mathewhe/aqua_rat huggingface dataset:
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 7
Rationale: Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 7 years ago?
i.e. D-7 = 14-7 = 7 years
ANSWER:E
Answer: (E) 7
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 25 miles per gallon, and from Town B to Town C, the car averaged 30 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
(A) 24
(B) 25
(C) 23
(D) 22
(E) 26.5
Rationale: step 1) took LCM of 25 and 30.. came as 150.
step 2) 150 distance between B to C... do 150/30 hence 5 gallons used
step 3) twice distance.. hence 150*2= 300... do as above.. 300/25= 12 gallons used
step 4) total gallons.. 5+12= 17 gallons
step ) total miles= 150+300= 450 miles
hence.. average of whole journey = 450/17 which comes to 26.5
Answer : E
Answer: (E) 26.5
Question: Five bells ring together and ring at intervals of 2, 6, 8, 12 and 15 seconds respectively. How many times will they ring together in 60 minutes?
(A) 34
(B) 33
(C) 32
(D) 31
(E) 30
Rationale: Explanation:
LCM of 2, 6, 8, 12 and 15 is 120
120 second = 2 minutes
Six bells rings in 2 min intervals
Therefore, Number of times they ring together in 60 min = 1 + (60/2) = 31
Answer: Option D
Answer: (D) 31
Question: Submarine M and Submarine N are equipped with sonar devices that can operate within a 5,000 yard range. Submarine M remains in place while Submarine N moves 4,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West
(A) I only
(B) II only
(C) I and III only
(D) III only
(E) II,III only
Rationale: It's evident if we make a diagram for the Movement of N respect to M.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : C
Answer: (C) I and III only
Question: In a group of 100 cars, 37 cars do not have air conditioning. If at least 41 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?
(A) 45
(B) 47
(C) 59
(D) 51
(E) 53
Rationale: Lets assume AC=63(includesonly AC carsandcars with AC and racing stripes)
lets assume RS(racing stripes)>=41(includescars with AC and racing stripesandonly racing stripes).
Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=41.. we have to assign atleast 4 tocars with AC and racing stripes.
Hence AC=63-4=59.
The answer is
Answer: (C) 59
Question: The difference between simple and compound interest on Rs. 1700 for one year at 10% per annum reckoned half-yearly is?
(A) 8.25
(B) 4.25
(C) 9.25
(D) 3.25
(E) 2.25
Rationale: S.I. = (1700 * 10 * 1)/100 = Rs. 170
C.I. = [1700 * (1 + 5/100)2 - 1700]
= Rs. 174.25 Difference = (174.25 - 174)
= Rs.4.25.
Answer:B
Answer: (B) 4.25
Question: Lines y=√5·x+1 and y=2√5·x−1 intersect at what height above the x axis?
(A) 3
(B) √5
(C) 3√5
(D) 0
(E) 5√5
Rationale: Solve two equations for y
y=√5·x+1
y=2√5·x−1
Set the two equations equal to each other and solve for x
√5·x+1=2√5·x−1
2 = √5·x
2/(√5) = x
Plug x = 2/(√5) into any one of the original equations to find the y value (height above x axis) where the two lines intersect
y=√5·x+1
y=√5·(2/(√5))+1
y = 2 + 1
y= 3
Final answer:
A) 3
Answer: (A) 3
Question: A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders E when the order of the divisors is reversed.
(A) 8,5,3
(B) 4,2,1
(C) E=3,2,1
(D) E=6,4,2
(E) None of above
Rationale: My approach would be
Three Divisors: 3, 5, 8
Three Remain: 1, 4, 7
Start from the bottom of the last column i.e. from the third remainder:
Go up diagonally and multiply by the second divisor: 5*7 = 35
Go down and add the second remainder: 35 + 4 = 39
Go up diagonally and multiply by the first divisor: 39* 3 = 117
Go down and add the first remainder: 117 + 1 = 118
Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2
Ans is D i.e. 6,4,2
Answer: (D) E=6,4,2
Question: Of the 100 athletes at a soccer club, 40 play defense and 60 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
(A) 10 to 20
(B) 10 to 40
(C) 20 to 40
(D) 30 to 70
(E) 40 to 70
Rationale: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 60 - {both} + {neither}
{both} = {neither} + 0
Since the least value of {neither} is given to be 20, then the least value of {both} is 20+0=20.Eliminate A and B.
Answer: C.
Answer: (C) 20 to 40
Question: What is the units digit of (12^3)(15^4)(31^7)?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: The units digit of 12^3 is the units digit of 2^3 which is 8.
The units digit of 15^4 is the units digit of 5^4 which is 5.
The units digit of 31^7 is the units digit of 1^7 which is 1.
The units digit of 8*5*1 is 0.
The answer is A.
Answer: (A) 0
Question: If the sum of n terms of two series in A.P. are in the ratio (5n + 4) : (9n + 6) then find the ratio of their 13th terms.
(A) 129/139
(B) 129/1378
(C) 129/136
(D) 129/134
(E) 129/131
Rationale: Explanation:
Formula for sum of n terms in AP = SnSn = n2n2(2a + (n – 1)d ]
5n + 4 ⇒ 5(n – 1) + 9 ⇒ [2(92)+(n−1)5][2(92)+(n−1)5]
Common difference (d) = 5, First term (a) = 9292
Similarly
Second series given 9n + 6 ⇒⇒ 9(n – 1) + 15 ⇒ [2(152)+(n−1)9][2(152)+(n−1)9]
Common difference (d) = 9, First term (a) = 152152
So
13th term for first series is = a + 12d = 129/2
13th terms for second series is = a + 12d = 231/2
Ratio = 129/131
Answer:E
Answer: (E) 129/131
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 7720 votes were polled, then how many valid votes did B get?
(A) 1888
(B) 2999
(C) 2834
(D) 2509
(E) 2991
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 7720
32.5k = 32.5k/100k * 7720 = 2509
The number of valid votes polled in favour of B is 2834.
Answer: D
Answer: (D) 2509
Question: We bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $368. How many math books did we buy?
(A) 28
(B) 32
(C) 36
(D) 40
(E) 44
Rationale: M + H = 80
H = 80 - M
4M + 5H = 368
4M + 5*(80 - M) = 368
M = 32
The answer is B.
Answer: (B) 32
Question: A train 90 meters long completely crosses a 270-meter long bridge in 30 seconds. What is the speed of the train in km/h?
(A) 34.2 km/h
(B) 37.2 km/h
(C) 40.2 km/h
(D) 43.2 km/h
(E) 46.2 km/h
Rationale: speed = distance / time = (90 + 270)/30 = 360/30 (m/s) * 3600/1000 = 43.2 km/h
The answer is D.
Answer: (D) 43.2 km/h
Question: The county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?
(A) 15
(B) 30
(C) 90
(D) 150
(E) 360
Rationale: There are three possibilities for the novel. With the plays, we are taken a combination of 2 from a set of 5 right n = 5, r = 2, n – r = 3
# of combinations = 5!/2!3! = (5)(4)(3)(2)(1)/(2)(1)(3)(2)(1) = (5)(4)/2 = 10
If the plays are P, Q, R, S, and T, then the 10 sets of two are PQ, PR, PS, PT, QR, QS, QT, RS, RT, & ST.
Any of the three novels can be grouped with any of the 10 possible pairs of plays, for a total of 30 possible reading lists.
Answer: B.
Answer: (B) 30
Question: Triangle ATriangle B are similar triangles with areas 2023 units square and 1792 units square respectively. The ratio of there corresponding height would be
(A) 9:10
(B) 17:16
(C) 23:27
(D) 13:17
(E) 15:23
Rationale: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=2023/1792
(x^2/y^2)=(17*17*7)/(16*16*7)
(x^2/y^2)=17^2/16^2
x/y=17/16
Ans=B
You need to take a hint from given options to find factors of 2013 and 2527.
Answer: (B) 17:16
Question: 7 letters have to be put into their 7 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?
(A) 1/30
(B) 1/720
(C) 1/5040
(D) 1/240
(E) 3/5
Rationale: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
7 letters (a, b, c, d, and e) can be assigned to 7 envelopes (arranged) in 7! ways, out of which only one will be correct, thus the probability is 1/7! = 1/5040.
Answer: C.
Answer: (C) 1/5040
Question: If an article is sold at 18% profit instead of 11% profit, then the profit would be $63 more. What is the cost price?
(A) $600
(B) $900
(C) $1200
(D) $1500
(E) $1800
Rationale: 7% * cost price = $63
1% * cost price = $63 / 7 = $9
The cost price is $900.
The answer is B.
Answer: (B) $900
Question: 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
(A) 12
(B) 18
(C) 22
(D) 24
(E) none of these
Rationale: Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x 27 * x = 36 * 18
x =	(36 * 18)/27
x = 24.
Answer is D.
Answer: (D) 24
Question: What is the present age of Kim, given that the ratio between her age and her sisters age 7 years ago was 4:3, and her sister is presently 31 years old.
(A) 23
(B) 19
(C) 22
(D) 21
(E) 24
Rationale: Let the present ages of Kim's sister and Kim be 4x years and 3x years respectively
4x+7 = 35
4x = 28
x = 7
Kim's age = 3x = 21 years
Answer is D
Answer: (D) 21
Question: What is the smallest positive perfect square that is divisible by 4, 9, and 18?
(A) 36
(B) 81
(C) 144
(D) 625
(E) 900
Rationale: The number needs to be divisible by 2^2, 3^2, and 2*3^2.
The smallest such perfect square is 2^2*3^2 = 36
The answer is A.
Answer: (A) 36
Question: In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ?
(A) 48
(B) 37
(C) 26
(D) 98
(E) 27
Rationale: Explanation:
3X + 4y = 240
by substitute through options 48 is correct
Answer: A
Answer: (A) 48
Question: A man sold 20 articles for $40 and gained 20%. How many articles should he sell for $90 to incur a loss 20%?
(A) 45
(B) 36
(C) 40
(D) 50
(E) 67.5
Rationale: Production cost per article: $40*(100%-20%) / 20 = $1.6
Required production costs for a loss of 20%: $90*(100% + 20%) = $108
Number of articles to be sold for $108 to incur a 20% loss: $108 / $1.6 = 67.5
Thus, solution E is correct.
Answer: (E) 67.5
Question: A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?
(A) 15 lit
(B) 20 lit
(C) 22.5 lit
(D) 25 lit
(E) 30 lit
Rationale: Solution:
Let x be the capacity of the bucket.then, initial mixture has 80% milk.
then after 5 lt replaced with water---->(80/100)∗(x−5)=(60/100)∗x(80/100)∗(x−5)=(60/100)∗x
x=20 lt.
Ans:- B.
Answer: (B) 20 lit
Question: How many ounces of a 60% salt solution must be added to 40 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?
(A) 16.67
(B) 40
(C) 50
(D) 60.33
(E) 70
Rationale: let x=ounces of 60% salt solution to be added
.2*40+.6x=.4(40+x)
x=40
Amswer B
Answer: (B) 40
Question: A and B start a business jointly. A invests Rs. 16,000 for 8 months and B remains in the business for 4 months, Out of total profit, B claims - of the profit. How much money was contributed by B ?
(A) 12822
(B) 12800
(C) 12819
(D) 12129
(E) 12811
Rationale: Let the total profit be Rs. x. Then, B = 2x/7 and A = (x - 2x /7) = 5x / 7.
So, A : B = 5x/7 : 2x/7 = 5 : 2.
Let B s capital be Rs. y. Then, (16000 * 8) / ( y * 4) = 5/2 <=> (16000 * 8 * 2) / (5 * 4) = 12800..
Answer: B
Answer: (B) 12800
Question: Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 7 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?
(A) 8 mph
(B) 5.25 mph
(C) 3.5 mph
(D) 4 mph
(E) 0.5 mph
Rationale: (1 mph +7 mph)/2 = 4 mph
Correct option is: D
Answer: (D) 4 mph
Question: A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 10 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?
(A) 7% loss
(B) 13% loss
(C) 5% profit
(D) 13% profit
(E) 15% profit
Rationale: Total cost 60*($250/1.1)=54.54*250;
# of cameras sold is 60-5=55 total revenue is 55*250;
# of cameras returned is 6 total refund 6*(250/1.1)*0.5;
So, total income 55*250+ 6*(250/1.1)*0.5
The dealer's approximate profit is (55*250+ 6*(250/1.1)*0.5-54.54*250)/(54.54*250)*100=5%
Answer: C.
Answer: (C) 5% profit
Question: A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points T that an individual player might have scored?
(A) 7
(B) 13
(C) 16
(D) 21
(E) 23
Rationale: General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.
Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11=77.
Therefore, the maximum number of points T for 12th player is 100-77=23.
Answer: E.
Answer: (E) 23
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
(A) 7
(B) 4
(C) 5
(D) 3
(E) 2
Rationale: S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = 100 x 80	year	=	1	year = 4 months.
1600 x 15	3
Answer:B
Answer: (B) 4
Question: In an election between two candidates, one got 55% of the total valid votes. 20% of the votes were invalid. If the total number of votes was 7500, what was the number of valid votes that the other candidate got?
(A) 2800
(B) 2700
(C) 2100
(D) 2500
(E) 3000
Rationale: Total no of votes = 7500
20 % invalid
=>80% valid
tot valid votes = 7500*80/100
=>valid for 2nd candidate got
7500*80/100*45/100
=2700
ANSWER B
Answer: (B) 2700
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 72 kmph and 90 kmph. In how much time will the trains cross each other?
(A) 80/8
(B) 80/9
(C) 80/5
(D) 80/3
(E) 80/1
Rationale: Relative speed = (72 + 90)* 5/18 = 9* 5 = 45 mps.
The time required = d/s = (100 + 100 + 200)/45
= 400/45 = 80/9 sec.
Answer: B
Answer: (B) 80/9
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
(A) 3/4
(B) 3/5
(C) 4/7
(D) 4/9
(E) 5/7
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: (B) 3/5
Question: If the mean of numbers 28, x, 42, 78 and 104 is 90, then what is the mean of 128, 255, 511, 1023 and x?
(A) 395
(B) 275
(C) 355
(D) 415
(E) 423
Rationale: The mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+104=90*5 --> x=198;
So, the mean of 128, 255, 511, 1023 and x is (128+255+511+1023+198)/5=423.
Answer: E.
Answer: (E) 423
Question: 42573y is exactly divisible by 72, then what is the minimum value of y?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: 72 = 9 x8, where 9 and 8 are co-prime.
The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
Required value of y is 6
C
Answer: (C) 6
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 R for the exam?
(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 R= 74.
Answer: A.
Answer: (A) 74
Question: 5 years ago, Paula was 3 times as old as Karl. In 6 years, Paula will be twice as old as Karl. What is the sum of their ages now?
(A) 42
(B) 46
(C) 50
(D) 54
(E) 58
Rationale: P-5 = 3(K-5) and so P = 3K-10
P+6 = 2(K+6)
(3K-10)+6 = 2K+12
K = 16
P = 38
P+K = 54
The answer is D.
Answer: (D) 54
Question: A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars. What is the probability that the team will contain at least 2 East All Stars?
(A) 29/33
(B) 81/169
(C) 57/120
(D) 47/144
(E) 119/720
Rationale: Teams can be formed as 2E-3W , 3E-2W , 4E-W and 5E
Possible ways to make a team 2E-3W = 6c2 * 6c3 = 300
Possible ways to make a team 3E-2W = 6c3 * 6c2 = 300
Possible ways to make a team 4E-W = 6c4 * 6c1 = 90
Possible ways to make a team 5E = 6c5 = 6
Number of ways to select a team of 5 out of 12 people = 12c5
=12!/(7!*5!)
= 792
Probability that the team will contain at least 2 East All Stars
= (300+300+90+6) / 792
=696/792
= 29/33
Answer A
Alternatively we can also calculate the number of possible ways to make a team of 5W and E-4W .
Possible ways to make a team 5W = 6c5 = 6
Possible ways to make a team E-4W = 6c1 * 6c4 = 90
Probability that the team will contain at least 2 East All Stars = 1 - (96/792)
= 29/33
Answer: (A) 29/33
Question: A rectangular park is 110 m long and 65 m wide.in this park there is 2.5m wide path all four side.on this path on the rate of 7.20 per sq. m what will be cost of spreading sand?
(A) 6120
(B) 7350
(C) 6250
(D) 8285
(E) 6565
Rationale: Area of park=110*65=7150sq.m
Area of park without path=[(110-2.5*2)×(65-2.5*2)]sq.m
(105*60) sq.m=6300 sq.m
Area of path=(7150-6300)=850 sq.m
Cost of spreading sand=[850×720/100]=6120
Answer A
Answer: (A) 6120
Question: 9 men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) 29.25
(B) 30
(C) 31.2
(D) 34
(E) 35
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25
A
Answer: (A) 29.25
Question: There are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?
(A) 4320
(B) 64800
(C) 8800
(D) 22000
(E) 6600
Rationale: From the six letters, we need four distinct letters
# of combinations = 6C4 = 15
From the four numerals, we need 2 distinct digits
4C2 = 6
Once we have our unique four letter and our unique 2 digits, we can put them in any order: each new order would be a different code. The number of orders would be
6! = 720
Total number of codes equals = 15*6*720
Without a calculator, first do 15*6 = 90. Then, 90 = 100 - 10, so
720*90 = 720*(100 - 10) = 72000 - 7200 = 64800
Answer = (B)
Answer: (B) 64800
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates Z apply to what fraction of a week?
(A)  1/2
(B)  5/8
(C)  9/14
(D)  16/21
(E)  9/10
Rationale: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates Z/Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Answer: (C)  9/14
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is a king?
(A) 1/52
(B) 1/26
(C) 2/13
(D) 1/4
(E) 1/13
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability that the spade we already have is a king is therefore 1/13.
Answer: E.
Answer: (E) 1/13
Question: Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 27 kg of zinc has been consumed in it?
(A) 58 kg
(B) 60 kg
(C) 64 kg
(D) 70 kg
(E) None
Rationale: Sol.
For 9 kg Zinc, mixture melted = (9+11) kg.
For 27 kg Zinc, mixture, melted = [20/9 x 27] kg
= 60 kg.
Answer B
Answer: (B) 60 kg
Question: A certain party consists of four different group of people 30 students, 35 politicians, 20 actors and 27 leaders. On a particular function day, the total cost spent on party members was Rs.9000. It was found that 6 students spent as much as 7 politicians, 15 politicians spent as much as 12 actors and 10 actors spent as much as 9 leaders. How much did students spent?
(A) 2191
(B) 2200
(C) 2291
(D) 2391
(E) 2491
Rationale: Let S be the amount spent for all students
Let P be the amount spent for all politicians
Let A be the amount spent for all actors and
Let L be the amount spent for all leaders.
given that 6 students spent as much as 7 politicians
i.e Amount spent per student x 6 = Amount spent per politician x 7
Or (Total amount spent on students / Total Students) x 6 = (Total amount spent on politicians / Total politicians)x 7
Or., (S/30)x 6 = (P/35)x7
=> S/5 = P/5
=> S = P ..... eqn 1
15 politicians spent as much as 12 actors :
Therefore, (P/35)x15 = (A/20)x12
=> 3P/7 = 3A/5
=> 5P = 7P
=> 5S = 7A (since S = P)
=> A = 5S/7 ........eqn2
and 10 actors spent as much as 9 leaders :
Therefore, (A/20)x10 = (L/27)x9
=> 3A = 2L
=> A = 2L/3
=> 5S/7 = 2L/3 (since A=5S/7)
=> L = 15S/14 ......eqn3
the total amount spent for the party is Rs.9000
i.e., S+P+A+L = 9000
from eqn1, eqn2, eqn3 we have
S + S + 5S/7 + 15S/14 = 9000
53S/14 = 9000
s=9000*14 / 53
s=2290.90 ~ 2291
Hence the answer is Rs.2291
ANSWER:C
Answer: (C) 2291