mathewhe/aqua_rat huggingface dataset:
Question: A Jar contains a mixture of AB in the ratio 4:1. When 40 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
(A) 12
(B) 15
(C) 16
(D) 64
(E) 25
Rationale: 40 litres of mixture that is replaced will contain 32 litres of A and 8 litres of B (as A:B = 4:1)
Let the initial volume of the mixture be 4K + 1K = 5K
So by condition ,
[ 4K-32 ]/ [ K-8+40 ] = 2/3 => 12K -96= 2K-16+80 => 10K = 160
Solve for K which is K = 16
So initial volume of liquid A = 4K = 64 litres
Answer : D
Answer: (D) 64
Question: The average of 11 numbers is 10.8. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 9.5
(B) 12.6
(C) 10.5
(D) 11.5
(E) 12
Rationale: Explanation:
1 to 11 = 11 * 10.8 = 118.8
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 118.8 = 12.6
6th number = 12.6
Option B
Answer: (B) 12.6
Question: John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
(A) 40 m
(B) 50 m
(C) 70 m
(D) 90 m
(E) 100 m
Rationale: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 =310
By rule of alligation,
concentration of water in mixture1 (29)
concentration of water in pure water (1)
Mean concentration
(310)
1−310=710
310−29=790
=> Quantity of mixture1 : Quantity of water
=710:790=110:190=1:19
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water =1:19
=> Quantity of water =630×19=70 ml
C
Answer: (C) 70 m
Question: The inverse ratio of 3: 6: 1 is?
(A) 2:3:7
(B) 2:3:9
(C) 2:1:6
(D) 2:3:6
(E) 2:3:1
Rationale: 1/3: 1/6: 1/1 = 2:1:6
Answer:C
Answer: (C) 2:1:6
Question: Two girls begin together to write out a book containing 900 lines. The first girl starts with the first line, writing at a speed of 150 lines per hour and the second girl starts writing from the last line at the rate of 200 lines per hour. At which line will they meet?
(A) 384th line
(B) 386th line
(C) 389th line
(D) 400th line
(E) None of these
Rationale: Explanation :
Solve this question as analogous to distance method,
At some x page they will meet, so
x/150 = (900 – x)/200, we get x = 385.7 = 386th line (approx.)
Answer –B
Answer: (B) 386th line
Question: A man can do a job in 5 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
(A) 6.3
(B) 6.9
(C) 3.5
(D) 6.1
(E) 6.2
Rationale: 1 day work of the three persons = (1/5 + 1/20 + 1/25) = 29/100
So, all three together will complete the work in 100/29 = 3.5 days.
Answer:C
Answer: (C) 3.5
Question: A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 30 paise per sq m is
(A) Rs. 223.20
(B) Rs. 323.20
(C) Rs. 423.20
(D) Rs. 523.20
(E) None of these
Rationale: Explanation:
Area to be plastered = [2(l + b) Ã— h] + (l Ã— b)
= [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m
Cost of plastering = 744 Ã— (30/100) = Rs.223.20 Answer: A
Answer: (A) Rs. 223.20
Question: A basket contains 2 blue, 2 red and 2 yellow marbles. If 2 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
(A) 2/5
(B) 3/25
(C) 1/6
(D) 9/28
(E) 11/24
Rationale: 6/6*4/5*2/4 = 2/5
the answer is (A)
Answer: (A) 2/5
Question: The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paise per meter is Rs. 36. The breadth of the room is ?
(A) 6 meters
(B) 7 meters
(C) 8 meters
(D) 9 meters
(E) 10 meters
Rationale: Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m2
= 90 m2
∴ Area of the room = 90 m2
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
Answer : A
Answer: (A) 6 meters
Question: A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.
(A) 10 sec
(B) 12 sec
(C) 14 sec
(D) 16 sec
(E) 20 sec
Rationale: ANSWER B
As we need to get answer in seconds, so never forget to convert speed into meter per second.
Speed = 30 km/hr = 30* 5/18 m/sec
= 25/3 m/sec
Distance = length of train = 100 meter
Required time = DIST/SPEED = 100/25/3 = 100*3/25 = 12sec
ANSWER B
Answer: (B) 12 sec
Question: Population of a city in 20004 was 1200000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
(A) 354354
(B) 545454
(C) 465785
(D) 456573
(E) 1300650
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1300650
E
Answer: (E) 1300650
Question: Gary’s Gas Station serves an average of 14 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?
(A) 1,104
(B) 1,200
(C) 1,240
(D) 1,280
(E) 1,320
Rationale: 6 a.m. to 10 p.m. = 16 hours
Number of cars serviced on weekdays = (16 * 9 * 5)
Number of cars serviced on Saturday = (16 * 14)
Number of cars serviced on Sunday = (16 * 10)
Number of cars served in a week = 16(45 + 14 + 10) = 16 * 69 = 1104
Answer: A
Answer: (A) 1,104
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 4 days
(B) 7 days
(C) 9 days
(D) 8 days
(E) 2 days
Rationale: C
3/12 + (3 + x)/16 = 1
x = 9 days
Answer: (C) 9 days
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently seven spaces behind player B, what is the probability that player B will be frozen after player A rolls?
(A) 1/12
(B) 5/36
(C) 1/6
(D) 1/3
(E) 17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 7 (as A is 7 spaces behind B) = 6 ( (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) )
So, the probability = 6/36 =1/6 (Option C)
Answer: (C) 1/6
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) 999
(C) 8289
(D) 2889
(E) 2132
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: (A) 1000
Question: n^(n/2)=6 is true when n=6 in the same way what is the value of n if n^(n/2) =10?
(A) 8
(B) 12
(C) 10
(D) 16
(E) 18
Rationale: n^(n/2)=10Apply logN/2logn=log10nlogn=2log10=log10^2=log100Logn=log100Now apply antilogn=100/nNow n=10.ANSWER:C
Answer: (C) 10
Question: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?
I. xy(z + 1) is even.
II. x(z + y) is even.
III. (x^2 - x)yz is even.
(A) I only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III
Rationale: If x is even, then the average of even number of odd consecutive integers (y), will be even. For example, the average of {1, 3} is 2.
If x is odd, then the average of odd number of odd consecutive integers (y), will be odd. For example, the average of {1, 3, 5} is 3.
Thus:
If x = even, then y = even;
If x = odd, then y = odd.
Next, |z - 6/4| = 1/2:
z - 6/4 = 1/2 --> z = 2;
-(z - 6/4) = 1/2 --> z = 1.
Since, z can be even as well as odd, then it takes no part in deciding whether the options are even or odd. So, we can ignore it.
I. xy(z + 1) is even: xy can be odd if both are odd and even if both are even. So, this option is not necessarily even. Discard.
II. x(z + y) is even: if x and y are odd, and z is even, then x(z + y) = odd(odd + even) = odd but if if x and y are odd, and z is odd too, then x(z + y) = odd(odd + odd) = even. So, this option is not necessarily even. Discard.
III. (x^2 - x)yz is even: (x^2 - x)yz = x(x - 1)yz. Since either x or x - 1 is even, then the whole expression must be even irrespective of the values of x, y, and z.
Answer: B.
Answer: (B) III only
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
(A) Rs.45
(B) Rs.78
(C) Rs.44
(D) Rs.40
(E) Rs.42
Rationale: Explanation:
Ï€ (152 - 132) = 176
176 * 1/4 = Rs.44
ANSWER IS C
Answer: (C) Rs.44
Question: 3 OUT OF 1000 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
(A) 11/50
(B) 2/9
(C) 1/45
(D) 2/7
(E) NONE OF THESE
Rationale: REQUIRED PERCENTAGE=(3/1000*100)%=2/7%
CORRECT OPTIONS: D
Answer: (D) 2/7
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
(A) 7189
(B) 7282
(C) 7298
(D) 1500
(E) 1576
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
Answer: D
Answer: (D) 1500
Question: The parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 16 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 28.28CM
(B) 25.45CM
(C) 26.45CM
(D) 20.18CM
(E) 32.14CM
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(20 + 16) = 72 cm Parameter of the square = 72 cm
i.e. 4a = 72
A = 18
Diameter of the semicircle = 18 cm
Circimference of the semicircle
= 1/2(∏)(18)
= 1/2(22/7)(18) = 396/14 = 28.28 cm to two decimal places
Answer: A
Answer: (A) 28.28CM
Question: The ratio of red, yellow, and green jelly beans in a jar is 2:3:4. If the number of jelly beans is increased by 50%, 40%, and 30% respectively, what will be the new ratio?
(A) 7:15:21
(B) 11:18:24
(C) 15:21:26
(D) 17:24:28
(E) 18:25:32
Rationale: The new ratio will be 3:4.2:5.2=30:42:52=15:21:26.
The answer is C.
Answer: (C) 15:21:26
Question: If x is an integer, then x(x - 1)(x - k) should be evenly divisible by three when k is any of the following values EXCEPT
(A) 4
(B) -4
(C) -1
(D) 2
(E) 5
Rationale: if we put k=-1 we get:
X(x-1)(X+1) rearrange:(x-1)X(X+1)
so it looks like a sequenc,
if we assume that X =2 and put number from the answer then we get:
(x – 1)x(x – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=4 =1.2.-2 not satisfied
so,the answer is A
Answer: (A) 4
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,560 ?
(A) $12
(B) $14
(C) $24
(D) $17
(E) $18
Rationale: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,560, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,560 --> (5+x)(20-x)=156 --> x=7 or x=8 --> price=10+$2*7=$24 or price=10+$2*8=$26.
Answer: 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 15m/sec,what is the length of the train?
(A) 150m
(B) 200m
(C) 300m
(D) 240
(E) None
Rationale: Length of the train= (15*20)m=300m
Let the length of the platform be x meters.
Then, (x+300)/36=15
x=240m
Answer:Option D
Answer: (D) 240
Question: How many seconds will a 100 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 6
(B) 30
(C) 8
(D) 12
(E) 1
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 100 * 3/50 = 6 sec.
Answer: Option A
Answer: (A) 6
Question: A cricket bat is sold for $900, making a profit of $300. The profit percentage would be
(A) 24%
(B) 25%
(C) 30%
(D) 50%
(E) 40%
Rationale: 300/(900 - 300) = 50%.
Answer: D
Answer: (D) 50%
Question: How many plants will be there in a circular bed whose outer edge measure 30 cms, allowing 4 cm2 for each plant ?
(A) 18
(B) 750
(C) 24
(D) 120
(E) None of these
Rationale: Circumference of circular bed = 30 cm
Area of circular bed = (30)2⁄4π
Space for each plant = 4 cm2
∴ Required number of plants
= (30)2⁄4π ÷ 4 = 17.89 = 18(approx)
Answer A
Answer: (A) 18
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 12 min
(B) 10 min
(C) 11 min
(D) 10 min
(E) 17 min
Rationale: A
12 min
T = 9/45 * 60 = 12
Answer: (A) 12 min
Question: A random number is picked following which, five guesses are to be made in order to find the correct number. All the guessed numbers are noted down in a paper. On another paper, all the differences between the guessed numbers and the picked numbers are written down by subtracting the smaller one from the bigger one.
Now, one number each is erased from both of the papers. As a result, four numbers remain on each paper:
Guesses: 27, 32, 44, 45
Differences: 5, 7, 10, 13
If this is all the information you need, can you find out what number was picked?
(A) 33
(B) 37
(C) 55
(D) 79
(E) 83
Rationale: B
The number is 37.
The missing guess can be either 24 or 50 and the missing difference is 8.
Answer: (B) 37
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) 69.5 km/hr
(B) 70 km/hr
(C) 79 km/hr
(D) 79.2 km/hr
(E) 62.2 km/hr
Rationale: Answer: Option D
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) 79.2 km/hr
Question: A train passes a man standing on the platform. If the train is 180 meters long and its speed is 108 kmph, how much time it took in doing so?
(A) 8 sec
(B) 5 sec
(C) 6 sec
(D) 1 sec
(E) 9 sec
Rationale: D = 180
S = 108 * 5/18 = 30 mps
T = 180/30 = 6 sec
Answer:C
Answer: (C) 6 sec
Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 40 candies for the discounted price of 14 candies. The store still makes a profit of 12% on this sale. What is the mark up percentage on each candy?
(A)  100%
(B)  80%
(C)  75%
(D)  66+2/3%
(E)  55%
Rationale: Hi Akhil, I can share the way I solved it..
Let's say Marked price = M
So, there's a discount of 20% on M So, new S.P. = 80% of M
Now, the child convinces the owner to sell 20 candies for the price of 14 candies .
Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of 6/20 *100 = 30%
So, the latest S.P. = 70% of 80% of M = 0.7* 0.8 M
Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,
0.7 * 0.8 * M = 1.12 C.P
So, we get, M= 2 C.P.
i.e. Marked price was kept 100% above C.P.
E
Answer: (E)  55%
Question: he average weight of 6 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
(A) 75 kg
(B) 55 kg
(C) 45 kg
(D) 80 kg
(E) 25 kg
Rationale: Explanation:
Total weight increased = (6 x 2.5) kg = 15 kg.
Weight of new person = (65 + 15) kg = 80 kg.
Answer: D
Answer: (D) 80 kg
Question: P and Q had the same number of candies. P gave Q 20 candies so that now Q has five times as many candies as P has. How many candies does Q have now?
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: Let P and Q be the number of candies they had at the start.
P = Q
5(P-20) = Q+20
5(Q-20) = Q+20
4Q = 120
Q = 30
Now person Q has 30+20 candies which is 50 candies.
The answer is A.
Answer: (A) 50
Question: What will be the compound interest on Rs. 50000 after 3 years at the rate of 12 % per annum
(A) Rs 20123.20
(B) Rs 20246.4
(C) Rs 20123.40
(D) Rs 20123.50
(E) None of these
Rationale: Explanation:
(50000×(1+12/100)3)
=>50000×28/25×28/25×28/25
=>70246.4
So Compound interest will be 70246.4 - 50000
= Rs 20246.4
Option B
Answer: (B) Rs 20246.4
Question: A large research project was scheduled over the course of a 30-month period, and a budget of $90,000 was allotted for the course of the entire project. After seven months, the project had spent $20,000. Was the project at this point over budget or under budget, and by how much?
(A) under, $4200
(B) under, $1200
(C) under, $1000
(D) over $1800
(E) over $5800
Rationale: cost per month = 90,000/30 = 3,000.
Now, multiply by seven months: 7*($3000) = $21,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget.
$21,000 â€“ #20,000 = $1000
Answer = (C)
Answer: (C) under, $1000
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 28 cm2
(B) 26 cm2
(C) 20 cm2
(D) 86 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 28/2
= 35 cm2
Answer: E
Answer: (E) 35 cm2
Question: If n is a 25-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 5
II. n is divisible by 10
III. n is divisible by 25
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III only
Rationale: Rule for divisibility by 5: The sum of the digits of the number should be multiple of 3
Rule for divisibility by 10: The sum of the nos digits of the number should be divisible by 5 or the number should be divisible by 5 two times.
Rules for divisibility by 25: The sum of the digits should a multiple of 25
Consider no 11111111...25 times = The sum 25*1=25----> divisbible by 5,10 and 25
consider number to be 222....25 times, then sum of the no. 25*2=50 divisibly by 5,10 and 25
So why so because when you sum the numbers either you can add the digits 25 times or multiply the digit *25..
Note that since 25 is divisble by 25,10 and 5 and thus the sum of the nos will be divisible by all the nos.
Ans is E
Answer: (E) I, II and III only
Question: Enrollment in City College in 1980 was 25 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
(A) 100%
(B) 300 %
(C) 200%
(D) 250%
(E) 183 1/3%
Rationale: Assume 100 enrollments present in 1990
25 % of 1990 = enrollments on 1980
enrollments on 1980 = 25
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 25) *100 / 25
= 7500 / 25
= 300 %
Ans - B
Answer: (B) 300 %
Question: 8!/(8-2)!=?
(A) 36
(B) 46
(C) 56
(D) 66
(E) 96
Rationale: 8!/(8-2)!=8!/6!=8*7=56. Hence, the correct answer is C.
Answer: (C) 56
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
(A) 6 PM
(B) 7 PM
(C) 8 PM
(D) 5 PM
(E) 9 PM
Rationale: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer:D
Answer: (D) 5 PM
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 9 minutes by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
(A)  3%
(B)  5%
(C)  8%
(D)  10%
(E)  12%
Rationale: Bob's time = 600 secs.
His sis' time = 540 secs.
Percent increase needed = (600-540/600) * 100 = 60/600 * 100 = 10%. Ans (D).
Answer: (D)  10%
Question: A jogger running at 9 km/hr along side a railway track is 120 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 89
(B) 20
(C) 36
(D) 24
(E) 34
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 120 + 120 = 360 m.
Time taken = 240/10 = 24 sec.
Answer: Option D
Answer: (D) 24
Question: Three students shared a group project, jack claimed that he do the project by himself in 20 hours, and Jane in 30 hours. Jack started working on the project for 10 hours, then Jane continued working on it another 10 hours. Lastly, Julie joined the team and working 10 hours, the project was completed. How many hours it takes Julie to finish the project by herself?
(A) 70 hours
(B) 60 hours
(C) 50 hours
(D) 40 hours
(E) 30 hours
Rationale: 10/20 + 10/30 + 10/x = 1x = 60 hoursANSWER:B
Answer: (B) 60 hours
Question: What is the maximum number of pieces that a circular pie can be divided into by four linear cuts?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Such kind of combinations problems are always about a pattern recognition.
Maximum pieces:
0 line gives 1 whole piece;
1 line will gives 2 pieces: 1+1=2;
2 lines will give 4 pieces: 2+2=4;
3 lines will give 7 pieces: 4+3=7;
4 lines will give 7+4=11 pieces.
ANSWER:E
Answer: (E) 11
Question: What is 15 percent of Rs. 34 ?
(A) Rs. 3.40
(B) Rs. 3.75
(C) Rs. 4.50
(D) Rs. 5.10
(E) None
Rationale: Sol.
15% of Rs. 34
= Rs. (15 / 100 x 34)
= Rs. 5.10
Answer D
Answer: (D) Rs. 5.10
Question: From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?
(A) 2
(B) 4
(C) 6
(D) 8
(E) Cannot be determined
Rationale: solution:
At least 2 interviews a day, so minimum 8 interviews in four days. Thus at least a total of 8 candidates should be there.
Let, total candidates = n
according to the question,
nCx = nC(x+2)
or, nCn-x = nCx+2 [nCr = nCn-r]
or, n-x = x+2
so, n = 2x+2
Remember total least number should be 8? So below 8 we can't expect anything.
Put x=2, then n=6 that is unacceptable.
so x is not equal to 2 . Answer: A
Answer: (A) 2
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 40% while buying and by 10% while selling. What is his percentage profit?
(A) 10.22%
(B) 20.22%
(C) 21.22%
(D) 40%
(E) Can't be calculated
Rationale: The owner buys 100kg but actually gets 140kg;
The owner sells 100kg but actually gives 90kg;
Profit: (140-90)/90*100=40%
Answer: D.
Answer: (D) 40%
Question: Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 2. What is P(A and B)?
(A) 1/8
(B) 1/6
(C) 1/5
(D) 1/3
(E) 1/2
Rationale: P(A and B) = 1/3*1/2 = 1/6
The answer is B.
Answer: (B) 1/6
Question: The expression 10^14−110 is divisible by all of the following integers EXCEPT
(A) 2
(B) 3
(C) 4
(D) 7
(E) 11
Rationale: Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (D) is correct.
Answer: (D) 7
Question: Tom drives from town Q to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between Q and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
(A) 12
(B) 20
(C) 24
(D) 30
(E) 36
Rationale: Let's assume that it takes 4 hours to go from point Q to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
Answer: (B) 20
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder X when N is divided by 30?
(A) (a) 4
(B) (b) 7
(C) (c) 11
(D) (d) 13
(E) (e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder X when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: (C) (c) 11