mathewhe/aqua_rat huggingface dataset:
Question: The ratio of two quantities is 7 to 12. If each of the quantities is divided by 3, what is the ratio of these 2 new quantities?
(A) 3.5:6
(B) 14:24
(C) 7:12
(D) 2.3:4
(E) It cannot be determined from the information given
Rationale: If both sides of a ratio are divided by the same number there is no change in the ratio.
5:6 means 7x:12x...
The ratio starts as 7/(1): 12/(1). So when you diveide by three it becomes 7/(3): 12/(3)..
So if the Xs are equal the ratio does not change..
ANSWER:C
Answer: (C) 7:12
Question: There are six cards in which it has two king cards. all cards are turned down and two cards are opened what is the possibility to get two kings.
(A) 1/15
(B) 2/15
(C) 3/15
(D) 4/15
(E) 6/15
Rationale: P0SSIBLITY TO GET TWO KINGS IS 2C2/6C2=1/15
ANSWER:A
Answer: (A) 1/15
Question: A fruit seller sells mangoes at the rate of Rs.8 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%
(A) Rs 8.5
(B) Rs 9.5
(C) Rs 10.5
(D) Rs 11.5
(E) None of these
Rationale: Explanation:
80 : 8 = 105 : x
x= (8×105/80)
= Rs 10.5
Option C
Answer: (C) Rs 10.5
Question: A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 44000. What is the share of C?
(A) Rs. 12000
(B) Rs. 13375
(C) Rs. 11750
(D) Rs. 11625
(E) None of these
Rationale: Explanation:
Let the investment of C be Rs. x.
The inverstment of B = Rs.(2x/3)
The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)
Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3
C's share = Rs. [(3/11) × 44000] = Rs. 12000
Answer: Option A
Answer: (A) Rs. 12000
Question: 7 points are marked on a straight line and another 6 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
(A) 91
(B) 105
(C) 196
(D) 21
(E) 231
Rationale: getting the answer 231 which is not in the choices, what is the source of the problem?
7C2* 6C1 + 6C2* 7C1 =231
E
Answer: (E) 231
Question: At exactly what time past 8:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
(A) 20 13/21 minutes past 7:00
(B) 21 9/11 minutes past 8:00
(C) 21 3/23 minutes past 7:00
(D) 21 9/11 minutes past 7:00
(E) 22 4/9 minutes past 7:00
Rationale: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?
That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 8:00. At 8:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.
So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of 210-90 = 120 degree at the rate of 5.5 degrees per minute ---> 120/5.5 = 21 9/11 minutes.
Thus, B is the correct answer.
Answer: (B) 21 9/11 minutes past 8:00
Question: Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
(A) a) 3y(7x+2xy)
(B) b) 3x+12y
(C) c) 3xy(7x+2)
(D) d) 3x(2y+7)
(E) e) 17x+6xy
Rationale: Payment of a week for 2 days a week = $2x
Payment of 4 weeks for 2 days a week = $2x*4 = $8x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 3 weeks for y days overtime a week = ($3x+$2xy)*3
Total Earnings = $8x + ($3x+$2xy)*3 = 17x+6xy
Answer: option E
Answer: (E) e) 17x+6xy
Question: Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?
(A) 90 min
(B) 100 min
(C) 110 min
(D) 120 min
(E) 130 min
Rationale: Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 100 min.
ANSWER:B
Answer: (B) 100 min
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 #-3# = 2, what is the value of #3#?
(A) -4
(B) 0
(C) -2
(D) -3
(E) -5
Rationale: #p# = ap^3 + bp - 1
#-3# = 2
putting p = -3 in above equation
-27a -(3b +1) = 2 or
#-5# = (27a+3b+1) = -2
therefore 27a+3b = -3 .....(1
now putting p = 3
#3# = 27 a+3b - 1
using equation 1(27a+3b = -3)
#3# = -3-1 = -4
hence A
Answer: (A) -4
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2400 ?
(A) s. 832
(B) s. 830
(C) s. 822
(D) s. 812
(E) s. 800
Rationale: Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
A's share in the profit of Rs. 2400 = 20 (2400/60) = Rs. 800.
Answer: E
Answer: (E) s. 800
Question: Jenny can divide her sweets equally to 5 people and also to 6 people equally but not to 12 people. What could be the number?
(A) 120
(B) 134
(C) 127
(D) 30
(E) 650
Rationale: Option (B) and (C) are ruled out as they are not divisilble by 5 and 6.
120 is both divisible by 5 and 6 but also by 12, so it wrong.
650 is divisible by 5 but not by 6.
hence,
(D) is the answer, as it is both divisible by 5 or 6 but not by 12
Answer: (D) 30
Question: If n=t^3 , when n and t are positive integers and 8, 9, 10 are each factors of n, which of the following must be a factor of n?
(A) 16
(B) 175
(C) 225
(D) 275
(E) 625
Rationale: n = 8p,n = 9q and n = 10r.Thus,n^3=t^6=2^4∗3^2∗5∗[k is some positive integers]
Thus, for t to be a positive integer, k must atleast have the value = 2^2∗3^4∗5^5
Thus,n=t3=2^3∗3^2∗5^2∗y[y is a positive integer]
225 is definitely a factor of n.
ANSWER:C
Answer: (C) 225
Question: Two letters from the word JARKHANT are selected at random. What is the probability that at least one of the selected letters is a consonant?
(A) 40/28
(B) 30/28
(C) 50/28
(D) 26/28
(E) 27/28
Rationale: There are 6 consonants and 2 vowels in JARKHANT .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : E
Answer: (E) 27/28
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 160 units?
(A) 50 hours
(B) 40 hours
(C) 20 hours
(D) 12 hours
(E) 8 hours
Rationale: Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by each machine every 10 hours
Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...
10 hours/4 units = 2.5 hours per unit when 1 machine is working.
The prompt asks us how long would it take 20 machines to produce 160 units.
If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 160 units is '8 times' 20, we need '8 times' more TIME.
(2.5 hours)(8 times) = 20 hours
Final Answer:
[Reveal]Spoiler:
C
Answer: (C) 20 hours
Question: How many numbers up to 100 and 300 are divisible by 11?
(A) 18 2/98
(B) 18 9/11
(C) 18 2/19
(D) 18 2/11
(E) 18 2/13
Rationale: Explanation:
(300 â€“ 100)/11 = 200/11 = 18 2/11
18 Numbers
Answer: D
Answer: (D) 18 2/11
Question: How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
(A) 27
(B) 25
(C) 24
(D) 22
(E) 20
Rationale: 9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}
3 odd multiples of 5: {5, 15, 25}
11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}
Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 9+3+11-1=22.
Answer: D.
Answer: (D) 22
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 6:8
(B) 6:1
(C) 6:5
(D) 6:2
(E) 6:3
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer: C
Answer: (C) 6:5
Question: A car is traveling 67 kilometers per hour. How many meters does the car travel in one minute?
(A) 1,250 meters / minute
(B) 1,350 meters / minute
(C) 1,450 meters / minute
(D) 1,550 meters / minute
(E) 1,116 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
67 kilometers per hour = 67 km/hr
= (67 * 1000 meters) / (60 minutes) = 1,116 meters / minute
correct answer E
Answer: (E) 1,116 meters / minute
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 39
(B) 42
(C) 45
(D) 47
(E) 54
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
Question: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?
(A) -10
(B) -5
(C) -4
(D) 3
(E) 7
Rationale: 2^y = 4^(5x + 3)
2^y=2^2(5x+3)
y=10x+6 ........... 1
3^(x - 7) = 9^y
3^(x-7)=3^2y
x-7=2y ............. 2
put value of y=10x+6 in eq 2
x-7=2(10x+6)
x-7=20x+12
19x=-19
x=-1
therefore, y= -10+6
y=-4
x+y= -1-4= -5
Answer: B
Answer: (B) -5
Question: A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: Number = ( 779 x a) + 47, where "a" is the quotient
= (19 x 41 x a) + (19 x 2) + 9
= 19 x (41a + 2) + 9
= 19 x (New quotient) + 9
\inline \fn_jvn \therefore Required remainder = 9
Answer:A
Answer: (A) 9
Question: A person travelled from his house to office at 36km/hr and office to house at 12km/hr. Then find the average speed?
(A) 15km/hr
(B) 20km/hr
(C) 32km/hr
(D) 24km/hr
(E) 18km/hr
Rationale: Average speed = (2*36*12)/(36+12)
= 18km/hr
Answer is E
Answer: (E) 18km/hr
Question: A alone finish a work in 12 days,where B finish same work in 15 days and C alone finish in 20 days.all three start work together but after 2 days A leave the work and B leave the work before 2 days of finishing the work.then in how many days work finished?
(A) 8
(B) 45/6
(C) 6
(D) 58/7
(E) 5
Rationale: work of A in 1 day=1/12,work of B in 1 day=1/15 and work of C in 1 day=1/20
(A+B+C) Work in 2 days=2(1/12+1/15+1/20)=2×12/60=2/5
work of C in 2 days=1/10
remaining work=1-(2/5+1/10)=1-1/2=1/2
this work done by both B and C together
(B+C) work in 1 days=7/60
1/2 work done by (B+C)=[1*60/7*1/2]=30/7 days
total time taken to finish the work=[2+2+30/7]=58/7 days
Answer D
Answer: (D) 58/7
Question: Bruce purchased 9kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1040
(B) B)1050
(C) C)1055
(D) D)1065
(E) E)1125
Rationale: Cost of 9 kg grapes = 70 × 9 = 630.
Cost of 9 kg of mangoes = 55 × 9 = 495
Total cost he has to pay = 630 + 495 = 1125
E
Answer: (E) E)1125
Question: A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?
(A) 253 mph.
(B) 378 mph.
(C) 565 mph.
(D) 431 mph.
(E) 642 mph.
Rationale: The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x – 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x – 23)
420(x – 23) = 350(x + 23)
420x – 9660 = 350x + 805
420x – 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253
Therefore, the speed of the plane in still air = 253 mph.
correct answer A
Answer: (A) 253 mph.
Question: Two trains of length 200 m and 100 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 18 kmph and 36 kmph. After how much time will the trains meet?
(A) 27/7 sec
(B) 20/3 sec
(C) 33/7 sec
(D) 21/7 sec
(E) 32/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (18 + 36)*5/18 = 3*5 = 15 mps.
The time required = d/s = 100/15 = 20/3 sec.
Answer : B
Answer: (B) 20/3 sec
Question: A trader marks his books 20% more than the cost price. If he allows 30% discount, then find his gain or loss percent?
(A) 2% profit
(B) 2% loss
(C) 16% loss
(D) No profit No loss
(E) None of these
Rationale: Let CP of an book = 100
MP of an book = 120
Discount 30 % on 120 = 36
SP of the book = 120 - 36 = 84
loss = 16%
Answer : C
Answer: (C) 16% loss
Question: If x and y are different integers, both divisible by 3, then which is not necessarily true?
(A) x^2 + y^2 is divisible by 3
(B) x - y is divisible by 3
(C) xy is divisible by 3
(D) x + y is divisible by 3
(E) x + y is divisible by 6
Rationale: Let x = 3k and let y = 3j.
Then x+y = 3(k+j) and k+j could be even or odd.
Thus 3(k+j) is not necessarily divisible by 6.
The answer is E.
Answer: (E) x + y is divisible by 6
Question: P and Q invested in a shop. The profits were divided in the ratio of 2 : 4 respectively. If P invested Rs. 500000, the amount invested by Q is:
(A) 5000000
(B) 4000000
(C) 1000000
(D) 6000000
(E) None
Rationale: Suppose Q invested Rs. y. Then, 500000/y = 2/4 or y = [500000 x 4 / 2] = 1000000.
Answer C
Answer: (C) 1000000
Question: The distance light travels in one year is approximately 5,840,000,000,000 miles. The distance light travels in 100 years is
(A) A) 587 × 108 miles
(B) B) 587 × 1010 miles
(C) C) 587 × 10-10 miles
(D) D) 584 × 1012 miles
(E) E) 587 × 10-12 miles
Rationale: The distance of the light travels in 100 years is:
5,840,000,000,000 × 100 miles.
= 584,000,000,000,000 miles.
= 584 × 1012 miles.
The answer is (D)
Answer: (D) D) 584 × 1012 miles
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 2 years ago?
(A) 8
(B) 12
(C) 12
(D) 14
(E) 16
Rationale: Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 2 years ago?
i.e. D-2= 14-2 = 12 years
ANSWER:B
Answer: (B) 12
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.7
(B) 31.2
(C) 31.6
(D) 31.1
(E) 31.3
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: C
Answer: (C) 31.6
Question: What is the remainder when 1034*1047*1050*1053 is divided by 33?
(A) 0
(B) 27
(C) 30
(D) 21
(E) 18
Rationale: take the remainder from each of 1034/33, 1047/33 and so on..
1034/33 gives remainder = 11
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 11*24*27*30
break them into pairs 11*24/33 gives remainder 0
and 27*30/33 gives remainder 18
so 0*18/33 gives remainder 0.
A
Answer: (A) 0
Question: Ms. Barton has four children. You are told correctly that she has at least two girls but you are not told which two of her four children are those girls. What is the probability that she also has two boys? (Assume that the probability of having a boy is the same as the probability of having a girl.)
(A) 1/4 
(B) 3/8
(C) 5/11
(D) 1/2
(E) 6/11
Rationale: Assume that there are 4 Ms. Barton's children in a row: 1-2-3-4. Let show all possible combinations of them being girl(G) or boy(B) giving that there at least two girls. We are seeing each child 1,2,3,4 a s a unique(so, we distinguish between them)
BBGG
BGBG
GBBG
BGGB
GBGB
GGBB
BGGG
GBGG
GGBG
GGGB
GGGG
Overall 11 variants. 6 of them satisfy the condition of 2 boys exactly (they are highlighted in bold)
Therefore the probability is 6/11
Answer:E
Answer: (E) 6/11
Question: A radio station has to choose 2 weeks of the four in a month to broadcast a certain program, and that set will repeat each month. The program can be broadcast equally on any of the four week —- 1st week vs. last week don’t matter at all —- nor does it matter whether the week the program airs are adjacent or not. Absolutely any 2 weeks of the 4 weeks can be chosen. How many different week combinations of the 4 weeks can be constructed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Pick 2 weeks out of 4.. 4C2 =6
Answer : A
Answer: (A) 6
Question: The average age of a husband and his wife was 32 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
(A) 11
(B) 53/3
(C) 19
(D) 25
(E) 27
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (32 * 2 + 5 * 2) + 1 = 75 years.
Required average = 75/3= 25 years.
Answer: D
Answer: (D) 25
Question: What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?
(A) 2 units
(B) 12 units
(C) 6.5 units
(D) 6 units
(E) 7.5 units
Rationale: Explanatory Answer
In a right angled triangle, the radius of the incircle = s - h, where 's' is the semi perimeter of the triangle and 'r' is the radius of the inscribed circle.
The semi perimeter of the triangle = a + b + c /2=5+12+13 /2 = 15
Therefore, r = 15 - 13 = 2 units.
Choice A
Answer: (A) 2 units
Question: There are 6 people in the elevator. Their average weight is 152 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.
(A) 145
(B) 168
(C) 189
(D) 190
(E) 200
Rationale: Solution
Average of 7 people after the last one enters = 151 .
âˆ´ Required weight = (7x151)-(6x152)
= 1057- 912
= 145.
Answer A
Answer: (A) 145
Question: In measuring the sides of a rectangle, one side is taken 7% in excess, and the other 6% in deficit. Find the error percent in the area calculated from these measurements.
(A) 0.11%
(B) 0.7%
(C) 0.4%
(D) 0.6%
(E) 0.58%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (61/57) x (47/50) y = (867/862 )(xy)
Error In measurement = (867/862)xy- xy = (5/862)xy
Error percentage = [(5/862)xy (1/xy)100] % = (29/50) % = 0.58%.
Answer is E.
Answer: (E) 0.58%
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
(A) 128
(B) 150
(C) 278
(D) 268
(E) 261
Rationale: 1/2 * 20(9 + 6)
= 150 cm2
Answer:B
Answer: (B) 150
Question: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance y before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%
Rationale: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance y before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.
If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15 = 5 hours to reach john. If John had not stopped, their combined rate would 10+15 = 25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.
ANSWER: A) 25%
Answer: (A) 25%
Question: 75% of x is greater than 1/3rd of x by 110.what is x?
(A) 160
(B) 264
(C) 360
(D) 354
(E) 400
Rationale: 75x/100-x/3=110
5x/12=110
x=264
ANSWER:B
Answer: (B) 264
Question: Raviraj invested an amount of 1000000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years?
(A) 12,310
(B) 13,210
(C) 13,320
(D) 13,120
(E) 1331000
Rationale: Amount = 1000000(1 + 10⁄100)3
= 1000000 × 11⁄10 × 11⁄10 × 11⁄10
= 1331000
Answer E
Answer: (E) 1331000
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 8 businessmen, how many possible team submissions are possible?
(A) 76
(B) 100
(C) 164
(D) 198
(E) 202
Rationale: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 8C2 = 112
2) 2 tech1 businessman: 4C2 x 8C1 = 48
3) 3 tech0 businessmen: 4C3 = 4
Total: 112+48+4 = 164
Answer: C
Answer: (C) 164
Question: Solution A contains 15% bleach per liter and solution B contains 45% bleach per liter. If solution A and solution B are mixed in a 1 to 1 ratio, what fraction of the mixed solution is NOT bleach?
(A) 1/3
(B) 7/10
(C) 2/5
(D) 1/4
(E) 2/3
Rationale: Amount of bleach in solution A: 15/100
Amount of bleach in solution B: 45/100
Amount of bleach in 1 liter of mixed solution: 1/2 x (15/100) + 1/2 x (45/100) = 60/200 = 3/10
Amount of solution that is not bleach: 1-3/10=7/10
Answer is B
Answer: (B) 7/10
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19.7
(B) 19.9
(C) 21.9
(D) 21.8
(E) 21.7
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A
Answer: (A) 19.7
Question: The price of a car is Rs. 3,25,000. It was insured to 85% of its price. The car was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the car and the amount received ?
(A) Rs. 76,375
(B) Rs. 34,000
(C) Rs. 82,150
(D) Rs. 70,000
(E) None of these
Rationale: Explanation :
Price of the car = Rs.3,25,000
Car insured to 85% of its price
=>Insured price=325000 × (85/100)
Insurance company paid 90% of the insurance
⇒Amount paid by Insurance company = Insured price × (90/100)
= 325000 × (85/100) × (90/100) = 325 × 85 × 9 = Rs.248625
Difference between the price of the car and the amount received
= Rs.325000 - Rs.248625 = Rs.76375
Answer : Option A
Answer: (A) Rs. 76,375
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 11
(B) 50
(C) 88
(D) 27
(E) 31
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer:B
Answer: (B) 50