RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 7 buckles is how many times that of 5 buckles and 6 buttons?
A.1/2
B.2/3
C.3/4
D.4/5
Answer: D.4/5
Explanation: Let x be the weight of a button and let y be the weight of a buckle.
2x + 2y = (1/3)(3x+11y)
3x = 5y
x = 5y/3
3x + 7y = a(6x+5y)
12y = a(15y)
a = 12/15 = 4/5
The answer is D.
Question: The speed of a railway engine is 42 kmph when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached.
If the speed of the train carried by this engine is 24 kmph when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is
A.47
B.48
C.49
D.50
Answer: B.48
Explanation: Explanation :
Let S = speed, and N = number of compartments, then
=> S = 42 - k * √N.
Where k is a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k * B and solve for k.
If N = 9, then S = 24
=> 24 = 42 - k*√9 = 42 - 3k.
=> 3k = 18.
=> k = 6.
Now, we need to know: what value of N makes S go to zero?
=> 0 = 42 - 6*√N
=> 6*√N = 42
=> √N= 7
=> n = 7(2) = 49.
With 49 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars.
Thus, 48 is the maximum number of cars the engine can pull and still move.
Answer : B
Question: A:B = 6:4, B:C = 1:4. Now if C is 38, what is A?
A.14.25
B.15.25
C.16.25
D.17.25
Answer: A.14.25
Explanation: b/c=1/4 && c=38
so b=c/4 => b=19/2
a=6b/4 => so a=57/4 => 14.25
ANSWER:A
Question: If x is an integer such that 0 < x < 7, 0 < x < 15, 5 > x > –1, 3 > x > 0, and x + 2 < 4, then x is
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: 0 < x < 7,
0 < x < 15,
5 > x > –1
3 > x > 0
x<2
From above: 0 < x < 2 --> x = 1.
Answer: A.
Question: The angles of a triangle are in the ratio 1:3:8. Find the measurement of the three angles of triangle.
A.90°
B.110°
C.120°
D.150°
Answer: C.120°
Explanation: If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
x = 15
The measures of the three angles are
x = 15°
3x = 3 × 15 = 45°
8x = 8 × 15 = 120°
C
Question: A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 40 meters apart,then at what speed is the train traveling?
A.100km/hr
B.120km/hr
C.50km/hr
D.150km/hr
Answer: B.120km/hr
Explanation: Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*40 = 2000m = 2.0km
Speed = 60*2.0=120km/hr
Answer is B
Question: In an elaction between two candidates, 20% of votes are were declares invalid. First candidate got 480 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
A.1000 votes
B.2000 votes
C.3000 votes
D.4000 votes
Answer: C.3000 votes
Explanation: (100%-20%=80%
48%-32%=16%
16% = 16×30 = 480
100% =100×30 =3000 votes)
C
Question: If n is a positive integer and n^2 is divisible by 62, then the largest positive integer that must divide n is
A.6
B.12
C.24
D.36
Answer: B.12
Explanation: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.
I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.
I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true
However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true
So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?
Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=12, is n divisible by 48? No. So, n is not always divisible by 48.
B
Question: Uncle Bruce is baking chocolate chip cookies. He has 72 ounces of dough (with no chocolate) and 50 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 40% chocolate?
A.4
B.6
C.8
D.2
Answer: D.2
Explanation: First, you must find the total weight of the mixture given that 80% of it will be dough.
60%*Total = 72 => (6/10)Total=72=> Total=720/6 => Total=120 oz,
From there, you must find 10% of the total 40 oz of the mixture.
40%*Total => (4/10)(120)=48 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 50-48 oz = 2 oz chocolate left over.
Answer : D
Question: Walking with 4/5 of my usual speed, I arrive at the bus stop 8 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
A.20
B.24
C.28
D.32
Answer: D.32
Explanation: Let t = usual time = distance / usual speed
t + 8 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4
t = 32
The answer is D.
Question: A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
A.1.85
B.3.75
C.4.95
D.2.45
Answer: C.4.95
Explanation: Explanation:
Speed downstream =22/4=5.5 kmph
Speed upstream=22/5=4.4 kmph
Speed of the boat in still water =5.5+4.4/2=4.95 kmph
Answer:C
Question: What is the lowest possible common multiple K of 2 distinct integers, each greater than 329?
A.330·331
B.330^2
C.33·331
D.660
Answer: D.660
Explanation: Lowest possible common multiple K of 2 distinct integers will have to be multiple of the number greater than 329...which 330..
so one number will be 330...another one will be 660..
Ans is D.
Question: If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?
A.a/2
B.b/2
C.(a+b)/2
D.(a+2)/2
Answer: D.(a+2)/2
Explanation: Initially substitute a and b with 8 and 2 respectively.
a = 8
b = 2
8 - 2 = even number
8/2 = even number
so these numbers satisfy requirements
a) a/2: 8/2 = 4 EVEN
b) b/2: 4/2 = 2 EVEN
c) (a+b)/2: (8+4)/2 = 6 EVEN
d) (a+2)/2: (8+2)/2 = 5 ODD
substitute another set (a=4 & b=2) for check
(4+2)/2 = 3 Again, ODD
e) (b+2)/2: (4+2)/2 = 3 ODD
substitute another set (a=4 & b=2) for check
(2+2)/2 = 2 EVEN
ANSWER: D
Question: In how many different number of ways 5 boys and 2 girls can sit on a bench?
A.5040
B.730
C.740
D.750
Answer: A.5040
Explanation: npn = n!
7p7 = 7 x 6 × 5 × 4 × 3 × 2 × 1 = 5040
A
Question: Three distinct single digit no A,B and c are in G.M ,if abs(x) for real x is the absolute value of x(x , if x is positive or zero,and -x if x is negative), then the number of different possible values of abs (A+B -C) is;
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: 1,2,4
2,4,8
4,2,1
8,4,2
1,3,9
9,3,1
total=6
ANSWER:D
Question: In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least one of each type of coin must be included?
A.49
B.69
C.73
D.91
Answer: C.73
Explanation: I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any dimes. We can't have all four coins represented if we have four quarters.
II. Case II = Three Quarters (75 cents)
This allows for two or one dime. Three dimes would bring us up to $1.05, and we wouldn't have room for any pennies or nickels.
Subcase 1 = 3 Q, 2 D (95 cents)
1) one nickel (N) and 5 pennies (P) (2 nickels would not allow for any pennies)
Subcase 2 = 3 Q, 1 D (85 cents)
2) 3 N and 5 P
3) 2 N and 10 P
4) 1 N and 15 P
Case II allows for a total of four ways.
III. Case III = Two Quarters (50 cents)
This allows for 1-4 dimes.
Subcase 1 = 2 Q, 4 D (90 cents)
(2 ways) we could have 1-2 nickels
Subcase 2 = 2 Q, 3 D (80 cents)
(4 ways) we could have 1-4 nickels
Subcase 3 = 2 Q, 2 D (70 cents)
(6 ways) we could have 1-6 nickels
Subcase 4 = 2 Q, 1 D (60 cents)
(8 ways) we could have 1-8 nickels
Case III allows for a total of 20 ways
IV. Case IV = One Quarter (25 cents)
This allows for 1-7 dimes
Subcase 1 = 1 Q, 7 D (95 cents)
(1 way) we could have 1 nickel
Subcase 2 = 1 Q, 6 D (85 cents)
(3 ways) we could have 1-3 nickels
Subcase 3 = 1 Q, 5 D (75 cents)
(5 ways) we could have 1-5 nickels
Subcase 4 = 1 Q, 4 D (65 cents)
(7 ways) we could have 1-7 nickels
Subcase 5 = 1 Q, 3 (55 cents)
(9 ways) we could have 1-9 nickels
Subcase 6 = 1 Q, 2 D (45 cents)
(11 ways) we could have 1-11 nickels
Subcase 7 = 1 Q, 1 D (35 cents)
(13 ways) we could have 1-13 nickels
Case IV allows for a total of 49 ways.
There's no other case, because we have to have at least one quarter and one dime. The total over the cases equals
Total = 4 + 20 + 49 =73 ways.
OA =(C)
Question: A cistern is filled by a tap in 5 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?
A.60
B.62
C.64
D.66
Answer: D.66
Explanation: filling rate - leak rate = net rate
1/5.5 - leak rate = 1/6
leak rate = 2/11 - 1/6 = 1/66
The answer is D.
Question: In baseball, the batting average is defined as the ratio of a player’s hits to at bats. If a player had anywhere from 5 to 7 at bats in a recent game and had anywhere from 2 to 3 hits in the same game, the player’s actual batting average for that game could fall anywhere between
A.0.25 and 1.00
B.0.25 and 0.75
C.0.25 and 0.75
D.0.33 and 0.50
Answer: C.0.25 and 0.75
Explanation: Average Range = Hits to Bats i.e 2/7 to 3/5 = 0.28 to 0.60
Answer: C
Question: An insect leaps 72 centimeters in 1.2 seconds. What is its speed?
A.6 centimeters per second
B.0.6 centimeters per second
C.0.6 meters per second
D.8.64 centimeters per second
Answer: C.0.6 meters per second
Explanation: 72 / 1.2 = 60 cm/s = 0.6 m/s
The answer is C.
Question: In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?
A.1 : 3
B.1 : 2
C.2 : 3
D.2 : 1
Answer: B.1 : 2
Explanation: TWO things to remember:-
1) the ratio of quantity mixed to get an average is related to the ratio of each qty's distance from average.
2) More the Qty of x from that of y, More CLOSER will be average to x..
Qty of 20%/Qty of 50%= (50−40)/(40−20)=1/2=1:2
ANSWER:B
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
A.6 km/hr
B.3 km/hr
C.1 km/hr
D.9 km/hr
Answer: B.3 km/hr
Explanation: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.
Answer: B
Question: What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 40 cm?
A.170
B.187
C.540
D.748
Answer: A.170
Explanation: The marbles used to tile the floor are square marbles.
Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble.
As we have to use whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 40. And it should be the highest factor of 5 m 78 cm and 3m 40.
5 m 78 cm = 578 cm and 3 m 40 cm = 340 cm.
The HCF of 578 and 340 = 34.
Hence, the side of the square is 34.
The number of such square marbles required,
=578×340/34×34
=170 marbles
Option(A)
Question: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $7.00 a pound. How many pounds of cashews must she use?
A.40
B.45
C.50
D.55
Answer: D.55
Explanation: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y
From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:
$2.5 * (x + 100 - x) = $1.5x + $4(100 - x)
If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.
You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)
Answer is D.
Question: How many prime numbers are between 13/3 and 83/6?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: 13/3 = 4.xxx
83/6 = 13.xxx
So we need to find Prime numbers between 4 (Exclusive) - 12 (Inclusive)
There are 2 Prime numbers 7 11
Hence answer will be (B) 2
B
Question: Find the odd man out. 1, 3, 9, 12, 19, 29
A.12
B.9
C.1
D.3
Answer: A.12
Explanation: Explanation :
12 is an even number. All other given numbers are odd.. Answer : Option A
Question: In a certain school, the ratio of boys to girls is 5 to 13. If there are 64 more girls than boys, how many boys are there?
A.27
B.40
C.45
D.72
Answer: B.40
Explanation: The ratio of b to G is 5:13 and the other data point is G are more than boys by 64...
Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 64. so 1 part corresponds to 64/8=8 and so
5 parts correspond to 5*8 = 40.
B
Question: If Sharon's weekly salary increased by 20 percent, she would earn $600 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week?
A.Rs.575
B.Rs.600
C.Rs.625
D.Rs.485
Answer: A.Rs.575
Explanation: Soln:-
(600/120)115=575
In this case long division does not take much time.
(5/1)115=Rs.575
ANSWER:A
Question: Convert the 13/36 m/s into kilometers per hour?
A.1.9kmph
B.2.9kmph
C.1.3 kmph
D.1.8kmph
Answer: C.1.3 kmph
Explanation: 13/36 m/s = 13/36 * 18/5
= 13/10 = 1.3 kmph.
Answer:C
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 305 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
A.600
B.610
C.500
D.520
Answer: B.610
Explanation: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 305) = 2 + 2(extra)
=> 2x - 610 = x => x = 610.
ANSWER:B
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.4. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
A.0.12
B.0.24
C.0.28
D.0.48
Answer: D.0.48
Explanation: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.6*0.2+0.4*0.3+0.6*0.4
= 0.12+0.12+0.24
=0.48
D
Question: What is the normal price of an article sold at $36 after two successive discounts of 10% and 20%?
A.$45
B.$48
C.$50
D.$54
Answer: C.$50
Explanation: 0.8*0.9*cost price = $36
cost price = $50
The answer is C.
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.12 sec
B.24 sec
C.48 sec
D.60 sec
Answer: C.48 sec
Explanation: Explanation:
Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
ANSWER IS C
Question: A cube 125 mt is colored pink on two opposite surfaces and then cut in to 125 smaller cubes then find how many number of cubes have pink color?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: Answer:B
Question: Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold six as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold six times as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
A.Andy
B.Bob
C.Cary
D.Dora
Answer: C.Cary
Explanation: a= 6e
b =3 +e
c = 6b = 18+ 6e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C
Question: Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 16 hours after they passed each other the ratio of the speeds of the two trains was
A.2:1
B.3:2
C.4:3
D.5:4
Answer: A.2:1
Explanation: Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 2 : 1. Answer: A
Question: The price of sugar is increased by 5%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
A.(700/107) %
B.(107/100) %
C.(500/105)%
D.(5/100)%
Answer: C.(500/105)%
Explanation: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $105.
We want the spendings to remain at $100.
(New consumption)*105 = 100 --> (New consumption) = 100/105 kg.
Percent decrease = Change/Original *100 = (1 - 100/105)/1*100 = 500/105%.
Answer: C.
Question: At a certain conference, 76% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
A. 18.0%
B. 62.0%
C. 79.2%
D. 84.4%
Answer: D. 84.4%
Explanation: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.
76% regestered at least 2 weeks and paid full fee.
10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.
90% *X=76% where X is the number of people who registerd 2 weeks in advance and paid full fee.(answer D)
Question: 7 + 7+ 7 + 7 × 7^2 + 7 × 7^3 + 7 × 7^4 + 7 × 7^5 + 7 × 7^6 + 7 × 7^7 =
A.7^3
B.7^8
C.7^2
D.7^7
Answer: B.7^8
Explanation: We have the sum of 9 terms. Now, if all terms were equal to the largest term 7*7^7 we would have: sum=9*(7*7^7)=63*7^7=~7^9, so the actual sum is less than 7^9 and more than 7^7 (option D) as the last term is already more than that. So the answer is clearly B.
Answer: B
Question: Mario and Nina each have a bag of marbles, each of which contains 6 blue marbles, 10 red marbles, and 4 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?
A.2/4
B.3/4
C.1/4
D.1/8
Answer: A.2/4
Explanation: Mario and Nina each select one marble from their respective bags.
Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble
Probability that either Mario or Nina select a red marble = (10/20)*(10/20) + (10/20)*(10/20) = 2*(1/4)
Probability that either Mario or Nina select a red marble = 1/2
Answer would be A.
Question: A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 10,500 sedans in Anytown, how many motorcycles are there?
A.1260
B.3000
C.3600
D.4200
Answer: B.3000
Explanation: Let the total number of trucks = 3x
total number of sedans = 7x
total number of motorcycles = 2x
total number of sedans = 10500
=> 7x = 10500
=> x = 1500
total number of motorcycles =2x = 2*1500
=3000
Answer B
Question: There are 23 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?
A.10
B.9
C.4
D.5
Answer: B.9
Explanation: 12 kids wear socks
8 kids wear shoes
6 wear both.
12 â€“ 6 = 6 (wear only socks)
8 â€“ 6 = 2 (wear only shoes)
6 (wear both)
hence, 23 -14 = 9
9 kids are with bare feet.
B
Question: Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
A.1040
B.1050
C.1055
D.1065
Answer: C.1055
Explanation: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055
C
Question: After his first semester in college, Thomas is applying for a scholarship that has a minimum Grade Point Average (GPA) requirement of 3.5. The point values of pertinent college grades are given in the table below. If Thomas took 4 courses, each with an equal weight for GPA calculations, and received two grades of A-, one grade of B+, and one grade of B, what is the lowest grade that Thomas could receive for his fifth class to qualify for the scholarship?
Point Values of Select Grades
Grade: A | A- | B+ | B | B- | C+ | C | C-
Value: 4 | 3.7 | 3.3 | 3 | 2.7 | 2.3 | 2 | 1.7
A. A
B. B+
C. B
D. B-
Answer: C. B
Explanation: Grade: A | A- | B+ | B | B- | C+ | C | C-
Value: 4 |3.7|3.3|3| 2.7 | 2.3 | 2 | 1.7
7.4 + 3.3 + 3 + x = 3.5 * 5
x = 17.5 - 13.7 = 3.8
Grade A is required to qualify
Answer = B
C
Question: If x and y are positive integers and 180x=y^3, which of the following must be an integer?
I. x/(2^2*3*5)
II. x/(2*3^2*5)
III. x/(2*3*5^2)
A.None
B.I only
C.II only
D.III only
Answer: D.III only
Explanation: x and y are integers and 180x=y^3 --> 180x equals to cube of an integer (y^3).
180x=2^2∗3^2∗5∗x=y^3 ,The smallest value of x for which 2^2∗3∗5∗x is a cube of an integer is when x=2∗3∗5^2.to complete powers of 2, 3 and 5 to cubes).
In this case 180x=(2^2∗3^2∗5)∗(2∗3∗5^2)=(2∗3∗5)^3=cube of an integer So x is definitely divisible by 2∗3∗5^2
Answer: D.
Question: A man can row 6.6 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
A.2.2 km/hr
B.12.5 km/hr
C.1 2.6 km/hr
D.22.5 km/hr
Answer: A.2.2 km/hr
Explanation: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=6.6
3x = 13.2
x = 4.4
i.e., speed upstream = 4.4 km/hr
Rate of stream = 1/2(2x−x)=x/2=4.4/2=2.2 km/hr
Answer is A
Question: 11 friends are living in 11 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 11 parking spots. In how many ways can they park their cars so that exactly 9 people park their cars in the spots allotted to them?
A.40
B.45
C.50
D.55
Answer: D.55
Explanation: 11C9 = 55
The remaining 2 people in each case will be parked in each other's parking spots.
The answer is D.
Question: A cube of edge 8 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
A.1:25
B.1:22
C.1:52
D.1:64
Answer: D.1:64
Explanation: Sol.
Required ratio = 6 * 1 * 1 / 6 * 8 * 8 = 1/64 = 1:64.
Answer D