.
Answer: E
Question: If c equals the sum of the even integers from 2 to 504, inclusive, and m equals the sum of the odd integers from 1 to 297, inclusive, what is the value of c + 2m?
Options:
A)85957
B)108158
C)299376
D)107860
E)150788
Rationale: Use following formulae for such problems:
Sum of evenly spaced integers = (# of integers)*(mean of integers)
# of integers = [(last - first)/2] + 1
Mean of integers = (last + first)/2
In above problem:
# of integers = [(504 - 2)/2] + 1= 252 and [(297-1)/2]+ 1 = 149
Mean of integers = (504 + 2)/2 = 253 and (297 + 1)/2 = 149
Sum of integers = (252*253) = 63756 and (149*149) = 22201
Thus their sum (c + 2m) = 63756 + (2 * 22201) = 108258
ANSWER:B
Answer: B
Question: A boy gives 15 percent of a pie to his mother, 10 percent to his father and 25 percent to his sister. What fraction of the pie is leftover?
Options:
A)4/5
B)3/5
C)1/2
D)1/5
E)1/10
Rationale: 100%-(15%+10%+25%)=50% of the pie remains --> 50% = 20/100 = 1/5.
Answer: C.
Answer: C
Question: How many times are the hands of a clock at right angle in a day?
Options:
A)11
B)22
C)33
D)44
E)55
Rationale: Sol.
In 12 hours, they are at right angles 22 times.
∴ In 24 hours, they are at right angles 44 times.
Answer D
Answer: D
Question: If xy > 0, 1/x + 1/y = 2, and 1/xy = 8, then (x+y)/4 = ?
Options:
A)1/16
B)1/6
C)1/5
D)5
E)6
Rationale: (1/X+1/Y)=2 canbe solved as {(x+y)/xy}=8. Substituting for 1/xy=8, we get
x+y=2/8
==> (x+y)/4= 2/(8*4)=1/16.
A
Answer: A
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 5 years older than B, the present age of B is
Options:
A)35
B)37
C)39
D)41
E)42
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 5) years.
(x+5+10)=2(x—10)
hence x=35.
Present age of B = 35 years
Answer: Option A
Answer: A
Question: Harriet planned to complete a certain task on Friday, January 1, but because of illness the completion date was postponed 48 days. On which day of the week in February was the task completed?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Thursday
E)Friday
Rationale: This type of story problem is essentially just about a repeating pattern and a 'remainder.'
We're told that Harriet planned to complete a certain task on FRIDAY, January 1, but because of illness the completion date was postponed 48 DAYS. We're asked on what day of the week the task was actually completed on.
Since the task was supposed to be completed on a Friday....
A 1 day postponement would be Saturday
A 2 day postponement would be Sunday
A 3 day postponement would be Monday
A 4 day postponement would be Tuesday
A 5 day postponement would be Wednesday
A 6 day postponement would be Thursday
A 7 day postponement would be Friday
A 8 day postponement would be Saturday
Etc.
So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 48 days.
48/7 = 6 remainder 6
This means that there are 6 full weeks AND 6 extra days after a Friday....Thus, the task was completed on a Thursday.
D
Answer: D
Question: what is 66.67% of 804 of 0.1666 ?
Options:
A)19.33
B)54.55
C)89.33
D)97.21
E)68.77
Rationale: 66.67 % = 2/3
2/3 of 804 = 2/3 * 804 = 536
536 of 0.166 = 536 * (1/6) = 89.33
.... Ans - C
Answer: C
Question: 397 x 397 + 104 x 104 + 2 x 400x 104 = x?
Options:
A)234341
B)235633
C)234677
D)315656
E)251501
Rationale: Given Exp.	= (397)2 + (104)2 + 2 x 397 x 104
= (397 + 104)2
= (501)2 = (500 + 1)2
= (5002) + (1)2 + (3 x 500 x 1)
= 250000 + 1 + 1500
= 251501
E
Answer: E
Question: A table is bought for Rs.1000/- and sold at Rs.1200/- find the loss percentage
Options:
A)10% Loss
B)10% Gain
C)20% Loss
D)20% Gain
E)30% Gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (1200 ~ 1000)/1000 = 20% Gain
D
Answer: D
Question: What is the place value of 8 in the numeral 8259
Options:
A)A)2700
B)B)2800
C)C)2900
D)D)2980
E)E)8000
Rationale: 8 * 1000 = 8000
E
Answer: E
Question: A bicycle wheel has a diameter of 0.61m. How many complete revolutions does it make in 1km?
Options:
A)246
B)522
C)1408
D)710
E)223
Rationale: 1 revolution = 3.14 * diameter.
Number of revolutions in 1km = 1000m / ( 3.14 * 0.61m ) = 522.1. Hence 522 complete revolutions.
Answer B
Answer: B
Question: Find the value for x from below equation: x/3=-7?
Options:
A)-6
B)-21
C)-2
D)-3
E)4
Rationale: 1. Multiply both sides by 3:
x*3/3= -7/3
Simplify both sides:
x = -21
B
Answer: B
Question: David covered a distance of 50 miles on his first trip. On a later trip he travelled 300 miles while going three times as fast. His new time compared with the old time was:
Options:
A)twice as much
B)three times as much
C)the same
D)half as much
E)a third as much
Rationale: B
Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: A
Question: Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 6 minutes. The waste pipe can empty the full cistern in?
Options:
A)6
B)8
C)10
D)9
E)2
Rationale: 1/5 + 1/15 - 1/x = 1/6
x = 10
Answer:C
Answer: C
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine V is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine V can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
Options:
A)14
B)13
C)11
D)9
E)7
Rationale: machine V finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts
Lets assume total work require 120 shifts
Therefore,
rate of V = 5 shifts/day
rate of B = 4 shifts/day
rate of (V+B) = 9 shifts/day
According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day
Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D
Answer: D
Question: How many words with or without meaning, can be formed by using all the letters of the word, â€˜POWERâ€™, using each letter exactly once?
Options:
A)700
B)720
C)750
D)800
E)120
Rationale: The word â€˜POWERâ€™ contains 5 different letters.
Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time
=5P5
= 5!
= 5*4*3*2*1
= 120
ANSWER:E
Answer: E
Question: Ramesh can finish a piece of work in 18 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
Options:
A)8/3 days
B)9/3 days
C)6 days
D)3 days
E)7 days
Rationale: Ramesh can finish a piece of work in 18 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 9 days.
days needed to finish the same amount of work = 1/(1/9+1/18)=6 days
ANSWER:C
Answer: C
Question: If log 27 = 1.431, then the value of log 9 is
Options:
A)0.95
B)0.952
C)0.954
D)0.951
E)0.9323
Rationale: log 27 = 1.431
{\color{Black} \Rightarrow \log (3^{3})=1.431}
3 log 3 = 1.431
log 3 = 0.477
log 9 = {\color{Black} \log (3^{2})} = 2 log 3 = (2 x 0.477) = 0.954
Answer: C) 0.954
Answer: C
Question: If n is an integer and 5^n > 400,000,000, what is the least possible value of n?
Options:
A)7
B)13
C)9
D)10
E)11
Rationale: When you seperate the 400000000 into factors of 5 and 2 you get - > 10^8 x 2^2 = 5^8 x 2^10
2 to the ^ 8 = 1024 so its 1024 x 5^8
that means 5^8 x 5^x must be greater
5^x > 1024
5^1=5
5^2=25
5^3= 125
5^5= 3125 - > so x must be at least 5
5^(8+5)= 5^13
B
Answer: B
Question: The ratio of the volumes of two cubes is 125 : 1728. What is the ratio of their total surface areas?
Options:
A)81 : 121
B)9 : 11
C)25 : 144
D)27 : 121
E)None of these
Rationale: Ratio of the sides = Â³âˆš125 : Â³âˆš1728 = 5 : 12
Ratio of surface areas = 5^2 : 12^2 = 25 : 144
ANSWER:C
Answer: C
Question: Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 14 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 14 questions did Zachary answer correctly?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: i got two equations:
3x-2y=25
x+y=14
3x-2(14-x)=25
3x-28+2x=25
5x=53
x=10.6 or between 10 and 11. (ANS E)
Answer: E
Question: Find the value of 72515 x 9999 = m?
Options:
A)345434667
B)246465757
C)465767867
D)725077485
E)645354643
Rationale: 72515 x 9999 = 72515 x (10000 - 1)
= 72515 x 10000 - 72515 x 1
= 725150000 - 72515
= 725077485
D
Answer: D
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB > AB
B)XB < YD
C)AX > XB
D)AX < XB
E)YD < AB
Rationale: A--X------B
C-----Y---D
YD < AB.
Answer: E.
Answer: E
Question: List I: 3, 6, 8, 9
List II: x, 3, 6, 8, 9
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: A.
Answer: A
Question: The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person?
Options:
A)76 kg
B)76.5 kg
C)75 kg
D)Data inadequate
E)None of these
Rationale: Explanation:
Total weight increased = (10 x 2.5) kg = 25 kg.
Weight of new person = (50 + 25) kg = 75 kg.
Answer: C
Answer: C
Question: how many terms are there in the G.P. 3,6,12,24,...,384?
Options:
A)8
B)9
C)10
D)11
E)7
Rationale: Here a=3 and r=6/3=2. let the number of items be n
then, t^n=384=> ar^n-1=384
= 3 x 2^n-1=384
=2^n-1=128 = 2^7
=n-1=7=>n=8
Therefore, number of terms is 8
Answer is A.
Answer: A
Question: If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265
Options:
A)344
B)800
C)388
D)377
E)289
Rationale: Explanation:
Let the cost of Production = Rs. P
Then, as per question,
\fn_jvn {\color{Black} \Rightarrow (\frac{125}{100}\times \frac{115}{100}\times \frac{110}{100}\times p)=1265}
\fn_jvn {\color{Black} \Rightarrow \frac{253}{160}\; p=1265}
\fn_jvn {\color{Blue} \Rightarrow p=800}
Answer: B) Rs. 800
Answer: B
Question: A and B form a study group and divide a 75 question study guide. If A answer 7 questions per hour, while B answer 5 every hour, what fraction of the study guide is incomplete after 4 hours?
Options:
A)48/75
B)20/75
C)27/75
D)28/75
E)16/75
Rationale: Number of questions A can answer per hour: 7
Number of questions B can answer per hour: 5
Number of questions A and B can answer per hour: 7+5=12
Number of questions A and B can answer in 4 hours: 4x12=48
Fraction of the study guide that is incomplete = 1-48/75=27/75
Answer is C
Answer: C
Question: 15 lts of water containing 20% alcohol, then added 5 lts of water. What is % alcohol
Options:
A)15%
B)18%
C)20%
D)22%
E)25%
Rationale: in 15 ltr of mixure, 3 ltr alcohal and 12 ltr pure water.
when 5 ltr water is added, then
3 ltr alcohal in 20 ltr mixture means 15% alcohal in mixture.
ANSWER: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 40 years now, the son's age 10 years back was:
Options:
A)10 years
B)19 years
C)33 years
D)38 years
E)39years
Rationale: Let the son's present age be x years. Then, (40 - x) = x
2x = 40.
x = 20
Son's age 5 years back (20 - 10) = 10 years.
Answer:A
Answer: A
Question: What is the probability of getting a sum 9 from two throws of a dice?
Options:
A)1/6
B)1/8
C)1/9
D)1/12
E)1/7
Rationale: Explanation:
In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)= 4/36 =	1/9	.
ANSWER : C
Answer: C
Question: Five years back, a father was 36 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?
Options:
A)15 years
B)14 years
C)13 years
D)12 years
E)11 years
Rationale: Using linear equations to convert the word problem:
** F = fathers current ageS = sons current age
#1 Five years back, a father was 36 years older than his son: F-5 = 30 + (S - 5)
#2 At present the father is 5 times as old as the son: F = 5*S
How old will the son be three years from now?: S + 3 = ?
With two variables and two linear equations we are able to solve the problem:
(S*5) - 5 = 36 +S -5
4S=36
S = 9
S + 3 = 9 + 3 = 12
Answer: D
Answer: D
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189.The amount of the bill is :
Options:
A)Rs. 1386
B)Rs. 1764
C)Rs. 1575
D)Rs. 2268
E)None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.189.
∴ x 16x9/12x1/100= 189 or x = 1575.
∴ P.W. = Rs. 1575.
∴Sum due =P.W. + T.D. =Rs.(1575 + 189)=Rs.1764.
Answer B
Answer: B
Question: What is the remainder when you divide 2^200-1 by 7?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: answer is C. this is very similar to the 32^32^32-1 divided by 7 question.
Answer: C
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What is the weight of the new person?
Options:
A)75 Kg
B)50 Kg
C)70 Kg
D)80 Kg
E)60 KG
Rationale: Explanation:
Total increase in weight = 8 Ã— 2.5 = 20
If x is the weight of the new person, total increase in weight = xâˆ’50
=> 20 = x - 50
=> x = 20 + 50 = 70
Answer: Option C
Answer: C
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)4567
B)4689
C)5004
D)5678
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: If x and y are positive integers and 11 + x + y + xy = 25, what is the value of x + y?
Options:
A)3
B)5
C)6
D)8
E)9
Rationale: Try each answer choices.
For A: 11 + 3 + xy = 25; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)
For B: 11 + 5 + xy = 25; xy = 9 (no combination of xy = 9 and x + y = 5)
For C: 11 + 6 + xy = 25; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)
For D: 11 + 8 + xy = 25; xy = 6 (no combination of xy = 6 and x + y = 8)
For E: 11 + 9 + xy = 25; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)
Therefore, answer C.
Answer: C