mathewhe/aqua_rat huggingface dataset:
Question: A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?
(A) 18
(B) 72
(C) 180
(D) 1,260
(E) 3,060
Rationale: This is a combination question since order is not important.
n!
k! (n-k!)
= 18!
4! 14!
= 18 * 17 * 16 * 15 * 14!
4 * 3 * 2 * 1 * 14!
= 3060 (Ans: E)
Answer: (E) 3,060
Question: What is the square root of 0.16
(A) 0.4
(B) 0.04
(C) 0.004
(D) 4
(E) 1
Rationale: Explanation:
as .4 * .4 = 0.16
Option A
Answer: (A) 0.4
Question: What is the rate percent when the simple interest on Rs.4000 amount to Rs.320 in 2 Years?
(A) 4%
(B) 4.1%
(C) 4.2%
(D) 4.3%
(E) 4.5%
Rationale: Interest for 1 year = 320/2 = 160
Interest on Rs 4000 p/a = 160
interest rate = 160/4000*100 = 4%
Answer : A
Answer: (A) 4%
Question: When n is divided by 20, the remainder is 5. What is the remainder when n + 16 is divided by 5?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Assume n = 15
Remainder (n/20) = 5
n+16 = 31
Remainder (31/5) = 1
Option A
Answer: (A) 1
Question: The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 174 lbs, how much does substance x weigh?
(A) 48
(B) 36
(C) 24
(D) 12
(E) 10
Rationale: x:y=4:6
if the ratio is halevd then x:y=2:6
The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.
x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)
so x:y:z= 12:36:10
and we know x + y + z = 174 lbs
from the ratio of x ,y and z we have x=12k y=36k z=10K
put it in the equation we have 12k+36k+10k=174
k=3
Hence x=12(3)=36
Ans B
Answer: (B) 36
Question: In how many years, Rs. 200 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?
(A) 4 years
(B) 6 years
(C) 8 years
(D) 9 years
(E) 12 years
Rationale: Explanation :
Let Simple Interest for Rs.200 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years
200×6×n/100=800×9/2×2/100
200×6×n=800×9/2×2
200×6×n=800×9
n=6 years
Answer : Option B
Answer: (B) 6 years
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 0 ?
(A) 1/8
(B) 1/2.
(C) 1/5.
(D) 3/8.
(E) 1/3.
Rationale: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
So answer will be 1/8. Option A.
Answer: (A) 1/8
Question: At a party, there were five ten as many females as males and four times as many adults as children. Which of the following could be the number of people at the party?
(A) 384
(B) 258
(C) 216
(D) 120
(E) 72
Rationale: Five times as many females as males --> F = 10M.
Three times as many adults as children --> (F + M) = 4C.
The number of people at the party = F + M + C = 4C + C = 5C.
The number of people at the party must be a multiple of 5. The only answer choice which is a multiple of 5 is D.
Answer: D.
Answer: (D) 120
Question: Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 144, how many more green disks than blue disks are in the bag?
(A) 25
(B) 28
(C) 30
(D) 35
(E) 40
Rationale: Let B:Y:G = 3x:7x:8x.
3x + 7x + 8x = 18x = 144 --> x= 8.
G - B = 8x - 3x = 5x = 40.
The answer is E.
Answer: (E) 40
Question: What approximate value should come in place of the question mark (?) in the following equation?
8.539 + 16.84 × 6.5 ÷ 4.2 = ?
(A) 25
(B) 42
(C) 44
(D) 35
(E) None of these
Rationale: ? 8.6 + 4 × 6.5 = 35
Answer D
Answer: (D) 35
Question: In a graduating class of 233 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
(A) 114
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 233 = 30
Greatest - Smallest is 144-30 = 114
So answer must be A. 114
Answer: (A) 114
Question: A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is:
(A) 10
(B) 20
(C) 40
(D) 73
(E) 50
Rationale: Let there be x pupils in the class.
Total increase in marks = (x × 1⁄2) = x⁄2.
∴ x⁄2 = (83 - 63) ⇒ x⁄2 = 20 ⇒ x = 40.
Answer C
Answer: (C) 40
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 8 girls and 8 guys. Assuming girls go on dates with guys, how many possible ways can these 16 medical interns date each other?
(A) A)36320
(B) B)37320
(C) C)38320
(D) D)39320
(E) E)40320
Rationale: 1st girl can go with 8 guys
2nd girl can go with remaining 7
3rd girl can go with remaining 6 and so on
so the total ways are 8!= 40320
E should be the answer
Answer: (E) E)40320
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
(A) 123
(B) 145
(C) 166
(D) 173
(E) 187
Rationale: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Answer: (C) 166
Question: In what ratio must water be added to 10 litres of milk at Rs.20 per litre so that cost of mixture is Rs.16 per litre?
(A) 3:2
(B) 1:4
(C) 2:3
(D) 4:1
(E) 4:3
Rationale: C.P of 1 Lt of water =Rs.0
C.p Of 1 lt of Milk= Rs.20
So,
o(Cheaper) 20(Dearer)
16(Mixture)
4 : 16
(Dearer-Mixture) (Mixture-Cheaper)
so,
(Note: Just cross check)
4:16=1:4
ANSWER:B
Answer: (B) 1:4
Question: If xy ≠ 0 and x^2y^2 − 2xy = 24, which of the following could be y in terms of x?
I. 6/x
II. -4/x
III. 1/x
(A) I only
(B) II only
(C) I and II only
(D) I and III
(E) II and III
Rationale: (x^2)(y^2) –2xy - 24 = 0
(xy – 6)(xy + 4) = 0
xy – 6 = 0 or xy + 4 = 0
xy = 6 or xy = -4
Since we need y in terms of x, we can isolate y in both of our equations.
y = 6/x or y = -4/x
Answer: C
Answer: (C) I and II only
Question: In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks D are made of cotton?
(A) 100
(B) 80
(C) 60
(D) 50
(E) 25
Rationale: I'll prefer to solve this with plug n play method.
As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks D has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.
100 fits perfectly after relevant calculations. Hence answer A.
Answer: (A) 100
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 14
(B) 19
(C) 20
(D) 24
(E) 26
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: Points M(13,22) and N(5,8) lie on the xy - plane. What is the midpoint of line segment MN?
(A) (5,0)
(B) (0,5)
(C) (0, (136^(1/2))/2)
(D) (3/2,0)
(E) (9,15)
Rationale: The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:-
The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.• Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.
So, x=(13+5)/2=9 and y=(22+8)/2=15 --> coordinates of the midpoint are (9, 15).
Answer: E.
Answer: (E) (9,15)
Question: In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?
(A)  100
(B)  300
(C)  400
(D)  1,000
(E)  2,500
Rationale: 3/5 republican voters = 0.6*x
Another 600 register as republican, with the total amount being 80% republican (4/5)
Total new voters is 1,100 (500+600)
So, 0.6x + 600 = 0.8(x+1,100)
0.6x + 600 = 0.8x + 880
answer is B
Answer: (B)  300
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
(A) 11
(B) 17
(C) 88
(D) 66
(E) 12
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.Answer: B
Answer: (B) 17
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 816 m
(B) 577 m
(C) 240 m
(D) 176 m
(E) 126 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer:C
Answer: (C) 240 m
Question: what is the next term of this series6,10,9,15,12,20,15...?
(A) 9
(B) 25
(C) 11
(D) 12
(E) 15
Rationale: 3&2=6;
5*2=10;
3*3=9;
3*5=15
3*4=12
5*4=20
3*5=15
5*5=25
ANSWER:B
Answer: (B) 25
Question: Light glows for every 20 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.
(A) 380 times
(B) 381 times
(C) 382 times
(D) 248 times
(E) 482 times
Rationale: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/20)=248 times.
ANSWER:D
Answer: (D) 248 times
Question: Andrew started saving at the beginning of the year and had saved $160 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
(A) 11%
(B) 25%
(C) 44%
(D) 56%
(E) 137.5%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 540
Saving in 2nd year + 160 = 540
Saving in 2nd year = 540 - 160 = 380
Change in Value = 380 - 160 = 220
Original Value = 160
Percentage Increase = (220 / 160 ) * 100 = 137.5 % ..... Answer E.....
Answer: (E) 137.5%
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1775 liters
(B) 8176 liters
(C) 1467 liters
(D) 1184 liters
(E) 1886 liters
Rationale: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148
=> 2k = 296 => k = 148
The initial quantity of water in
A = 8k
= 8 * 148
=1184 liters.
Answer:D
Answer: (D) 1184 liters
Question: How many words with or without meaning, can be formed by using all the letters of the word, â€˜RAMâ€™, using each letter exactly once?
(A) 6
(B) 8
(C) 5
(D) 9
(E) 1
Rationale: The word â€˜RAMâ€™ contains 3 different letters.
Therefore, Required number of words= Number of arrangement of 3 letters, taken all at a time
=3P3
= 3!
= 3*2*1
= 6
ANSWER:A
Answer: (A) 6
Question: As part of a game, two people each must secretly choose an integer between 1 and 2, inclusive. What is the approximate likelihood that all two people will choose different numbers?
(A) 9%
(B) 12%
(C) 16%
(D) 20%
(E) 50%
Rationale: Ans:E
1st person has option no's- (1,2) - there fore probability of getting a no = 2c1/2c1 = 1
2nd person has only one option
- there fore probability of getting a no = 1c1/2c1 =1/2
=1*1/2 =50%
Answer: (E) 50%
Question: Find (7x + 8y ) / (x-2y) if x/2y = 3/2 ?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 29
Rationale: x/2y=3/2
=>x=6y/2=3y
=>(7x+8y)/(x-2y)=((7*(3y))+8y)/(3y-2y)
=>29y/y=29
ANSWER:E
Answer: (E) 29
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
(A) A)1/8
(B) B)1/3
(C) C)1/9
(D) D)1/2
(E) E)1/4
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer:B
Answer: (B) B)1/3
Question: 80 pie square inches of material of negligible thickness are required to construct a 1/16 scale model of a cylindrical barrel. If the diameter of the base of the barrel is 160 inches, then what is the volume of the barrel, to the nearest cubic foot?
(A) 2pie
(B) 11pie
(C) 178 pie
(D) 711 pie
(E) 1280 pie
Rationale: radius of barrel, R=80
radius of model, r=80/16=5
surface area of the model =2∗pi∗r(r+h)=80∗pi
which gives h=3 and H=3∗16=48
So, volume of the barrel =pi∗R2∗H=pi∗(80)2∗(48) in cubic inches
Converting in cubic ft results: volume =pi∗(80)2∗(48)/(12)3=178pi cubic ft approximately
Answer [C]
Answer: (C) 178 pie
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 12 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) 16 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph
ANSWER:C
Answer: (C) 14 kmph
Question: What is the units digit of (147^17)^47 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 17 has the form 4n+1 so the units digit is 7 inside the bracket. The exponent 47 has the form 4n+3, so the units digit is 3. The answer is B.
Answer: (B) 3
Question: P is three times as old as Q. In 9 years, P will be twice as old as Q. How old was P three years ago?
(A) 18
(B) 21
(C) 24
(D) 27
(E) 30
Rationale: P = 3Q so Q = P/3
P+9 = 2(Q+9) = 2(P/3+9)
P/3 = 9
P = 27
Three years ago, P was 24.
The answer is C.
Answer: (C) 24
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 210
(B) 220
(C) 240
(D) 250
(E) 260
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: Option C
Answer: (C) 240
Question: On a track for remote controlled racing cars, racing car A completes the track in 55 seconds, while racing car B completes it in 36 seconds. If they both start at the same time after how many seconds will they be side by side again.
(A) 275
(B) 325
(C) 1980
(D) 425
(E) None of these
Rationale: Time required in seconds will be LCM ( 36, 55 ) = 1980
Hence, answer will be (C) 1980
Answer: (C) 1980
Question: Data sufficiency question:
Is x has only '3' factors?
(A) 213
(B) 278
(C) 208
(D) 17
(E) 101
Rationale: Only squares of primes has 3 factors. For example, 4 has three factors. 1, 2, 4.
Now when we square 4, we get 16, which has 5 factors. 1, 2, 4, 8, 16. So Statement 1 is sufficient.
Statement two says that one of the factor must be prime number. 10 has 4 factors. i.e., 1, 2, 5, 10 and one of which is prime. but we cannot say whether numbers of this format always have three factors or not. So statement 2 is insufficient.
Answer:B
Answer: (B) 278
Question: Ramesh can finish a work in 15 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
(A) 4 days
(B) 7 days
(C) 6 days
(D) 9 days
(E) 5 days
Rationale: (5 + x)/15 + 5/25 = 1 => x =7 days
ANSWER:B
Answer: (B) 7 days
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:42
(C) 39:19
(D) 39:29
(E) 39:26
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: (A) 39:40
Question: A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However, as it turned out, 50% of the components were rejected. What is the loss to the manufacturer?
(A) Rs.12000
(B) Rs.13000
(C) Rs.14000
(D) Rs.15000
(E) Rs.16000
Rationale: Sale according to 5% loss = 1900*25 = 47500
original production cost = 47500/1.25 = 38000
Sale according to 50% loss = 10000* 25 = 25000
so loss = 38000-25000 = 13000
ANSWER:B
Answer: (B) Rs.13000
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 25 as remainder. Find the no. is?
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220025
Rationale: (555 + 445) * 2 * 110 + 25 = 220000 + 25 = 220025
E
Answer: (E) 220025
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: (30*30)/100 = 9%loss
Answer: A
Answer: (A) 9
Question: A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is
(A) 2347
(B) 1277
(C) 2288
(D) 1250
(E) 7178
Rationale: Explanation:
speed = (5x5/18)m/sec
= 25/18 m/sec.
Distance covered in 15 minutes = (25/18 x 15 x 60)m
= 1250 m.
Answer: D) 1250
Answer: (D) 1250
Question: When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is
(A)  0.005
(B)  0.002
(C)  0.001
(D)  0.0003
(E)  0.0002
Rationale: It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=0.3 then x=0.3/1000=0.0003.
The answer is D
Answer: (D)  0.0003
Question: P, Q and R have Rs.6000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
(A) Rs.3000
(B) Rs.3600
(C) Rs.2400
(D) Rs.4000
(E) None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(6000 - r) => 3r = 12000 - 2r
=> 5r = 12000 => r = 2400.
ANSWER:C
Answer: (C) Rs.2400
Question: A 5-letter code word consists of letters A, B, C and D. If the code includes all the gour letters, how many such codes are possible?
(A) 72
(B) 48
(C) 36
(D) 240
(E) 18
Rationale: A-ABCD can be arranged in 5!/2!=60 ways;
B-ABCD can be arranged in 5!/2!=60 ways;
C-ABCD can be arranged in 5!/2!=60 ways;
D-ABCD can be arranged in 5!/2!=60 ways;
Total: 60+60+60+60=240.
Answer: D.
Answer: (D) 240
Question: Varma can read a book in k minutes. What part of the book can he read in 4 minutes?(k>8)
(A) (k - 8)/k
(B) k/8
(C) 8 + k
(D) k-8
(E) 4/k
Rationale: Option E
Explanation:
Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 8 minutes =4/k.
Answer: (E) 4/k
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
(A) 430
(B) 288
(C) 761
(D) 122
(E) 234
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172
=> 4x = 1720 => x = 430.
Answer:A
Answer: (A) 430
Question: A mixture contains milk and water in the ratio 5:4. On adding 30 litters of water, the ratio of milk to water becomes 5:7. Total quantity of milk & water before adding water to it?
(A) 90
(B) 120
(C) 80
(D) 70
(E) 60
Rationale: Explanation:
milk: water = 5:4
5x : 4x + 30 = 5 : 7
7[5x] = 5[4x + 30]
35x = 20x + 150
35x - 20x = 150
15x = 150
x = 10
The quantity of milk in the original mixture is = 5 : 4 = 5 + 4 = 9
9x = 90
Short cut method:
milk:water = 5 : 4
after adding 30 liters of water
milk:water = 5 : 7
milk is same but water increse 30liters then the water ratio is increse 3 parts
3 part -----> 30 liters
The quantity of milk in the original mixture is = 5 : 4 = 5 + 4 = 9
9 parts -----> 9 liters (Answer is = 90)
Short cut method - 2 : for Only milk problems
milk : water
5 : 4
5 : 7
milk ratio same but water ratio 3 parts incress per 30 liters
3 part of ratio -------> 30 liters
1 part of ratio -------> 10 liters
9 part of ratio ------> 90 liters
Answer: Option A
Answer: (A) 90
Question: While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:
The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are to go!
(A) 45 Years
(B) 49 Years
(C) 41 Years
(D) 36 Years
(E) 30 Years
Rationale: A
45 Years
Answer: (A) 45 Years
Question: If {h} denote the remainder when 3h is divided by 2 then which of the following is equal to 1 for all positive integers h?
I. {2h+1}
II. {2h}+1
III. 2{h+1}
(A) I only
(B) II only
(C) I and II
(D) III only
(E) II and III
Rationale: C - I and II
3h/2 = 0 or 1
I just substituted 1 in the equations and solved.
Answer: (C) I and II
Question: At what price must an article costing Rs.150 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 30% on the cost price?
(A) 62.5
(B) 62.0
(C) 62.6
(D) 216.67
(E) 62.2
Rationale: CP = 150
SP = 150*(130/100) = 195
MP*(90/100) = 195
MP = 216.67
Answer: D
Answer: (D) 216.67
Question: A boat can travel 1.5 times the distance down the stream than up the stream in the same time. If the speed of the current is 4 KMPH, Find the speed of the boat in still water
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Simple question, messy language.
Lets say boat's speed is B and current's speed is C.
Upstream speed : B - C
Downstream speed : B + C
Distance will be the same both times. lets say D.
given : time it takes upstream = 1.5 times time it takes downstream
D/(B + C) = 1.5 * [D/(B - C)]
Solving B = 5 C
given : C is 4 KMPH
So B is 20 KMPH
D
Answer: (D) 20
Question: Set A consists of all the prime numbers between 15 and 36. What is the range of set A?
(A) 12
(B) 13
(C) 14
(D) 17
(E) 23
Rationale: The range of a set of data is the difference between the highest and lowest values in the set
In this set,
Highest number = 31
Lowest number = 17
Range = Highest - Lowest = 31 - 17 = 14
Option C
Answer: (C) 14