mathewhe/aqua_rat huggingface dataset:
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 9 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
(A)  11/20
(B)  2/5
(C)  1/2
(D)  3/5
(E)  3/4
Rationale: x * 6/100 * 1 + (20000 - x) * 9/100 * 1 = 1440
6x - 8x = 144000 - 180000
=> -2x = -18000
=> x = 9000
So 11000/20000 = 11/20
Answer - A
Answer: (A)  11/20
Question: The average height of 35 boys in a class was calculated as 185cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
(A) 178.27 cm
(B) 183.29 cm
(C) 978.29 cm
(D) 178.89 cm
(E) 176.29 cm
Rationale: Calculated average height of 35 boys = 185 cm.
Wrong total height of 35 boys = 185 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 185 cm - (166 cm - 106 cm)/35
=185 cm - 60 /35 cm
= 185 cm - 1.71 cm = 183.29 cm.
Answer: B
Answer: (B) 183.29 cm
Question: How many numbers from 12 to 82 are exactly divisible by 6?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 12
Rationale: Option 'D'
12/6 = 2 and 82/6 = 13 ==> 13 - 2 = 11 Numbers
Answer: (D) 11
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700
(E) Rs. 760
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: (C) Rs. 698
Question: 2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 3/4 of the red fish and 2/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?
(A) 1/2
(B) 1/4
(C) 2/5
(D) 3/10
(E) 7/20
Rationale: 3/4*2/5 + 2/5*1/4 = 2/5
The answer is C.
Answer: (C) 2/5
Question: Jennifer had $30 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket
to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
(A) $4
(B) $14
(C) $5
(D) $15
(E) $0
Rationale: 1/5 x $30 = $6 for sandwich
1/6 x $30 = $5 for museum
1/2 x $30 = $15 for book
$6 + $5 + $15 = $26 spent
$30 - $26 = $4 left over
correct answer A
Answer: (A) $4
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $146 million, which represented 8 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
(A) 7,010
(B) 2,100
(C) 1,825
(D) 1,701
(E) 210
Rationale: 8% ---- 146 millions
for 100% => ( 146 * 100% )/8% = 1825.
Option C.
Answer: (C) 1,825
Question: Train R leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?
(A) 8:15 am
(B) 8:45 am
(C) 9:00 am
(D) 9:30 am
(E) Cannot be determined from the information given
Rationale: train R will cover 60 kms in 45 min at 7:45, the time when train B starts...
distance left to cover is 210-60=150..
combined speed=80+70=150..
so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45
B
Answer: (B) 8:45 am
Question: A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Six employees have done just two courses and only one made ​​the three courses. How many employees have no training?
(A) A)7
(B) B)9
(C) C)10
(D) D)11
(E) E)26
Rationale: Total employees=50
studied accounting=22
studied finance=15
studied marketing=14
6 employees have been double counted and one employee has been counted thrice.
Therefore employees who have received training=22+15+14-6-(2*1)
=51-8
=43
Employees with no training
=50-43
=7
Ans=A
Answer: (A) A)7
Question: A car takes 6 hours to cover a distance of 270 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 60
(B) 50
(C) 40
(D) 70
(E) 30
Rationale: Time = 6
Distance = 270
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 270/9 = 30 Kmph
Answer E.
Answer: (E) 30
Question: Calculate Renee's average score in an exam if she obtained the following marks 71, 57, 61, 80 and 88 out of 100 in different subjects.
(A) 71.9
(B) 73.4
(C) 72.4
(D) 71.4
(E) 70.4
Rationale: Explanation:
(71+57+61+80+88)/5=71.4
Answer: Option D
Answer: (D) 71.4
Question: how many different digit number are there which have digit 1,2,3,4,5,6,7,8, such that digit 1 appears exactly once ?
(A) 4C1 * 7^2
(B) 4C1 * 7^3
(C) 4C1 * 7^4
(D) 4C1 * 7^5
(E) 4C1 * 7^6
Rationale: Digit 1 can appear in any of the 4 positions of a 4 digit number => 4C1
Further,as repetition is allowed,the othe three digits can have any of the remaining 7 numbers
So total no of different 4 digit numbers possible = 4C1 * 7 * 7 *7 = 4C1 * 7^3
ANSWER:B
Answer: (B) 4C1 * 7^3
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.99 sq m
(B) 3.34 sq m
(C) 2.98 sq m
(D) 2.98 sq m
(E) 8.29 sq m
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2
= (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer:B
Answer: (B) 3.34 sq m
Question: Williams works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 10 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
(A) 5/8
(B) 7/8
(C) 6/8
(D) 2/9
(E) 1/7
Rationale: First notice the number of months for which he worked - March to Sept i.e. 7 months
Avg of monthly totals in tips for months other than August = x
Tips in August = 10x
Total tips for all months = 6*x + 10x = 16x
Tips for August/Total tips for all months = 10x/16x = 5/8
Answer : A
Answer: (A) 5/8
Question: The product of three consecutive odd numbers is 9177. What is the sum of the
numbers?
(A) 51
(B) 57
(C) 60
(D) 63
(E) 69
Rationale: Since 20 20 20 = 8000 and 30 30 30 = 27 000, then we might guess that the three
consecutive odd numbers whose product is 9177 are closer to 20 than they are to 30.
Using trial and error, we determine that 21 23 25 = 12 075, which is too large.
The next smallest set of three consecutive odd numbers is 19; 21; 23 and the product of these
three numbers is 19 21 23 = 9177, as required.
Thus, the sum of the three consecutive odd numbers whose product is 9177 is 19+21+23 = 63.
correct answer D
Answer: (D) 63
Question: In how many ways a team of 11 must be selected from 5 men and 11 women such that the team must comprise of not more than 3 men?
(A) 3337
(B) 2456
(C) 7887
(D) 2777
(E) 2911
Rationale: The team may consist of 0 men + 11 women, 1 men + 10 women, 2 men + 9 women, or 3 men + 8 women.
So Number of ways are = 11C11+5C1×11C10+5C2×11C9+5C3×11C8
= 2456
Answer:B
Answer: (B) 2456
Question: We can create number 100 by using all numbers, i.e.0123456789 and mathematical operators (+/-) in many ways.
Example
98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
But if we add a condition that the use of the number 21 is the must. Then there are only a few solutions.
One of such solution is:
98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
Can you tell any other solution?
(A) 7 - 8 + 76 - 5 + 4 + 3 + 21 = 100
(B) 8 - 8 + 76 - 5 + 4 + 3 + 21 = 100
(C) 9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
(D) None of these
(E) Cannot be determined
Rationale: Solution:
9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
Other ways of making number 100 (withiout using number 32)
98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
98 - 7 + 6 + 5 + 4 - 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100
98 - 7 + 6 + 5 - 4 + 3 - 2 + 1 = 100
98 - 7 + 6 - 5 + 4 + 3 + 2 - 1 = 100
98 + 7 - 6 - 5 + 4 + 3 - 2 + 1 = 100
98 - 7 - 6 + 5 + 4 + 3 + 2 + 1 = 100
9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100
9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100
Answer C
Answer: (C) 9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
Question: The average age of a committee of 8 members is 40 years. A member aged 59 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
(A) 39 years
(B) 38 years
(C) 37.5 years
(D) 35 years
(E) 34 years
Rationale: Exp. Total age of the committee = 40*8 = 320,
Total age when a member is retired
and a new one was joined = 320-59 +39, =300
Average age of present committee = 300/8 = 37.5.
Answer: C
Answer: (C) 37.5 years
Question: In how many ways a committee consisting of 3 men and 2 women can be formed from 5 men and 3 women?
(A) A)30
(B) B)15
(C) C)20
(D) D)18
(E) E)21
Rationale: Required number of ways = 5C3*3C2 = 10*3 = 30
Answer is A
Answer: (A) A)30
Question: One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?
(A) 15 km
(B) 14 km
(C) 16 km
(D) 20 km
(E) 21 km
Rationale: Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9
4 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
C
Answer: (C) 16 km
Question: Each factor of 150 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 15?
(A) 1/16
(B) 5/42
(C) 1/8
(D) 3/16
(E) 1/3
Rationale: the # of factors 150 has is 12
so out of 12 factors only four are multiples of 15: 15, 30,75 and 150, itself;
So, the probability is 4/12=1/3.
Answer: C.
Answer: (C) 1/8
Question: The side of a square is increased by 10% then how much % does its area increases?
(A) 21
(B) 56.25
(C) 50.75
(D) 42.75
(E) 52.75
Rationale: a = 100 a2 = 10000
a = 110 a2 = 12100
----------------
10000 --------- 2100
100 -------? => 21 %
ANSWER: A
Answer: (A) 21
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 80. Find the average marks of all the students?
(A) 52.5
(B) 52.9
(C) 52.1
(D) 52.3
(E) 65
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 80 = 4000
Sum of the marks for the class of 80 students =
1200 + 4000 = 5200
Average marks of all the students = 5200/80
= 65
Answer:E
Answer: (E) 65
Question: Anne traveled from City A to City B in 4 hours, and her speed was between 35 miles per hour and 50 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 50 miles per hour and 90 miles per hour. Which of the following could be the distance, in miles, from City A to City B?
(A) 95
(B) 115
(C) 125
(D) 135
(E) 170
Rationale: In four hours Anne must travel 4 times her speed
so Anne's possible distances =
4(35 -50) or 140-200 miles
in two hours John travels 2 times his speed or
2(50-90) or 100-180 miles
the statement is only true if both distances are possible,
so you can tell its between or equal to
140-180
E is the answer.
Answer: (E) 170
Question: Two trains 130 meters and 160 meters long are running in the same direction with speeds of 85 km/hr, 67km/hr. In how much time will the first train cross the second
(A) 62 sec
(B) 55 sec
(C) 58 sec
(D) 60 sec
(E) 65 sec
Rationale: Explanation:
Relative speed of the trains = (85 - 67) km/hr = 18 km/hr
= (18Ã— 5/18) m/sec = 5 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (150 + 160) m at 5 m /sec = (310/5) sec = 62 sec.
Answer: Option A
Answer: (A) 62 sec
Question: 0.0006?=0.03
(A) 2
(B) 20
(C) 0.2
(D) 0.02
(E) None of these
Rationale: Explanation :
Required Answer = 0.0006/0.03 = 0.06/3 = 0.02. Answer : Option D
Answer: (D) 0.02
Question: A beaker contains 180 lts of wine. Each day 60lts of wine is replaced with same amount of water what is the amount of wine after 3 days?
(A) 160/3
(B) 170/3
(C) 180/3
(D) 190/3
(E) 200/3
Rationale: wine left= total wine*(1-capacity of wine withdrawn/total wine)^n
wine left=180*(1-60/180)^3
=160/3
ANSWER:A
Answer: (A) 160/3
Question: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
(A) $21
(B) $27
(C) $31
(D) $41
(E) It cannot be determined
Rationale: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:
3B+7S+C=120
4B+10S+C=164.5
Subtracting the first equation from the second gives us B+3S=44.5
Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=31. In any case, there is no necessity to know each item's price, just the sum.
Answer: C
Answer: (C) $31
Question: The sum of two numbers is 528 and their H.C.F. is 33. The number of pairs of numbers satisfying the above conditions is :
(A) 4
(B) 6
(C) 8
(D) 12
(E) 15
Rationale: Explanation:
Let the required numbers be 33a and 33b.
Then, 33a + 33b = 528.
=> a + b= 16.
Now, co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9).
âˆ´
Required numbers are
(33 * 1, 33 * 15), (33 * 3, 33 * 13), (33 * 5, 33 * 11),(33 x 7, 33 x 9).
The number of such pairs is 4.
ANSWER IS A
Answer: (A) 4
Question: The area of the GiftBox is 40 m2 that of a longer side 10 m2 and of the shorter side 4 m2, find the edge of the new cube?
(A) 40 m3
(B) 10 m2
(C) 60 m3
(D) 80 m3
(E) 50 m3
Rationale: lb = 40 ; lh = 10 ; fh = 4
(lbh)2 = 40 * 10 * 4 => lbh = 40 m3
ANSWER:A
Answer: (A) 40 m3
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/4 + 4^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/8
Rationale: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/7
Answer D
Answer: (D) 1/7
Question: what is the sum of the first 15 odd natural numbers
(A) 300
(B) 400
(C) 500
(D) 600
(E) 225
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 15 odd natural numbers=(15)^2=225
ans 225
ANSWER:E
Answer: (E) 225
Question: The simple interest at x% for x years will be $x on a sum of
(A) $ (1000)/x
(B) $(100)x^2
(C) $ x
(D) $ (100)/x
(E) $ 100x
Rationale: Principal =$(100*x)/(x*x)=$(100/x).
Answer is D
Answer: (D) $ (100)/x
Question: How many times the keys of a writter haveto be pressedin order to write first 400 counting no.'s?
(A) 998
(B) 1000
(C) 1092
(D) 1100
(E) 1200
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
C
Answer: (C) 1092
Question: Celeste worked for h hours each day for d consecutive days. If she earns $9.50 per hour, what is the total amount she earned?
(A) 9.50/d + h
(B) 9.50 + d + h
(C) 9.50 + dh
(D) 9.50h + d
(E) 9.50dh
Rationale: H hours for d days.
Income each day = 9.5*h
Total income = 9.5*h*d
Correct option: E
Answer: (E) 9.50dh
Question: A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is
(A) 20%
(B) 27%
(C) 31%
(D) 43%
(E) None
Rationale: Solution
Let C.P	=Rs.100
Then, marked price	=Rs.135,
S.P	=Rs.108.
Discount %	=(27/135×100)%
= 20%
Answer A
Answer: (A) 20%
Question: Ketchup, Mustard and Mayo bottles at a hot dog stand are in the ratio of 3: 3: 2. If there are 6 Ketchup bottles, the number of Mayo bottles at the hot dog stand is:
(A) 12
(B) 6
(C) 3
(D) 1
(E) 4
Rationale: Explanation :
Let Ketchup = 3x, Mustard = 3x & Mayo = 2x. Now, 3x = 6 hence x = 2.
Number of Mayo Bottles = 2x which is 4.
Answer : E
Answer: (E) 4
Question: The ratio of the volumes of two cubes is 2197 : 1331. What is the ratio of their total surface areas?
(A) 169 : 121
(B) 169 : 127
(C) 169 : 191
(D) 121 : 169
(E) 121 : 182
Rationale: Explanation:
Ratio of the sides = ³√2197 : ³√1331 = 13 : 11
Ratio of surface areas = 13^2 : 11^2 = 169 : 121
Answer: Option A
Answer: (A) 169 : 121
Question: In how many different ways can the letters of the word â€˜EXTENTâ€™ be arranged?
(A) 250
(B) 180
(C) 300
(D) 310
(E) 360
Rationale: Number of ways = 6!/2!2! = 6X5X4X3X2X1/2X1X2X1 = 180
B
Answer: (B) 180
Question: In April's entire movie collection she has only 4 movies she likes, even though she has 13 movies. If she picks 2 movies randomly and simultaneously from her collection, what is the probability that exactly 1 of the movies will be one that she likes?
(A) 4/13
(B) 21/36
(C) 1/12
(D) 6/13
(E) 9/26
Rationale: The probability is equal to the number of desired choices divided by the total number of possibilities.
Probability = Favorable/Total
Total = 13C2 = 13*12/2 = 78
Favorable:
Pick 1 out of 4 movies she likes
AND
Pick 1 out of 9 movies she doesn't like
4C1*9C1 = 4*9 = 36
P = 36/78 = 6/13
When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.
Thus,
Total Probability:
Probability of choosing a movie she likes first AND Probability of choosing a movie she doesn't like
OR
Probability of choosing a movie she doesn't like first AND Probability of choosing a movie she likes
Answer: (D) 6/13
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder S when N is divided by 30?
(A) (a) 4
(B) (b) 7
(C) (c) 11
(D) (d) 13
(E) (e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder S when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: (C) (c) 11
Question: Joseph has a bag with 2 red balls and 3 blue balls. If he pulls out two at random and simultaneously, what is the probability of him pulling one red and one blue ball?
(A) 3/5
(B) 2/3
(C) 8/15
(D) 4/12
(E) 7/18
Rationale: The probability is equal to the number of desired choices divided by the total number of possibilities.
Probability = Favorable/Total
Total = 5C2 = 5*4/2 = 10
Favorable:
Pick 1 red ball out of 2 red balls
AND
Pick 1 blue ball out of 3 blue balls
2C1*3C1 = 2*3=6
P=6/10=3/5
When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.
Thus,
Total Probability:
Probability of choosing a red ball first AND Probability of choosing a blue ball
OR
Probability of choosing a blue ball first AND Probability of choosing a red ball
Answer: A
Answer: (A) 3/5
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years. The present age of the husband is
(A) 35 years
(B) 40 years
(C) 45 years
(D) 50 years
(E) NOne
Rationale: Sol.
Sum of the present ages ofH husband, wife and child
= (27 × 3 + 3 × 3)years = 90 years.
Sum of present ages of wife and child = (20 × 2 + 5 × 2) = 50 years.
∴ Husband's present age = (90 - 50)years = 40 years.
Answer B
Answer: (B) 40 years
Question: A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 12 days, how long will a woman take to complete the work?
(A) 12days
(B) 10days
(C) 9days
(D) 8days
(E) 11days
Rationale: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3
1 man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/1
(1 Man + 1 boy) ‘s 1 day’s work = 1/6 + 1/12 = 1/4
Therefore, 1 woman’s 1 day’s work = 1/3 – 1/4 = 1/12
Therefore, the woman alone can finish the work in 12days.
Answer: Option A
Answer: (A) 12days
Question: Set A: 3, r, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – r?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: So we have even no. of elements in the Set
So median is the average of Middle two numbers
(r+8)/2= (y+9)/2
y - r= -1
Answer B
Answer: (B) -1
Question: A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?
(A) 5 cms
(B) 2 cms
(C) 3 cms
(D) 4 cms
(E) 6 cms
Rationale: since the sphere is made out of the cylinder material their volume will be same
volume of cylinder = pi * 3^2 * 6
volume of one sphere = 4/3 * pi * r ^3 (where r is radius of sphere)
so if there are N such sphere's
equating the volumes,
pi*r^2*h = N*(4/3)*pi*R^3
N is the number of spheres,
substituting the, r and h
9*6 = N*(4/3)*(D/2)^3
D is the diameter of a sphere,
N = (9*6*3*8)/(4*D^3)
N = 324/D^3
now substitute the given answers for D and find the values for N, since a N has to be an integer only value fit for D is 3,
ANSWER:C
Answer: (C) 3 cms
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 80%
(C) 20%
(D) 27%
(E) 50%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Answer: (A) 20%
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 7-sided polygon)?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/7
Rationale: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.
So the remaining n-3 vertices make diagonals.
There are 2 of these diagonals which are the shortest.
The probability of choosing one of the shortest diagonals is 2/4 = 1/2.
The answer is A.
Answer: (A) 1/2
Question: In a triangle, one side is 6 Cm and another side is 6 Cm. which of the following can be the perimeter of the triangle?
(A) 18.
(B) 25.
(C) 20.
(D) 32.
(E) 34.
Rationale: Given : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 20. Hence C.
Answer: (C) 20.
Question: A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 105, how much must C pay as his share of rent?
(A) 27
(B) 50
(C) 55
(D) 65
(E) none
Rationale: Sol.
A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.
âˆ´ Câ€™s rent = Rs. [105 * 9/35] = Rs. 27.
Answer A
Answer: (A) 27
Question: Find the value of X, Y by solving the below equations
2X - Y = 16
X - Y = -5
(A) 15, 18
(B) 15, 13
(C) 13, 28
(D) 21, 26
(E) 25, 24
Rationale: 2X - Y = 16 ----(I)
X - Y = -5 -----(II) by Subtract (II) From (I)
------------
X = 21
By Replacing the value of X in (I) we get 2*21 - Y = 16 ==>
-Y = 16 - 42 = -26 ===> Y = 26.
So, X = 21, Y = 26
Answer D) 21, 26
Answer: (D) 21, 26