mathewhe/aqua_rat huggingface dataset:
Question: A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
(A) 95
(B) 92
(C) 88
(D) 82
(E) 85
Rationale: Explanation:
Solution 1
Area of the field =680 sq. feet.
Length of the adjacent sides are
20 feet and 680/20=34 feet.
Required length of the fencing
=20+34+34= 88 feet
Answer: Option C
Answer: (C) 88
Question: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 500 funds on the list have 3-star ratings, how many funds are on the list?
(A) 500
(B) 750
(C) 1,000
(D) 1,250
(E) 1,500
Rationale: D
Fraction of 5- and 4-star funds: 1/3 + (2/5)*(2/3) = 5/15 + 4/15 = 9/15
Fraction of 3-star funds = 1 - 9/15 = 6/15
(6/15)*Total = 500
Total = 1250
Answer: (D) 1,250
Question: The length of a rectangle is twice its breadth. If its length is decreased by 10 cm and breadth is increased by 10 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
(A) 25 cm
(B) 35 cm
(C) 30 cm
(D) 45 cm
(E) 55 cm
Rationale: Let breadth =x cm
Then, length =2x cm
Area =x×2x=2x^2 sq.cm.
New length =(2x−10) cm
New breadth =(x+10) cm
New area =(2x−10)(x+10) sq.cm.
Given that, new area = initial area +75 sq.cm.
⇒(2x−10)(x+10)=2x^2+75
⇒2x^2+20x−10x−100=2x^2+75
⇒10x−100=75
⇒10x=75+100=175
⇒x=175/10=17.5 cm
Length =2x=2×17.5=35 cm
ANSWER:B
Answer: (B) 35 cm
Question: Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has twuenty iron coins and thuenty copper coins, how many different sums from 1¢ to 140¢ can he make with a combination of his coins?
(A) 137
(B) 140
(C) 166
(D) 136
(E) 2
Rationale: The total sum is 20*2 + 20*5 = 140¢. If you can make each sum from 1 to 140 (1¢, 2¢, 3¢, ..., 140¢), then the answer would be 140 (maximum possible).
Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 139¢ and 137¢ (since total sum is 140¢ we cannot remove 1¢ or 3¢ to get 139¢ or 137¢).
So, out of 140 sums 4 are for sure not possible, so the answer must be 140 - 4 = 136 sums or less. Only A fits.
Answer: D.
Answer: (D) 136
Question: A man sitting in a train which is traveling at 55 kmph observes that a goods train, traveling in opposite direction, takes 10 seconds to pass him. If the goods train is 320 m long, find its speed
(A) 52 kmph
(B) 56 kmph
(C) 60 kmph
(D) 62 kmph
(E) 72 kmph
Rationale: Explanation:
Relative speed = 320/10 m / sec = ((320/10)×(18/5)) kmph = 115 kmph.
Speed of goods train = (115 - 55) kmph = 60 kmph
Answer: Option C
Answer: (C) 60 kmph
Question: Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 12 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
(A) 54
(B) 66
(C) 80
(D) 36
(E) 96
Rationale: D
36
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 12 MPH = 36 miles
Answer: (D) 36
Question: Find the largest number of four digits which is exactly divisible by 27,18,12,16
(A) 9906
(B) 9916
(C) 9936
(D) 9736
(E) 9746
Rationale: Explanation:
LCM of 27-18-12-16 is 432.
After dividing 9999 by 432 we get 63 remainder.
So answer will be 9999-63 = 9936
Option C
Answer: (C) 9936
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 8 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 13
(B) 24
(C) 18
(D) 19
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/8
=> 1/x = 1/6 - 1/8 = (4 - 3)/24 = 1/24
=> x = 24.
Answer: B
Answer: (B) 24
Question: A train 700 m long passes a man, running at 20 km/hr in the same direction in which the train is going, in 40 sec. The speed of the train is?
(A) 40 km/hr
(B) 41 km/hr
(C) 42 km/hr
(D) 43 km/hr
(E) 44 km/hr
Rationale: Speed of the train relative to man = 700/40 = 35/2 m/sec.
= 35/2 * 18/5 = 63 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 20) km/hr.
x - 20 = 63 => x = 43 km/hr.
Answer: D
Answer: (D) 43 km/hr
Question: The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 20 on the fourth day, his average earning for the whole week is ?
(A) Rs . 18.95
(B) Rs 16
(C) Rs. 20
(D) Rs. 25.71
(E) None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -20
= Rs. 140
∴ Average earning = 140 / 7
= Rs. 20
Correct Option: C
Answer: (C) Rs. 20
Question: If 15% of 40 is greater than 25% of a number by 2,then find the number is?
(A) 20
(B) 15
(C) 16
(D) 25
(E) 30
Rationale: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16
ANSWER C
Answer: (C) 16
Question: Sandy is younger than Molly by 20 years. If the ratio of their ages is 7:9, how old is Sandy?
(A) 42
(B) 49
(C) 56
(D) 63
(E) 70
Rationale: Let Sandy's age be 7x and let Molly's age be 9x.
9x - 7x = 20
x = 10
Sandy is 70 years old.
The answer is E.
Answer: (E) 70
Question: A certain company charges $5 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $5 plus $1 per pound. If the company charged $30 to ship a certain package, which of the following was the weight of the package, in pounds?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: Let the weight of the package be X. Then the cost is 1*X + 5= 30 ---> X=25 ---> X=25
Answer : B
Answer: (B) 25
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 247
(B) 249
(C) 245
(D) 882
(E) 279
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer: C
Answer: (C) 245
Question: For a,q,d are the positive integers, and d|a means that “a is divisible by d”, if d|aq, which of the following must be true?
(A) d|a
(B) d|q
(C) d|2aq
(D) d|(a+q)
(E) d|(a-q)
Rationale: d/a means a is divisible by d
d/aq means ab divisible by d.
all are integers so ,
if ab is divisible by d,
1 a can be divisible by d
or
2 q can be divisble by d.
so the question stem asks must true.
so option a and b are could but not must.
option c is 2aq divisible by d. if ab is divisible by d then 2aq is divisible by d.
option d and e we can't predict.
so option C is correct.
Answer: (C) d|2aq
Question: A bus takes 4 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 4/3th of the previous time?
(A) 50 Kmph
(B) 90 Kmph
(C) 95.9 Kmph
(D) 95.4 Kmph
(E) 90.5 Kmph
Rationale: Time = 4
Distance = 480
4/3 of 4 hours = 4 * 4/3 = 5.3 Hours
Required speed = 480/5.3 = 90.5 Kmph
E
Answer: (E) 90.5 Kmph
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 8 months, find for how much time did Q invest the money?
(A) 11
(B) 10
(C) 18
(D) 16
(E) 12
Rationale: 7*5: 8*x = 7:10
x = 16
Answer:D
Answer: (D) 16
Question: When positive integer f is divided by 6, the remainder is 1. Which of the following must be true?
I. f is a prime number
II. f is odd
III. f is divisible by 7
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: f=6q+1
Examine II) put q=0,1,2,3....... we have f=1,7,13,...25 so f must be odd
Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true
Examine I) f= 7 true but while 2 is prime, it does not give reminder 1
Answer: B
Answer: (B) II only
Question: A train 124 m long running at 68 kmph crosses a platform in 19 sec. What is the length of the platform?
(A) 338
(B) 234
(C) 240
(D) 881
(E) 271
Rationale: D = 68 * 5/18 = 19 = 358 – 124 = 234
Answer: B
Answer: (B) 234
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 65 kg. What might be the weight of the new person?
(A) 60 kg
(B) 75 kg
(C) 80 kg
(D) 85 kg
(E) 90 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg
Option D
Answer: (D) 85 kg
Question: My boss has $243,986 in the business account. What is the least amount of money (in whole number of dollars) that he must add to his account if she wants to split this money evenly among his nine employees?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount he should add to his saving account to split the money evenly among his employees,
he needs to make the total divisible by 9
Simply add the individual digits of the total = 2+4+3+9+8+6 =
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: (D) $4
Question: If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q?
(A) 6
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: 4500+10q+d+8737=13003+100q+10d
13237+10 q+d=13003+100q+10d
234=90q+9d
26=10 q+d
d=6 ^ q=2
==> d-q= 4
ANSWER B
Answer: (B) 4
Question: Two bags are randomly selected from a flight at the airport to be searched, one at a time, then sent through after being searched (this means: without return). Five smugglers are watching this and they each have three bags with contraband. There are 20 bags on the flight. What is the probability that they will get away? (Answer in lowest terms).
(A) 5/75
(B) 3/12
(C) 5/76
(D) 2/19
(E) 1/2
Rationale: The flight has 20 bags total. There are (5 smugglers)(3 bags) = 15 bags with contraband, and 20 - 15 = 5 with no contraband, so the probability of getting a bag with no contraband is P(N) = 5/20 on the first selected bag.
Because selection is (without return), the P(N) has changed for following selections. Now, there are 19 bags, but the number bags with contraband stay the same; since, we are only calculating for success as no bag with contraband... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:
Formula = P(A\B) = P(A and B)/P(B).
2 bags are selected; so,
P(A\B) = (5/20)(5/19) = 25/380 = 5/76
Answer: C
Answer: (C) 5/76
Question: A, B, C, D and E are 5 consecutive points on a straight line. If BC = 2CD, DE = 4, AB = 5 and AC = 11, what is the length of AE?
(A) 21
(B) 26
(C) 30
(D) 18
(E) 16
Rationale: A-----B----C--------D----E
Given: DE = 4 - (i)
AB = 5 - (ii)
AC = 11 - (iii)
BC = 2CD - (iv)
From (ii) and (iii), BC = 6
From (iv), CD = 3
Length of AE = AC + CD + DE = 11 + 3 + 4 = 18
Correct Option: D
Answer: (D) 18
Question: The top and bottom of a tower were seen
to be at angles of depression 30° and 60° from the top of a
hill of height 100 m. Find the height of the tower
(A) 64.67 m
(B) 66.67 m
(C) 68.67 m
(D) 56.67 m
(E) 46.67 m
Rationale: By making A diagram
AC represents the hill and DE represents the pole
Given that AC = 100 m
angleXAD = angleADB = 30° (∵ AX || BD )
angleXAE = angleAEC = 60° (∵ AX || CE)
Let DE = h
Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE
tan 60°=ACCE=>3√=100CE=>CE = 1003√--- (1)
tan 30°=ABBD=>13√=100−hBD=>13√=100−h(1003√)
(∵ BD = CE and Substituted the value of CE from equation 1 )=>(100−h)=13√×1003√=1003=33.33=>h=100−33.33=66.67 m
i.e., the height of the pole = 66.67 m
ANSWER:B
Answer: (B) 66.67 m
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) Rs.6725
(B) Rs.6727
(C) Rs.6908
(D) Rs.6725
(E) Rs.6728
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs.6725.
Answer: D
Answer: (D) Rs.6725
Question: A customer pays 80 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
(A) 100
(B) 40
(C) 70
(D) 90
(E) 20
Rationale: Let x be the original price.
x - 20 = 80
x - 20 + 20 = 80 + 20
x + 0 = 100
x = 100
Answer is A
Answer: (A) 100
Question: An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.90 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?
(A) 130,000
(B) 300,000
(C) 380,000
(D) 400,000
(E) 420,000
Rationale: Total royalties for first 100.000 books = .8*100,000= 80,000
Total royalties for the rest of the books = 260,000-80,000 = 180,000
Remaining books = 180,000/0.9 = 200,000
Total books = 200,000+100,000 = 300,000 Answer B
Answer: (B) 300,000
Question: Look at this series: 2, 4, 6, 8, 10, ... What number should come next?
(A) 10
(B) 11
(C) 16
(D) 13
(E) 12
Rationale: E
12
This is a simple addition series. Each number increases by 2.
Answer: (E) 12
Question: Nitin ranks 27th in a class of 89 students. What is rank from the last ?
(A) 63
(B) 65
(C) 67
(D) 87
(E) 89
Rationale: Explanation:
Number students behind the nitin in rank = (89 - 27) = 62
Nitin is 63th from the last
Answer: A) 63
Answer: (A) 63
Question: If a woman buys 700 pencils for $70 and sold them for $3 dollars for a 10 pack, determine her profit per pack.
(A) 2
(B) 3
(C) 20
(D) 30
(E) 70
Rationale: Cost of 700 pencils = $70
700 pencils/$70 = 10 pencils for $1
Sold 10 pencils for $3
Profit per 10 pencils = $(3-1) = $2 per pack
Therefore, her profit is $2 per 10 pack
answer :A
Answer: (A) 2
Question: The average of the daily income of A, B and C is Rs . 60 . If B earns Rs . 20 more than C and A earns double of what C earns. What is the daily income of C ?
(A) Rs. 70
(B) Rs. 60
(C) Rs. 40
(D) None of these
(E) Cannot be determined
Rationale: Answer
Let C's earning = Rs. y.
Then, B's earning = Rs. (y + 20)
and A's earning = Rs. 2y
∵ 2y + y + 20 + y= 3 x 60
⇒ 4x = 160
∴ x = 40
Correct Option: C
Answer: (C) Rs. 40
Question: Insert the missing number
2, 9, 28, 65, ...
(A) 126
(B) 195
(C) 121
(D) 103
(E) 112
Rationale: the series are 2,9,28,65,126
logic is 1cube+1,2cube+1, 3cube+1,4cube+1, 5cube+1
so the answer is 126
ANSWER:A
Answer: (A) 126
Question: 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability C that one more throw to this series will increase the mean score?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability C is 1/2.C
Answer: (C) 1/2
Question: Find the total number of prime factors in the expression (4)^13 x (7)^5 x (11)^2
(A) 26
(B) 22
(C) 25
(D) 27
(E) 33
Rationale: (4)^13x (7)^5 x (11)^2
= (2 x 2)^13 x (7)^5 x (11)^2
= 2^13 x 2^13 x7^5x 11^2
= 2^26 x 7^5 x11^2
Total number of prime factors = (26 + 5 + 2) = 33.
Answer is E.
Answer: (E) 33
Question: P is three times as fast as Q and working together, they can complete a work in 6 days. In how many days can Q alone complete the work?
(A) 16
(B) 77
(C) 88
(D) 55
(E) 8
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 6 days, which means Q can do the work in 24 days.
Hence, P can do the work in 8 days.
Answer:E
Answer: (E) 8
Question: If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 25 overs in an ideal case scenario?
(A) 900
(B) 850
(C) 828
(D) 825
(E) None
Rationale: Solution:
828
Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 24th over. In the 25th over, he can hit a six in the last ball as well as that will be the last ball of his destination.
Thus runs for the 25th over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 24 + 36 = 828
Answer C
Answer: (C) 828
Question: Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is:
(A) 1000
(B) 2000
(C) 2300
(D) 3400
(E) 2830
Rationale: Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each horse = Rs. 2000.
Answer: Option B
Answer: (B) 2000
Question: 0.02 x 0.000197 is equal to:
(A) 6.48 x 10(power -6)
(B) 6.84 x 10(power -6)
(C) 3.94 x 10(power -6)
(D) 5.48 x 10(power -6)
(E) None of them
Rationale: 2 x 197 = 394. Sum of decimal places = 8
So, 0.02 x 0.000197 = 0.00000394 = 3.94 x 10(power -6)
Answer is C
Answer: (C) 3.94 x 10(power -6)
Question: There are seven leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
(A) 7 leopard and 3 sheep
(B) 4 leopard and 7 sheep
(C) 6 leopard and 1 sheep
(D) 5 leopard and 1 sheep
(E) 2 leopard and 5 sheep
Rationale: C
6 leopard and 1 sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: (C) 6 leopard and 1 sheep
Question: A fruit seller sells mangoes at the rate of Rs.12 per kg and thereby loses 10%. At what price per kg, he should have sold them to make a profit of 15%?
(A) Rs.11.81
(B) Rs.12
(C) Rs.15.33
(D) Rs.12.31
(E) None
Rationale: Solution
90 : 12 = 115 : x
x= (12Ã—115/90)
= Rs.15.33
Hence, S.p per Kg	= Rs.15.33
Answer C
Answer: (C) Rs.15.33
Question: What least number should be added to 1056, so that the sum is completely divisible by 23?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Explanation :
1056 ÷ 23 = 45 with remainder = 21
Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be
divisible by 23. Answer : Option C
Answer: (C) 2
Question: Find the circumference and area of radius 8 cm.
(A) 124 cm²
(B) 201 cm²
(C) 210 cm²
(D) 184 cm²
(E) 194 cm²
Rationale: Area of circle = πr²
= 22/7 × 8 × 8 cm²
= 201 cm²
ANSWER:B
Answer: (B) 201 cm²
Question: the first half of the 20th century, the population of a particular country increased by 200 percent. In the second half of the century, the population increased by 300 percent. What was the percent increase for the 20th century as a whole?
(A)  500%
(B)  600%
(C)  800%
(D)  1100%
(E)  1200%
Rationale: Say initially population was 100.
What is 200% of 100? It is 200/100 * 100 = 200.
An increase of 200% means the new population became 100 + 200 = 300
What is 300% of 300? It is 300/100 * 300 = 900
An increase of 300% means the new population now is 300 + 900 = 1200
So from 100, the population increased to 1200 i.e. an increase of 1100.
1100 is what percent of 100?
1100 = x/100 * 100
i.e. it is 1100% D
Answer: (D)  1100%
Question: Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspapers sales was from Newspaper A and if q percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of q?
(A) 100p / (125 - p)
(B) 150p / (250 - p)
(C) 300p / (375 - p)
(D) 400q / (500 - q)
(E) 500q / (625 - q)
Rationale: I have just started with qunats section .. I solved this by making two equations and got the answer ... However it was long way of doing it ...
I got the answer as : 100q /(125 - .25 q)...
Multiply this equation by 4 and you get D as the answer ,...
Answer: (D) 400q / (500 - q)
Question: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Z/Y?
(A) -4.5.
(B) -2.
(C) -0.5.
(D) 3.
(E) 2.5.
Rationale: X+Y = 2X-2Z
X-Y = 2Z---------- 1
X-2Y = 4Z--------- 2
Subtracting equation 1 from equation 2
2Z = -Y
Z/Y= -0.5
C is the answer
Answer: (C) -0.5.
Question: If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week?
(A) $374
(B) $382
(C) $385
(D) $392
(E) $399
Rationale: Soln:-
(406/116)110 =385
In this case long division does not take much time.
(406/116)=3.5
35*11=385(350+35)
ANSWER:C
Answer: (C) $385
Question: A Women can cover a distance in 1 hr 24 min by covering 2/3 of the distance at 4 km/h and the rest at 5 km/h. The total distance is
(A) 4 km
(B) 8 km
(C) 2 km
(D) 6 km
(E) 9 km
Rationale: D
6 km
Distance = 2/3S
distance=1-2/3S=1/3S
21/15 hr=2/3 S/4 + 1/3s /5
84=14/3S * 3
S= 6km
Answer: (D) 6 km
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 8
(B) 4
(C) 9
(D) 6
(E) 1
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: (B) 4
Question: Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years. What is definitely the difference between R and Q's age?
(A) 50
(B) 99
(C) 88
(D) 77
(E) 23
Rationale: R - Q = R - T
Q = T.
Also R + T = 50; R + Q = 50
So, (R - Q) cannot be determined.
Answer:D
Answer: (D) 77
Question: If there is exactly one root of the equation x^2 + ax - b, where a and b are positive constants, what is b in terms of a?
(A) a/2
(B) a
(C) -a^2/4
(D) a^2/2
(E) a^2/4
Rationale: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = a
c= b
a = 1
substituting these values in 1, we have
a^2 = -4b => b =-a^2/4
Answer is C.
Answer: (C) -a^2/4
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.5 years. The ration of the number of boys to the number of girls in the class is?
(A) 2:6
(B) 2:3
(C) 2:5
(D) 2:1
(E) 1:2
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.5 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.5)
= k = 0.3/0.6 =1/2
Required ratio = 1/2 : 1 = 1:2.
Answer:E
Answer: (E) 1:2
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 56 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320.8$
(B) 387.8$
(C) 420.8$
(D) 457.8$
(E) 480.8$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 56 ) =457.8
Hence answer will be (D)
Answer: (D) 457.8$
Question: If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 1 = ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) 32
Rationale: 4 Ø 2 = 2^4/2^2 = 4
4 Ø 1 = 2^4/2 = 8
The answer is C.
Answer: (C) 8
Question: 378 × ? = 252
(A) 2/3
(B) 3/4
(C) 1/2
(D) 2/8
(E) None of these
Rationale: Explanation :
378 × ? = 252
?=252/378=126/189=14/21=2/3
Answer is A
Answer: (A) 2/3
Question: If 1st October is Sunday, then 1st November will be
(A) Saturday
(B) Thursday
(C) Wednesday
(D) Tuesday
(E) Monday
Rationale: Explanation:
Given that 1st October is Sunday
Number of days in October = 31
31 days = 3 odd days
(As we can reduce multiples of 7 from odd days which will not change anything)
Hence 1st November = (Sunday + 3 odd days) = Wednesday
Answer: Option C
Answer: (C) Wednesday
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 7 years ago ? (RBI Assistant 2015)
(A) 24
(B) 18
(C) 14
(D) 15
(E) 13
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 7 years ago = 21 - 7 = 14 years
answer :C
Answer: (C) 14