mathewhe/aqua_rat huggingface dataset:
Question: Ravi and Kavi start a business by investing â‚¹ 2000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
(A) 2 : 36
(B) 5 : 36
(C) 7 : 36
(D) 1 : 36
(E) 3 : 36
Rationale: Ratio of profit = Ratio of investments
= 2000 : 72000 = 1 : 36
Answer : D
Answer: (D) 1 : 36
Question: On the average Mr.Jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed.How much hours should jackson and assistant has t plan for 30 min meeting?
(A) 4.5 hr
(B) 4.8 hr
(C) 4.9 hr
(D) 5.5 hr
(E) 6.5 hr
Rationale: for a 1 hour talk he took total of 9 hr time
1hr=9hr(2+7)
30 min=1/2hr =?
so 9*1/2 div by 1
4.5 hr
ANSWER:A
Answer: (A) 4.5 hr
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 30 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
(A) a. 43
(B) b. 45
(C) c. 55
(D) d. 68
(E) e. 60
Rationale: 30 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (30 * 12.5 * 100) / (2.5 * 200)
thus, X = 75
Thus, more men needed to finish the task = 75-30=45
hence Answer is B
Answer: (B) b. 45
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 180, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 31
(B) 33
(C) 55
(D) 77
(E) 88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 180 => .1x + 3/4x = 180 => x = 211
211 - 180 = pure gala = 31.
A
Answer: (A) 31
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 3/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 63/280
(B) 1/280
(C) 3/56
(D) 3/35
(E) 7/40
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*4/7 + 1/5*5/8*3/7 + 4/5*3/8*3/7 = 63/280.
Answer: A
Answer: (A) 63/280
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 7
(B) 6
(C) 2
(D) 8
(E) 4
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B
Answer: (B) 6
Question: A sum of money at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is :
(A) 400
(B) 500
(C) 600
(D) 700
(E) 800
Rationale: SI of 5 year = (1020-720)=300
so, SI of 1 year=300/5=60
so, SI of 2 year=60*2=120
so, sum is =(720-120)=600
ANSWER:C
Answer: (C) 600
Question: Jack and Jill are marathon runners. Jack can finish a marathon (43 km) in 4.5 hours and Jill can run a marathon in 4.3 hours.What is the ratio of their average running speed? (Jack: Jill)
(A) 14/15
(B) 43/45
(C) 4/5
(D) 5/4
(E) Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 43 /(9/2) = 86/9
Average Speed of Jill = 43/(4.2) = 10
Ratio of Average speed of Jack to Jill = (86/9)/10 = 86/90 = 43/45
Answer B
Answer: (B) 43/45
Question: The owner of a furniture shop charges his customer 10% more than the cost price. If a customer paid Rs. 7350 for a computer table, then what was the cost price of the computer table?
(A) Rs.6289
(B) Rs.6298
(C) Rs.6681
(D) Rs.6725
(E) Rs.6708
Rationale: CP = SP * (100/(100 + profit%))
= 7350(100/110) = Rs.6681.
Answer: C
Answer: (C) Rs.6681
Question: Find the number of zero’s in 173! (173 Factorial)?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: no of zeroes in 173! is
173/5=34(quotient)
34/5=6(quotient)
6/5=1(quotient)
34+6+1=41
ans 41 zeroes
ANSWER:D
Answer: (D) 41
Question: A small water pump would take 4 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
(A) 1/6
(B) 4/9
(C) 1/4
(D) 5/9
(E) 1/3
Rationale: Rate of the small pump is 1/4 tank/hour
Rate of the larger pump is 1/(1/2) or 2 tank/hour;
Combined rate of the two pumps is 1/4+2=9/4 tank/hour, together they will fill the empty tank in 1/(9/4)) = 4/9 hours (time=job/rate).
Answer: B
Answer: (B) 4/9
Question: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 71.2 , what is the value of n?
(A) 9
(B) 20
(C) 55
(D) 70
(E) 80
Rationale: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:
We're told that K and N are both INTEGERS.
Since K/N = 81.2, we can say that K = 81.2(N)
N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.
With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)
Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.
Final Answer:
E
Answer: (E) 80
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 8.
(A) 161
(B) 152
(C) 154
(D) 158
(E) 144
Rationale: D = d * Q + R
D = 17 * 9 + 8
D = 153 + 8
D = 161
ANSWER A
Answer: (A) 161
Question: Find the product of the localvalue and absolutevalue of 6 in 20618?
(A) 6300
(B) 1100
(C) 1200
(D) 1300
(E) 3600
Rationale: Local value of 6 = 6 x 100 = 600
Place value of 6 = 6
There fore = 6 x 600 = 3600
E
Answer: (E) 3600
Question: If the day before yesterday was Wednesday, what day will be the day after tomorrow?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Friday
(E) Saturday
Rationale: Explanation:
Day before yesterday was Wednesday
=>Yesterday was a Thursday
=>Today is a Friday
=>Tomorrow is a Saturday
=>The day after tomorrow will be a Sunday
Answer: Option A
Answer: (A) Sunday
Question: If x, y, and z are positive integers, and 3x = 5y = 6z, then the least possible value of x + y + z is
(A) 21
(B) 28
(C) 37
(D) 42
(E) 60
Rationale: Take LCM of 3,5 and 6 = 30
Now 3x = 30 => x =10
5y = 30 => y = 6
6z = 30 => z =5
10+6+5 = 21.
Option A.
Answer: (A) 21
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 10/21
(B) 1/21
(C) 9/11
(D) 7/11
(E) 6/11
Rationale: Total number of balls = 2 + 3 + 2 = 7
n(S) =Total number of ways 7 = 7C2
let E = event of drawing 2 balls, none of them is blue
n(E) = no of ways of drawing 2 balls, none of them is blue
=No of ways of drawing 2 balls from the total= 5C2
5*4/7*6 = 10/21
ANSWER A
Answer: (A) 10/21
Question: Out of 10 students in a class, 4 are from Maharashtra, 3 are from Karnataka, and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
(A) 1/3
(B) 4/9
(C) 5/6
(D) 3/7
(E) 1/4
Rationale: Total possible ways of selecting 4students out of 10= 10C4 = (10*9*8*7)/(4*3*2*1) =210
The number of ways of selecting a 4 students in which no student belongs to Karnataka = 7C4
Number of ways of selecting atleast one student from Karnataka = 15C4-7C4 = 175
Probability = 175/210 = 5/6
Answer is C
Answer: (C) 5/6
Question: The product of face value of 3 and local value of 6 in the numeral 78934064 is
(A) 18
(B) 24
(C) 180
(D) 240
(E) 108
Rationale: (Face value of 3) x (Local value of 6) = (3 x 60) = 180
C
Answer: (C) 180
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2882
(C) 2799
(D) 2778
(E) 2901
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: (A) 1000
Question: Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 3/140
(B) 1/28
(C) 7/40
(D) 3/35
(E) 5/40
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.
Answer: C.
Answer: (C) 7/40
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability T that a + b is prime?
(A)  0
(B)  1/12
(C)  5/12
(D)  7/18
(E)  4/9
Rationale: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
T=15/36.
Answer: C.
Answer: (C)  5/12
Question: Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?
(A) 4
(B) 4 2/3
(C) 5 1/3
(D) 6
(E) 6 1/4
Rationale: Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?
a) 4
b) 4 and 2/3
c) 5 and 1/3
d) 6
e) 6 and 1/4
To minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.
Answer: A.
Answer: (A) 4
Question: In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
(A) 12540
(B) 11450
(C) 11760
(D) 13250
(E) 12450
Rationale: Required number of ways = 8C5*10C5 = 8C3*10C4 = 11760
Answer is C
Answer: (C) 11760
Question: In a survey of university students, 64 had taken mathematics course, 94 had taken computer science course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and computer science, 22 had taken computer science and physics course, and 14 had taken all the three courses. Find how many had taken mathematics course only.
(A) 64
(B) 14
(C) 12
(D) 14
(E) 24
Rationale: Let us represent the given data in a Venn diagram. Let M, C, P represent sets of students who had taken mathematics, computer science and physics respectively.
M=64
M and C and P=14
M and C not P=26-14=12
M and P not C=28-14=14
M only = 64-12-14-14=24
ANSWER E 24
Answer: (E) 24
Question: A woman spends 15% of her income in house rent, 15% of the rest on his children’s education, 10% of the rest miscellaneous causes and 15% in medical expenses. If she now posses Rs. 5548 then her income is?
(A) 10058
(B) 10068
(C) 10078
(D) 10088
(E) 10038
Rationale: X * (85/100) * (85/100) * (90/100) * (85/100)= 5548
X * 0.85 * 0.85 * 0.9 * 0.85 = 5548
X = 5548/0.5527
X = 10038
ANSWER:E
Answer: (E) 10038
Question: 66.2 is what percent of 1000?
(A) 6.62
(B) 66.2
(C) 662
(D) 0.662
(E) 0.0662
Rationale: We assume that 1000 is 100%
assume 'x' is value we looking for
here,
1000 = 100% and
x% = 66.2
therefore,
100/x = 1000/66.2
100/x = 15.105
x = 6.62
A
Answer: (A) 6.62
Question: If b/c = 1.25, then c is what percent of b?
(A) 0.008
(B) 0.08
(C) 0.8
(D) 8
(E) 80
Rationale: You are given , b/c =1.25 ---> c < b but only 'just'. This eliminates A-C as you are asked % and as such these values will be further reduced by 1/100, making them even smaller.
Also, as c iscloseto 'b', eliminate D and mark E as the correct answer.
Alternatively, 1.25 = 5/4 ---> b/c=5/4 --> c = 4/5 (b) = 0.8b ---> c = 80% of b. E is the correct answer.
Answer: (E) 80
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer m?
(A) (2m-2)/(m^2- m)
(B) (2m-1)/(m^2- m)
(C) (2m-1)/(m^4- m)
(D) (3m-1)/(m^2- m)
(E) (2m-1)
Rationale: Let two consecutive positive integers be m and m-1 (Greater integer is m)
So,
(1/m) + [1/(m-1)]
= (2m-1)/m(m-1)
=(2m-1)/(m^2- m)
Answer : B
Answer: (B) (2m-1)/(m^2- m)
Question: (998-1)(998-2)(998-3)........(998-n)=....... when n>1000
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: The term (998-998) makes the whole expression = 0.
ANSWER:E
Answer: (E) 0
Question: How many numbers from 10 to 50 are exactly divisible by 3?
(A) 13
(B) 14
(C) 15
(D) 17
(E) 19
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48.
13 Numbers.
10/3 = 3 and 50/3 = 16 ==> 16 - 3 = 13. Therefore 13 digits.
A)
Answer: (A) 13
Question: A garage has a bin that is used by an "add stuff" worker and a "throw away" worker. Working alone, the "add stuff" worker can fill the bin in 5 hours. Working alone, the "throw away" worker can empty the bin in 15 hours. If it is desired that the bin should be filled, from empty, exactly 6 hours after the "add stuff" worker begins his shift at 9:30am, then at what time should the "throw away" worker begin his own shift?
(A) 10:00am
(B) 10:45am
(C) 12:00pm
(D) 12:30pm
(E) 1:30pm
Rationale: In 6 hours the "add stuff" worker can fill the bin equal to 6*1/5 = 6/5 of the bin. So, 1/5 more than necessary, which should be compensated by the "Throw away" worker. To get rid of 1/5 of the inventory the "throw away"worker needs 15/5 = 3 hours.
Therefore, the "throw away" worker should begin his shift at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Answer: (D) 12:30pm
Question: The ratio of flour to water to sugar in a recipe is 7:2:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 2 cups of water, how much sugar is required?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The ratio of flour to water is 14:2.
The ratio of flour to sugar is 3.5:1=14:4.
The new ratio of flour to water to sugar is 14:2:4
If we need 2 cups of water, then we need 4 cups of sugar.
The answer is C.
Answer: (C) 4
Question: All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.
How many small cubes will be formed having only one face coloured ?
(A) 54
(B) 8
(C) 16
(D) 24
(E) 34
Rationale: no.of small cubes will have only one face painted=(X-2)2*6
Here x=side of the small cube=5
therfore(X-2)2*6=54
ANSWER:A
Answer: (A) 54
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) 14009
(B) 14409
(C) 14006
(D) 14000
(E) 14001
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Answer: (D) 14000
Question: A cab driver 5days income was $400, $250, $650, $400 , $500. Then his average income is?
(A) $400
(B) $420
(C) $440
(D) $460
(E) $480
Rationale: avg = sum of observations/number of observations
avg income=(400+250+650+400+500)/5 = 440
Answer is C
Answer: (C) $440
Question: A train 50 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
(A) 3 sec.
(B) 7 sec.
(C) 9 sec.
(D) 11 sec.
(E) None
Rationale: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 50 m at (50 /3)m/sec	= (112 - 50)kmph
= (50 x 3/50)sec
= 3 sec.
Answer A
Answer: (A) 3 sec.
Question: 15th august 2010 was which day of the week?
(A) Thursday
(B) Friday
(C) Wednesday
(D) Sunday
(E) Monday
Rationale: ANSWER: Sunday
Explanation:
15th August 2010 can be written as 2009 + days from 1st January 2010 to 15th August 2010.
=> Total number of odd days in 400 years = 0
Hence, total number of odd days in 2000 years = 0 (as 2000 is a perfect multiple of 400)
Odd in days in the period 2001-2009:
7 normal years + 2 leap yeas
=> (7*1) + (2*2) = 11
=> Odd days will be 11- (7*1) = 4
Days from January 1 to August 15 in 2010: 31+28+31+30+31+30+31+15
= 227 days.
= 32 weeks and 3 days, this gives additional 3 odd days.
=> Total odd days= 3+4=7
=> 7 odd days=1 week= 0 odd days
=> 0 odd days= Sunday
Thus, 15th August 2010 was a Sunday.
Answer: D
Answer: (D) Sunday
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?
(A) 2.5 kmph
(B) 6.5 kmph
(C) 1.5 kmph
(D) 8.5 kmph
(E) 1.7 kmph
Rationale: Explanation:
72 --- 9
? ---- 1
=> Down Stream = 8
45 ---- 9
? ---- 1
=> Up Stream = 5
Speed od current S = ?
S = (8 - 5)/2 = 1.5 kmph.
Answer: C
Answer: (C) 1.5 kmph
Question: How many different arrangements of A, B, C, D, and E are possible where A is not adjacent to B ?
(A) 72
(B) 48
(C) 32
(D) 30
(E) 1
Rationale: So you have A,B,C,D,E
five possible ways to arrange it = 5! = 120
AB cannot be adjacents
(AB),C,D,E = 4! = 24 x 2(because it can be (AB) or (BA) ) = 48
120 -48- = 72 possible ways
A
Answer: (A) 72
Question: Bottle R contains 350 capsules and costs $6.25. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
(A)  $0.25
(B)  $0.12
(C)  $0.0052
(D)  $0.003
(E)  $0.002
Rationale: Cost per capsule in R is 6.25/350=0.0178
Cost per capsule in T is 2.99/130=0.023
The difference is 0.0052
The answer is C
Answer: (C)  $0.0052
Question: 45 litres of mixture is created by mixing Liquid A and Liquid B in the ratio 3:2. How much more Liquid B must be added to make the ratio 9:11?
(A) 9 Litres
(B) 10 Litres
(C) 12 Litres
(D) 15 Litres
(E) 16 Litres
Rationale: In current ratio A = (3/5) * 45 = 27
B is 18
Suppose "b" amount of b is added
new ratio = 27/(b+18) = 9/11
=> b+18 = 33
=> b = 15
So, answer will be D
Answer: (D) 15 Litres
Question: When 3 fair coins are tossed together, what is the probability of getting 2 tails?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 3/4
(E) 2/3
Rationale: We can get 2 tails in 3C2 ways.
We can get 3 tails in exactly one way.
Also, there are a total out 8 possible outcomes.
Thus, the required probability = (3 + 1)/8 = 1/2
ANSWER:A
Answer: (A) 1/2
Question: A certain galaxy is known to comprise approximately 4 x 10^12 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 1,250
(C) 80,000
(D) 12,000
(E) 80,000
Rationale: Total no. of stars on galaxy = 4 * 10^12
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 4 * 10^12 / 50 * 10^6
=40 * 10^4 /5
= 80000
therefore answer is C
Answer: (C) 80,000
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.5
(B) 12.1
(C) 12.9
(D) 12.7
(E) 12.2
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: (B) 12.1
Question: Apple Infotech has 4 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of two managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Apple Infotech possibly provide guidance for?
(A)  16
(B)  20
(C)  26
(D)  54
(E)  64
Rationale: P(at least 1 S D) = P(Total) - P(0 Senior Director)
=9C2 - 5C2
= 26
Answer: (C)  26
Question: Rebecca's annual income is $15, and Jimmy's annual income is $18. By how much must Rebecca's annual income increase so that it constitutes 50% of Rebecca and Jimmy's combined income?
(A) 7
(B) 8
(C) 9
(D) 3
(E) 10
Rationale: total rebecca = x+15; total = x+20+18
x+15/x+33 = 50/100 therefore x =3
D
Answer: (D) 3
Question: In a ratio which is equal to 4:6, if the antecedent is 50, then the consequent is?
(A) 75
(B) 85
(C) 64
(D) 51
(E) 45
Rationale: We have 4/6 = 50/x
4x = 50*6
x = 75
consequent = 75
Answer is A
Answer: (A) 75
Question: In what ratio must tea at Rs.60 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.67.5 per Kg?
(A) 3 : 1
(B) 3 : 2
(C) 4 : 3
(D) 1 : 3
(E) None
Rationale: Required ratio = 250 : 750 = 1 : 3
Answer D
Answer: (D) 1 : 3
Question: Which of the following represents 1<x<9?
(A) |x|<3
(B) |x+5|<4
(C) |x-1|<9
(D) |-5+x|<4
(E) |3+x|<5
Rationale: |x| is the distance of x from the origin on the number line.
|x - 5| is the distance of x from the point 5 on the number line.
|x + 3| is the distance of x from the point -3 on the number line. (That's because x + 3 = x - (-3))
So, we want to write 1<x<9 as a distance statement.
Step #1: find the middle of that region. The midpoint is at 5. So, this is about distance from 5 ---> |x - 5|
Step #2: how far can we get from 5? Well, up to almost 9, or down to almost 1 -- that is, almost 4. Thus:
distance from 5 < 4
|x - 5| < 4
ANSWER:D
Answer: (D) |-5+x|<4
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) 288
(B) 270
(C) 999
(D) 278
(E) 121
Rationale: I = (500*9*6)/100 = 270
Answer:B
Answer: (B) 270
Question: An old priest fell on a bottom of the well of a church.
The well is 20 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
(A) 16-days
(B) 14-days
(C) 11-days
(D) 19-days
(E) 10-days
Rationale: A
16-days
In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: (A) 16-days
Question: Find the odd one out:
125, 106, 84, 76, 65, 58, 53
(A) 33
(B) 84
(C) 26
(D) 18
(E) 222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 84 is the answer.
ANSWER: B
Answer: (B) 84
Question: If Josh, Doug, and Brad have a total of $72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Brad have?
(A) $8
(B) $9
(C) $27
(D) $32
(E) $36
Rationale: Josh+Doug+Brad = 72 ; Joush = 3 brad, Josh =3/4 doug
Josh+1/3 Josh+ 4/3 Josh = 72 (substituted the given values)
Josh = 27. 27= 3/4 doug => doug =36
Josh+Doug+Brad = 72
27 + 36 + Brad = 72
Brad = 9
Answer is B.
Answer: (B) $9
Question: In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.
(A) 33
(B) Monday
(C) 299
(D) 299
(E) 277
Rationale: Ans: If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month start with Monday.
Answer:B
Answer: (B) Monday