mathewhe/aqua_rat huggingface dataset:
Question: In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 90 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?
(A) 2%
(B) 5%
(C) 8%
(D) 10%
(E) 20%
Rationale: Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 30:20 represents the number ratio of Republicans:Democrats. If 90% of Republicans (which is (60*0.9) = 54) and 15% of Democrats (40*0.15 = 6) voted for candidate X, means that out of total of 100 voters; 60 (54 + 6) voters voted for candidate X and 40 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 20 (60-40) votes. Therefore candidate X is expected to win the election by (20/100) votes which is equivalent to 20%.
I think the answer is E.
Answer: (E) 20%
Question: Find the smallest number that must be added to 1780 to make it a perfect
square.
(A) 17
(B) 42
(C) 69
(D) 47
(E) 52
Rationale: 4 1780 (42
16
82	180
164
16
Number to be added = (43)2 - 1780 = 1849 - 1780 = 69.
ANSWER C 69
Answer: (C) 69
Question: In a certain football league, the only way to score is to kick a eld goal
for 3 points or score a touchdown for 7 points. Thus the scores 1, 4
and 8 are not possible. How many positive scores are not possible?
(A) 5
(B) 6
(C) 9
(D) 11
(E) infinitely many
Rationale: One checks directly that the following list of scores up to 14 is the complete list
of obtainable scores up to that point: 3, 6, 7, 9, 10, 12, 13, 14. Now, we have 3 consecutive
scores, namely 12, 13, and 14, which are obtainable, and this implies every score > 14 is
obtainable. To see this, observe that if n is an obtainable score, then so is n + 3 (simply
add another eld goal to whatever it took to get n points); hence, 15 = 12+3, 16 = 13+3,
and 17 = 14+3 are all obtainable and so are 18 = 15+3, 19 = 16+3, 20 = 17+3, and so
on. Therefore, the positive integral scores which are not obtainable are 1, 2, 4, 5, 8, and
11. Thus, the answer is 6
correct answer B
Answer: (B) 6
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?
(A) 200
(B) 190
(C) 95
(D) 100
(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) 380
Question: There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 12,000 after 3 years at the same rate?
(A) 2345
(B) 3546
(C) 4556
(D) 6343
(E) 3972
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 12000 x 1 + 10 3 - 1
100
= Rs. 12000 x 331
1000
= 3972.
E
Answer: (E) 3972
Question: How many three digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 297
(C) 288
(D) 179
(E) 120
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is
6P3 = 6 * 5 * 4
= 120.
Answer: E
Answer: (E) 120
Question: Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?
(A) 339
(B) 33
(C) 27
(D) 28
(E) 19
Rationale: Let the son's present age be x years.then father's present age will be 3x + 3 years.
After 3 years,3x + 3 + 3 = 2 (x + 3) + 10
Solving we get, x = 10.
Substituting x =10 in 3x + 3,
Hence father's present age will be x = 33 years.
Answer:B
Answer: (B) 33
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 6 hours. Harvesting machine K harvested how many acres of wheat per hour?
(A)  4
(B)  8
(C)  12
(D)  13
(E)  15
Rationale: Rate of H = 6 acres/hr
Remaining land to be harvested = 100 - 40 = 60
Rate of H and K = 60/6 = 10 acres/hr
Rate of K = 10 - 6 = 4
Answer: A
Answer: (A)  4
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/8
(B) 5/9
(C) 5/5
(D) 5/2
(E) 5/1
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36
= 5/9
Answer: B
Answer: (B) 5/9
Question: In a stream running at 3 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 57 minutes. Find the speed of motor boat in still water?
(A) 18 kmph
(B) 22 kmph
(C) 16 kmph
(D) 20 kmph
(E) None of these
Rationale: Explanation:
Let the speed of motor boat instill water be X kmph
Then, speed in downstream = (X + 3) km
and. speed in upstream = (X - 3) kmph
Time taken to row 10km & back = (10/X+3,10/X-3)
10/X+3 + 10/X-3 = 57/60
11X2 - 240X - 44 = 0
(X - 22)(11x + 2) = 0
X = 22 or X = -2/11
Then X = 22 kmph
Answer: Option B
Answer: (B) 22 kmph
Question: Gio, the circus Elephant, is currently three times older than Lee, the circus Lion. In ten years from now, Lee the circus Lion will be exactly half as old as Gio, the circus Elephant. How old is Gio today?
(A) 20
(B) 23
(C) 30
(D) 28
(E) 29
Rationale: Gio, the circus Elephant, is currently three times older than Lee, the circus Lion.
Gio = 3*Lee
Usually, ages are integers so there is a good possibility that the age of Gio is 30 (the only option that is a multiple of 3).
Then age of Lee would be 10. In 10 yrs, Gio would be 40 and Lee would be 20 - so Lee would be half as old as Gio.
Answer (C)
Answer: (C) 30
Question: The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
(A) 279
(B) 283
(C) 308
(D) 318
(E) 328
Rationale: Other number =	(11 x 7700)/275	= 308.
ANSWER :C
Answer: (C) 308
Question: Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 16 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.
(A) 80 days
(B) 100/3 days
(C) 120 days
(D) 110 days
(E) 90 days
Rationale: Rate of both = 1/20
Together they do = 1/20*16 = 4/5
Left work = 1 - 4/5 = 1/5
Adam completes 1/5 work in 10 day
so he took 10*5 = 50 days to complete the left work alone.
Thus the rate of adam is 1/50
Rate of Micheal = 1/20 - 1/50 = 1/(100/3)
Thus micheal takes 100/3 days to complete the whole work.
ans. B.
Answer: (B) 100/3 days
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 90 km/hr. What is the length of the platform?
(A) 400
(B) 488
(C) 477
(D) 426
(E) 422
Rationale: Speed = 90* 5/18 = 25 m/sec.
Length of the train = 25 * 20 = 500 m.
Let the length of the platform be x m . Then,
(x + 500)/36 = 25 => x =400 m.
Answer: A
Answer: (A) 400
Question: In how many V ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?
(A) 720
(B) 864
(C) 900
(D) 936
(E) 1,296
Rationale: Total number of four letter passwords = 6*6*6*6= 1296 ------(1)
Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2)
therefore required value V= (1)-(2)= 1296-360=936.D
Answer: (D) 936
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months .Find the age of the teacher.
(A) 22
(B) 25
(C) 8
(D) 27
(E) 19
Rationale: Sum of the ages of the students = 39×15 = 585
New average = 15 years 3 months = 15 + 1414 year
Sum of the ages of students and teacher = 40×15141514 = 40×614614 = 610
Teacher age = 610 – 585 = 25 years.
Answer:B
Answer: (B) 25
Question: x+(1/x) = 4 find x^2 + (1/x^2)
(A) 2.25
(B) 3.25
(C) 4.25
(D) 14
(E) 6.25
Rationale: squaring on both sides (x+1/x)^2=4^2
x^2+1/X^2=16-2
x^2+1/X^2=14
ANSWER:D
Answer: (D) 14
Question: 24 oz of juice P and 25 oz of juice Q are mixed to make smothies X and Y . The ratio of p to Q in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to Q ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice V will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice V = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice Q = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Answer: (D) 20
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
(A) 7%
(B) 5%
(C) 9%
(D) 1%
(E) 3%
Rationale: (30 * 30)/100
= 9% decrease
Answer:C
Answer: (C) 9%
Question: Dhoni bought 5 toys with the average cost of $10. If David also buys the sixth toy with the price of $ 16, what is the average (arithmetic mean) price of those 6 toys?
(A) $10
(B) $7
(C) $8.5
(D) $9
(E) $11
Rationale: 5 toys -> Total cost = 5 * Avg cost = 5*10 = 50
Sixth toy cost = 16
Total cost for 6 toys= 50+16 = 66
AM = 66/6= 11
Hence E
Answer: (E) $11
Question: An amount of Rs. 75000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
(A) s. 46875; Rs. 28125
(B) s. 62500; Rs. 37500
(C) s. 72500; Rs. 27500
(D) s. 82500; Rs. 17500
(E) s. 72500; Rs. 17500
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (75000 - x). Then,
(x * 9 * 1)/100 + [(75000 - x) * 11 * 1]/100 = (75000 * 39/4 * 1/100)
(9x + 825000 - 11x)/100 = 39000/4 = 14625/2
x = 46875
Sum invested at 9% = Rs. 46875
Sum invested at 11% = Rs. (75000 - 46875) = Rs. 28125.
ANSWER:A
Answer: (A) s. 46875; Rs. 28125
Question: A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in.
(A) 17 days
(B) 97 days
(C) 19 days
(D) 60 days
(E) 15 days
Rationale: A = 140 days
B = 105 days
1/140 + 1/105 = 7/420 = 1/60
=>60 days
Answer: D
Answer: (D) 60 days
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 399
(B) 788
(C) 350
(D) 888
(E) 21
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m. Answer: C
Answer: (C) 350
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 50. What is the value of x?
(A)  50
(B)  100
(C)  200
(D)  140
(E)  2,000
Rationale: y = 50% of 50% 0f x
= x/4
and
y/100 of x = 50
y /100 *4y =50
y = 35
and x= 140
Answer - D
Answer: (D)  140
Question: Which of the following values of A satisfies the inequality?
A(A – 2) = 5A – 10
(A) A > 5 or A < 2
(B) 2 < A < 5
(C) 2 < A = 5
(D) A = 5, A = -2
(E) None of these
Rationale: Explanation:
A ( A – 2) = 5 A – 10
A( A – 2) = 5 ( A – 2)
A = 5 if A – 2 > 0
A = 5, A > 2
i.e. 2 < A = 5
ANSWER: C
Answer: (C) 2 < A = 5
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 25 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 9x/80
(B) 13x/20
(C) 80/9x
(D) 16x
(E) 80x/9
Rationale: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 25% of the sales of imported tools = 0.25*{total}/4 = 1/4*{total}/4 = 1*{total}/16.
Since the sales of of Japanese tools was x, then 1*{total}/16 = x --> {total} = 16x.
Answer: D.
Answer: (D) 16x
Question: The average age of an adult class is 40years. 18 new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
(A) 8
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Let original strength = y
Then , 40y + 18 x 32 = ( y + 18) x 36
â‡’ 40y +576 = 36y + 648
â‡’ 4y = 72
âˆ´ y = 18
E
Answer: (E) 18
Question: Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/3 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?
(A) 20
(B) 60
(C) 108
(D) 144
(E) 180
Rationale: The number of ornaments = a
Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6
1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12
1/3 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/3
=> 5 + a/12 = a/3 => a = 200
Ans: A
Answer: (A) 20
Question: If (x +3 )^2 = 144, which of the following could be the value of 2x?
(A) –26
(B) –22
(C) –30
(D) 12
(E) 13
Rationale: You can also get to the answer by backsolving using answer choices
Starting with x = -15
(x + 3)^2 = 144
(-15+3)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -15 will result in 144 in the equation so x must be -11,
Then 2x = 2 * -15 = -30
Answer: C
Answer: (C) –30
Question: Solve:-
333 x 333 x 333 + 555 x 555 x 555 = ?(333 x 333 - 333 x 555 + 555 x 555)
(A) 888
(B) 333
(C) 555
(D) 988
(E) 889
Rationale: Given Exp. = (a3 + b3) = (a + b) = (333 + 555) = 888(a2 - ab + b2)
Answer A
Answer: (A) 888
Question: The average speed of a bus from Koyambedu to Salem is 57 km per hour. The bus is scheduled to leave Koyambedu Bus station at 10 pm and reach Salem at 4.35 am on the next day. The distance between Salem and Koyambedu bus station is 342 km. On the way in between Koyambedu and Salem a halt is scheduled compulsorily. Find out the duration of this halt scheduled?
(A) 45 minutes
(B) 35 minutes
(C) 60 minutes
(D) cannot be determined
(E) None of these
Rationale: Actual time takes= 342/57 = 6 hrs
Duration of journey frm 10pm to 4.35am= 6 hrs 35 min
duration of halt scheduled= 35min
ANSWER:B
Answer: (B) 35 minutes
Question: If a and t are positive integers, at + a + t cannot be
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let at + t + a = x
Add 1 on both sides:
at + t + a + 1 = x + 1
t(a + 1) + a + 1 = x + 1
(a + 1)(t + 1) = x + 1
Minimum value of (a + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime -->at + t + a cannot be 6
Answer: B
Answer: (B) 6
Question: A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 350-meter long platform?
(A) 43
(B) 45
(C) 47
(D) 49
(E) 51
Rationale: Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 14 * 10 = 140 m.
The time taken to pass the platform = (140 +350)/ 10 = 49 seconds
The answer is D.
Answer: (D) 49
Question: The cross-section of a river bank is a trapezium in shape. If the river bank is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 500 sq m, the depth of river bank is?
(A) 20 m
(B) 60 m
(C) 40 m
(D) 50 m
(E) 90 m
Rationale: 1/2 * d (12 + 8) = 500
d = 50
ANSWER:D
Answer: (D) 50 m
Question: A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
(A) A)1km
(B) B)500m
(C) C)650m
(D) D)750m
(E) E)400m
Rationale: Relative speed of the policeman = 20-16 = 4 km/hr
time taken by policeman to cover 100m = (100/1000)*(1/4) = 1/40 hr
In 1/40 hr the thief covers a distance of 16/40 km = 2/5 km = 400m
Answer is E
Answer: (E) E)400m
Question: A, B and C enter into a partnership in the ratio 7/2:4/3:6/5.After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:
(A) Rs. 2100
(B) Rs. 2400
(C) Rs. 3600
(D) Rs. 4000
(E) Rs. 3800
Rationale: Explanation:
Ratio of initial investments =(7/2:4/3:6/5)=105 : 40 : 36.
Let the initial investments be 105x, 40x and 36x.
A : B : C =(105 X4+150/100X105X8):(40X X 12):(36x x 12)
= 1680x : 480x : 432x = 35 : 10 : 9.
Hence, B's share = Rs.(21600 X 10/54)=Rs. 4000.
ANSWER IS D
Answer: (D) Rs. 4000
Question: What is the tens digit of 7^957?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
957= 4*239 + 1
The ten's digit will be 0 .
Answer D
Answer: (D) 3
Question: If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost?
(A) 65 paise
(B) 70 paise
(C) 52 paise
(D) 48 paise
(E) 75 paise
Rationale: Explanation:
(Chain Rule)
Let 200 gm potato costs x paise
Cost of 14 Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise (∵1/4 kg=1000/4 gm=250 gm)
More quantity, More Paise (direct proportion)
Hence we can write as
(Quantity) 200 : 250 :: x : 60
⇒200×60=250 × x
⇒4×60=5 × x
⇒4×12= x
⇒x=48
Answer: Option D
Answer: (D) 48 paise
Question: A man watched his wife run around the neighborhood block 4 times. He was curious how fast she was running. Each block is 500 meters and she ran the distance in one hour. How fast was his wife running in kilometers per hour?
(A) 3
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: The distance of each block was 500 meters.
She made the roundtrip 4 times.
Multiply 4 by 500 to get 2000 meters or 2 km.
Because it took her one hour to run the distance the answer is already in kilometers per hour.
Correct answer is 2km/hour
Answer: (C) 2
Question: Having scored 95 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?
(A) 28
(B) 27
(C) 23
(D) 22
(E) 24
Rationale: Explanation :
Let the average score of the first 18 innings be n
18n + 95 = 19(n+4)=> n = 19
So, Average score after 19th innings = x+4 =23.
Answer : C
Answer: (C) 23
Question: Joan gave harvey 60 out of 500 nuts. He then gave Joan 66 out of the remainder. What will be the percentage increase in the ratio of nust given to nuts owned?
(A) A) 22%
(B) B) 60%
(C) C) .8%
(D) D) 80%
(E) E) 44%
Rationale: Ratio in 1st instance: 6/50
Ratio in the 2nd instance:66/(500-60)= 66/440 =(6/40)
percentage increase is (difference/initial quantity)*100
(6/50)/(6/40 )* 100= 80%
Correct answer is D
Answer: (D) D) 80%
Question: A and B together can do a work in7 days. If A alone can do it in 14 days. In how many days can B alone do it?
(A) 14
(B) 10
(C) 21
(D) 20
(E) 25
Rationale: A
14
1/7 â€“ 1/14 = 1/14 => 14
Answer: (A) 14
Question: A trained covered x km at 90 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 22
(B) 99
(C) 27
(D) 66
(E) 887
Rationale: Total time taken = x/90 + 2x/20 hours
= x/9 hours
Average speed = 3x/(x/9) = 27 kmph
Answer: C
Answer: (C) 27
Question: All factors of a positive integer A are multiplied and the product obtained is A^3. If A is greater than 1, how many factors does A have?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: Answer = D = 6
Number ................ Factors ........................ Product
2 ............................. 1, 2 ................................. 2
3 ............................... 1, 3 ............................... 3
4 ................................ 1, 2, 4 ............................... 8
5 ............................... 1, 5 .................................. 5
6 ............................... 1, 2, 3, 6 ......................... 36
7 ................................ 1, 7 ................................. 7
8 ................................. 1, 2, 4, 8 ........................... 64
9 ............................... 1, 3, 9 ............................ 27
10 ................................ 1, 2, 5 ............................ 10
11.................................... 1, 11 ........................... 11
12 ................................... 1, 2, 3, 4, 6, 12 ................. 12 * 12 * 12
Number which we are looking for = 12
Answer = D
Answer: (D) 6
Question: Three-twentieths of the members of a social club are retirees who are also bridge players, nine-twentieths of the members are retirees, and one-half of the members are bridge players. If 120 of the members are neither retirees nor bridge players, what is the total number of members in the social club?
(A) 150
(B) 300
(C) 360
(D) 400
(E) 480
Rationale: {Total} = {Retirees} + {Bridge players} - {Both} + {Neither}
x = 9/20*x + x/2 - 3/20*x + 120
20x = 9x + 10x - 3x + 120*20 (multiply by 20)
16x = 120*20
x = 150
Answer: A
Answer: (A) 150
Question: In the following sequence: [x, y, z, 6, 8, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+y?
(A) 2
(B) 3
(C) 4
(D) 5
(E) -2
Rationale: lets start from z, as per the question stem
z + 6 + 8 = 16
-->> z= 2
similarly, y +2 + 6 = 8
--> y = 0
similarly,, x + 0 + 2 = 6
--> x = 4
hence , x+y = 4-0 = 4 --> x+y=4
ANSWER:C
Answer: (C) 4
Question: A certain sum becomes three times itself at simple interest in five years. the sum become 1200 after 9 year.calculate the principal amount.
(A) 250
(B) 260.86
(C) 288.6
(D) 265.66
(E) 280
Rationale: Let the sum be Rs. x, then it becomes Rs. 3x in five years Rs. 2x is the interest on x for five years.
R = (100 * 2x)/(x * 5) = 40 %
s.i=p*r*t/100=x*40*9/100=3.6x
x+3.6x=1200=4.6x=1200,x=1200/4.6=260.86
ANSWER:B
Answer: (B) 260.86
Question: How many ways are there to award a gold, silver and bronze medal to 6 contending teams?
(A) 10 × 9 × 8
(B) 10!/(3!7!)
(C) 6!/3!
(D) 564
(E) 6 * 5 * 4
Rationale: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways
if gold medal is given to 1 of the teams then only possible 5 teams can be considered for silver medal. we can do selection in 5 ways
similarly if gold and silver medals are awarded then only remaining 4 teams can be considered for a bronze medal. we can do the selection in 4 ways
Total number of ways to select the 3 possible medal winners = 6 * 5 * 4
Correct answer - E
Answer: (E) 6 * 5 * 4
Question: A is 25% bigger than B B is 20% less than C then the relation between A, B, C ?
(A) 5:4:5
(B) 5:4:6
(C) 5:4:7
(D) 5:4:8
(E) 6:4:5
Rationale: Assume C = 100 Then
B is 20%less than C
Therefore, 20*100/100 = 20 ;
B= 100-20 = 80
B =80
A = 25% more than B :
So,
A = B + 25% of B
= 80 + 20
= 100
So, the proportion are 100:80:100 = 5:4:5
ANSWER:A
Answer: (A) 5:4:5
Question: The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side.
(A) Rs. 850
(B) Rs. 860
(C) 876 RUPEES
(D) Rs. 886
(E) None of these
Rationale: Explanation:
We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.
Here we go,
Surface area =6a2=6∗8(2)=384sq feet
Quantity required =38416=24kg
Cost of painting =36.50∗24= Rs.876
Option C
Answer: (C) 876 RUPEES