mathewhe/aqua_rat huggingface dataset:
Question: The diameter of the wheel of a car is 120m. How many revolution/min mustthe wheel makeing order to keep a speed of 60 km/hour approximately?
(A) 140
(B) 160
(C) 220
(D) 250
(E) 265
Rationale: Distance to be covered in 1 min. = (60 X 1000)/(60) m = 1000 m.
Circumference of the wheel = (2 x (22/7) x 0.60) m = 3.77 m.
Number of revolutions per min. =(1000/3.77) = 265
E
Answer: (E) 265
Question: In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
(A) 11760
(B) 266
(C) 5040
(D) 3000
(E) 2000
Rationale: Req no of ways = 8C5 * 10C6
=11760
ANSWER A
Answer: (A) 11760
Question: P is three times as fast as Q and working together, they can complete a work in 14 days. In how many days can Q alone complete the work?
(A) 18 1/2 days
(B) 17 1/2 days
(C) 19 1/2 days
(D) 14 1/4 days
(E) 10 1/2 days
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 14 days, which means Q can do the work in 48 days.
Hence, P can do the work in 18 1/2 days.
Answer:A
Answer: (A) 18 1/2 days
Question: If an investor puts $800 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?
(A) $878
(B) $880
(C) $882
(D) $884
(E) $886
Rationale: 1.05*1.05*800=$882
The answer is C.
Answer: (C) $882
Question: There are 3 bags, in 1st there are 9 Mangoes, in 2nd 8 apples & in 3rd 6 bananas. There are how many ways you can buy one fruit if all the mangoes are identical, all the apples are identical, & also all the Bananas are identical?
(A) 648
(B) 432
(C) 23
(D) 2 to the power(23)-1
(E) 25
Rationale: Since bags are different so it should be 9+8+6=23
ANSWER:C
Answer: (C) 23
Question: How many three digits number can be formed by using the digits 1,2,3,4,5?
(A) 152
(B) 125
(C) 225
(D) 325
(E) 252
Rationale: Here the repetition of digits allowed. The unit place of the number can be filled in by any of the given numbers in 5 ways. Simillarly each one of the ten's and the hundred's place can be filled in 5 ways. Therefor the total number of required numbers =5*5*5 =125 Answer : B
Answer: (B) 125
Question: One out of every 250 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 5,000
(C) 10,000
(D) 50,000
(E) 25,000
Rationale: 20 broken glasses indicates that 10*10= 100 defected bulbs are present.
100 defected bulbs indicates that 100*250= 25,000 light bulbs are present.
E is the answer
Answer: (E) 25,000
Question: Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-5# = 6, what is the value of #5#?
(A) 5
(B) 0
(C) -8
(D) -3
(E) -5
Rationale: #p# = ap^3 + bp - 1
#-5# = 6
putting p = -5 in above equation
-125a -(5b +1) = 6 or
#-5# = (125a+5b+1) = -6
therefore 125a+5b = -7 .....(1
now putting p = 5
#5# = 125 a+5b - 1
using equation 1(125a+5b = -7)
#5# = -7-1 = -8
hence C
Answer: (C) -8
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
(A) 81.6
(B) 81.7
(C) 81.0
(D) 281.6
(E) 81.2
Rationale: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6.Answer: A
Answer: (A) 81.6
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) 3.34 sq m
(B) 3.38 sq m
(C) 3.24 sq m
(D) 3.36 sq m
(E) 5.34 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:A
Answer: (A) 3.34 sq m
Question: If the gross salary for first year is Rs. 45000 and an employee has two options to choose from for increment .Either he can opt for 4% yearly increase or Rs. 25000/- yearly increase on the gross salary. If an employee choose the first option, after how many years his salary will be more than the option two ?
(A) 15 years
(B) 16 years
(C) 17 years
(D) 18 years
(E) 19 years
Rationale: if initial annual gross salary = Rs. 450000/-
check when
450000+25000*n = 450*(1+4/100)^n
After 18 years
ANSWER:D
Answer: (D) 18 years
Question: A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
(A) 33
(B) 37
(C) 41
(D) 45
(E) 49
Rationale: 5/7*P are ponies with horseshoes, so P is a multiple of 7.
2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21.
The minimum value of P is 21. Then H = P+3 = 24.
The minimum number of horses and ponies is 45.
The answer is D.
Answer: (D) 45
Question: An empty wooden vessel weighs 14% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
(A) 3/5
(B) 5/9
(C) 1/24
(D) 4/9
(E) 7/13
Rationale: An empty wooden vessel weighs 14% of its total weight when filled with paint:
Vessel = 0.1(Vessel + Paint);
14V = V + P (so the weight of completely filled vessel is 10V)
P = 13V (so the weight of the paint when the vessels is completely filled is 9V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*14V;
P' = 7V (so the weight of the paint when the vessels is partially filled is 7V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 7V/13V = 7/13.
Answer: E.
Answer: (E) 7/13
Question: In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?
(A) 16 2/3 %
(B) 25 %
(C) 33 1/3 %
(D) 50%
(E) 75%
Rationale: 1986; 2/3
1988; 1/2
% decrease = change/original*100
2/3−1/2 / 2/3∗100
1/6∗3/2∗100=14∗100=25
Answer: "B"
Answer: (B) 25 %
Question: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values Q are within three standard deviations of the mean?
(A) 0
(B) 1
(C) 3
(D) 6
(E) 7
Rationale: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.
With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.B
Answer: (B) 1
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:
(A) 70 km/hr
(B) 75 km/hr
(C) 80 km/hr
(D) 87.5 km/hr.
(E) 97.5 km/hr.
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
Let the speed of two trains be 7x and 8x km/hr.
x = 100/8 = 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Answer : D.
Answer: (D) 87.5 km/hr.
Question: Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 60% problems right. How many more questions he would have to answer more to get
passed
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 75 = 45.
He would have to answer 45 - 40 = 5
Answer: Option A
Answer: (A) 5
Question: A wheel that has 6 cogs is meshed with a larger wheel of 9 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 49
(B) 4
(C) 12
(D) 14
(E) 27
Rationale: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
9 : 6 :: 21 : x 9 * x = 6 x 21
x =	(6 x 21)/9
x = 14.
Answer is D.
Answer: (D) 14
Question: A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?
(A) 60
(B) 80
(C) 90
(D) 115
(E) 170
Rationale: b+c=250_______(1)
1.5b+0.75c=315
2b+c=420_______(2)
(2)-(1)
b=170
c=80
b-c=170-80=90
ANSWER:C
Answer: (C) 90
Question: The probability that a visitor at the mall buys a pack of candy is 10%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
(A) 0.009
(B) 0.015
(C) 0.027
(D) 0.036
(E) 0.054
Rationale: One case is: candy - candy - no candy
The probability is 1/10*1/10*9/10 = 9/1000
There are 3 such cases, so we should multiply this probability by 3.
P(exactly 2 buy candy) = 9/1000 * 3 = 27/1000 = 0.027
The answer is C.
Answer: (C) 0.027
Question: Two years ago, Ram put $1,000 into a savings account. At the end of the first year, his account had accrued $100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 20%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of $1,000 ?
(A) 40%
(B) 25%
(C) 35%
(D) 30%
(E) 32%
Rationale: investment 1000 dollars
1 st year total gained = 100
total amount end of first year = 1100
second year account increased by 20 % = 1100*0.2 = 220
therefore total amount by second year end = 1320
so total percentage increase in money = (1320-1000)*100/1000 = 32 %
Correct Answer E=32%
Answer: (E) 32%
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
(A) 1222
(B) 1289
(C) 1210
(D) 1129
(E) 1123
Rationale: π (232 – 122)
= 1210
Answer:C
Answer: (C) 1210
Question: A number increased by 40% gives 1680. The number is?
(A) 1680
(B) 1600
(C) 1200
(D) 1500
(E) 600
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 40 % = 140 %
140 % -------> 1680 (140 Ã— 12= 1680)
100 % -------> 1200 (100 Ã— 12 = 1200)
Option 'C'
Answer: (C) 1200
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 40% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 714 1/7 grams
(B) 714 2/7 grams
(C) 714 8/3 grams
(D) 714 1/3 grams
(E) 732 1/3 grams
Rationale: If the cost price is Rs.100, then to get a profit of 40%, the selling price should be Rs.140.
If 140kg are to be sold, and the dealer gives only 100kg, to get a profit of 40%.
How many grams he has to give instead of one kilogram(1000 gm).
140 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/140 = 714 2/7 grams.
Answer:B
Answer: (B) 714 2/7 grams
Question: Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 1500
(B) 3100
(C) 4400
(D) 6200
(E) 7400
Rationale: Each term in set B is 60 more than the corresponding term in set A.
The difference of the sums = 25 * 60 = 1500.
The answer is A.
Answer: (A) 1500
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 3 books, how many shelves does the bookcase have?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let x be the number of shelves.
12x - 21 = 8(x-1) + 3
4x = 16
x= 4
The answer is A.
Answer: (A) 4
Question: Lanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
(A) 1/24
(B) 1/8
(C) 1/4
(D) 1/3
(E) 3/8
Rationale: Total Lanya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.?
Answer: (D) 1/3
Question: If x is a randomly chosen integer between 1 and 20, inclusive, and y is a randomly chosen integer between 21 and 40, inclusive, what is the probability that xy is a multiple of 4?
(A)  1/4
(B)  1/3
(C)  3/8
(D)  7/16
(E)  ½
Rationale: There are two ways that I see of getting a multiple of 4
1) x and/or y is a multiple of 4
2) x is a multiple of 2 and y is a multiple of 2
for 1 we have
P(option 1) = (5/20)(20/20) + (5/20)(20/20) - (5/20)(5/20) = 1/2 - 1/16
since 5 of the numbers in each range are divisible by 4, and if either x or y is selected to be divisible by 4 the selection of the other variable does not matter. Notice the last subtraction term which corrects the fact that we have counted the possibility of both being divisible by 4 twice (e.g. P(A union B) = P(A) + P(B) - P(A and B)).
Notice at this point that the probability of option one is already 7/16, the second largest available option. If we can come up with any other possibilities for getting xy divisble by 4 we must go with option E.
Of course this is the case because if we select a multiple of 2 that is not a multiple of 4 from both ranges of numbers, the product is divisible by 4.
We can formally compute this as:
P(option 2) = (5/20) * (5/20) = 1/16
since we do not wish to double count possibilities that fall into category 1, we only count the probability of selecting even numbers from each set that are not divisible by 4 (e.g. the other 5 even integers in each set).
Total probability is then P(option 1) + P(option 2) = 1/2
Answer: (E)  ½
Question: 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is ?
(A) 1
(B) 7
(C) 3
(D) 9
(E) 2
Rationale: Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be years.
Then, age of the elder child = years.
So,
Age of younger child = 3 years.
Answer: C
Answer: (C) 3
Question: In a sample of graduate students in a program, 20 percent are second-year students, and 80 percent are not first-year students. What percentage of the students at the law firm have been there for more than two years?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: 80 percent are not first-year students --> This means 80 percent of students are either two or more than two years
Already, we know % of second-year students = 20 %
So, % of students there for more than two years = 80 % - 20 % = 60 % .. => (E)
Answer: (E) 60
Question: If x+y=25 and x2y3 + y2x3=25, what is the value of xy?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: xy=1
As x+y=25
x2y3+y2x3=25
x2y2(y+x)=25
Substituting x+y
x2y2=1
xy=1
ANSWER:A
Answer: (A) 1
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 79.4
(B) 79.0
(C) 79.5
(D) 79.2
(E) 79.1
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer:D
Answer: (D) 79.2
Question: If 12 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A)  10•9•8•7•6•5•4•3•2•1
(B)  10•10
(C)  10•9
(D)  66
(E)  36
Rationale: We got #12 people who shake each other's hands once ==> a pair of 2
12!/10!2! = 12*11 / 2*1 = 66.
Hence answer D.
Answer: (D)  66
Question: A pupil's marks were wrongly entered as 79 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
(A) 30
(B) 80
(C) 20
(D) 68
(E) 26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (79 - 45)
=> X/2 = 34
=> X = 68.
ANSWER:D
Answer: (D) 68
Question: A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) days
(B) days
(C) days
(D) 1/2 days
(E) days
Rationale: Explanation:
10/40 + 10/30 + 10/x = 1
x = 24 days
Answer: A
Answer: (A) days
Question: What will be the day of the week 15th August, 2010?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Thursday
(E) Friday
Rationale: 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.
Jan. Feb. March April May June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days.
Given day is Sunday.
Answer: Option A
Answer: (A) Sunday
Question: What must be added to each of the numbers 7, 11 and 19, so that the resulting numbers may be in continued proportion?
(A) 3
(B) 5
(C) 4
(D) -3
(E) -2
Rationale: Let X be the required number, then
(7 + X) : (11 + X) :: (11 +X) : (19 + X)
(7 + X) (19 + X) = (11 + X)2
X2 + 26X + 133 = X2 + 22X + 121
4X = - 12 or X = - 3
ANSWER:D
Answer: (D) -3
Question: Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent E of all the possible subcommittees that include Michael also include Anthony?
(A)  20%
(B)  30%
(C)  40%
(D)  50%
(E)  60%
Rationale: The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability E= 1/5+4/5*1/4 = 2/5.C
Answer: (C)  40%
Question: Find the simple interest on Rs.520 for 7 months at 8 paisa per month?
(A) 277
(B) 270
(C) 291
(D) 266
(E) 121
Rationale: I = (520*7*8)/100 = 291
Answer: C
Answer: (C) 291
Question: If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 18. If the sum of the two digits of the number is 14. What is the original number ?
(A) 68
(B) 77
(C) 95
(D) 86
(E) 89
Rationale: Explanation :
Let the no. be 10x + y.
No. formed by the interchange of digits = 10y + x
We have y - x = 2 .....(i)
y + x = 14 .....(ii)
Solving (i) and (ii), we get x = 6, and y = 8
∴ the no. is 68.
Answer : Option A
Answer: (A) 68
Question: Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 20mph, what was his average speed over the three hour portion of his ride?
(A) 14 mph
(B) 20/3 mph
(C) 70/3 mph
(D) 80/3 mph
(E) 34 mph
Rationale: Average speed for first two hours, S1 = 40 mph
Distance travelled in these two hours, D1 = 80 miles
Average speed for the entire 5 hour ride, S = 20 mph
Total Distance traveller in the entire 5 hour ride, D = 20 x 5 = 100 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 100 - 80 = 20
Average speed for the latter 3 hour period S2 = D2/3 = 20/3
Hence, the correct answer is B
Answer: (B) 20/3 mph
Question: If n=4p where p is a prime number greater than 1, how many different positive even divisors does n have, including n?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We're told that N = 4P and that P is a prime number greater than 1. Let's TEST P = 2; so N = 8
The question now asks how many DIFFERENT positive EVEN divisors does 8 have, including 8?
8:
1,8
4,2
How many of these divisors are EVEN? 2,4,8…..3 even divisors.
ANSWER:C
Answer: (C) 3
Question: The perimeter of one square is 24m & that of another is 32m. Perimeter of a square whose area is equal to the sum of the areas of the 2 squares will be
(A) 20 m
(B) 24 m
(C) 28 m
(D) 40 m
(E) 43 m
Rationale: Perimeter of square = 4 * Side
Perimeter of first square = 24 m.
Side of first square =
∴ Area of first square =
Perimeter of second square = 32 m.
Side of second square =
∴ Area of second square =
Sum of the areas of two squares = 36 + 64 = 100 m2
∴ Side of square =
∴ Perimeter of square = 4 * 10 = 40 m.
D
Answer: (D) 40 m
Question: The price of a gallon of gasoline was $30 on the 15th of March. By the 15th of April, the price per gallon had increased by 20%, and by the 15th of May the price had increased again to a total of $45 per gallon. What was the percent change in the price of a gallon of gasoline between the 15th of April and the 15th of May?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 50%
Rationale: Price of a gallon of gasoline was $30 on the 15th of March
Price of a gallon of gasoline increased by 20 %so the price on 15th of April = 1.2*30 = $36
Price of a gallon of gasoline was $45 on 15th of May
so there was a increase of $9 from 15th of april to 15 th of may
% increase = 9/36 * 100 = 25 %
Correct answer - B
Answer: (B) 25%
Question: In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.
(A) 2:3
(B) 4:5
(C) 16:9
(D) 7:9
(E) 8:5
Rationale: Sol. Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then,
((1/2) X xX 3h)/(1/2) X y X 4h) =4/3  x/y =(4/3 X 4/3)=16/9
Required ratio = 16 : 9.
Ans: C
Answer: (C) 16:9
Question: Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=4/5, what is the ratio of rectangle A’s area to rectangle B’s area?
(A) 5/4
(B) 25/16
(C) 4/5
(D) 16/25
(E) 16/5
Rationale: The area of rectangle A is ab.
c=5a/4 and d=5b/4.
The area of rectangle B is cd=25ab/16.
The ratio of rectangle A's area to rectangle B's area is ab / (25ab/16) = 16/25.
The answer is D.
Answer: (D) 16/25
Question: There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 18, then find the smaller number?
(A) 30
(B) 66
(C) 77
(D) 88
(E) 44
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 18
3x = 18 => x = 6
=> Smaller number = 5x = 30.
Answer: A
Answer: (A) 30
Question: A 100-litre mixture of milk and water contains 49 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?
(A) 27.5 litres
(B) 26.67 litres
(C) 27.67 litres
(D) 28.57 litres
(E) 26 litres
Rationale: Working formula ...
Initial Concentration*Initial Volume=Final Concentration*Final Volume.
Let X is the part removed from 100 lts.
49%(1-X/100)^2 = 25% * 100%
(1-x/100)^2=25/49------>(1-x/100)^2=(5/7)^2
100-X=500/7
x=28.57...
Ans D
Answer: (D) 28.57 litres
Question: A marble shop contains 6 blue marbles, 7 red marbles, and 7 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be blue?
(A) 5/19
(B) 9/20
(C) 1/57
(D) 15/57
(E) 15/684
Rationale: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 6/20
Probability of choosing 2nd card of the same type: 5/19
Probability of choosing 3rd card of the same type: 4/18
Multiply and you get 1/57
Answer C.
Answer: (C) 1/57
Question: Which greatest possible length can be used to measure exactly 12 meter 65 cm, 15 meter 25 cm and 10 meter 65 cm
(A) 45cm
(B) 5cm
(C) 4cm
(D) 15cm
(E) 50cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1265 cm, 1525cm, 1065cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 5.
Option B
Answer: (B) 5cm