mathewhe/aqua_rat huggingface dataset:
Question: On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 30. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?
(A) (−2, 30)
(B) (−4, 12)
(C) (6, −9)
(D) (9, −8)
(E) (10, −3)
Rationale: The area of the triangle formed will be:
1/2 * base * height =
1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 30
Thus |product of coordinates of point C| = 60
The answer is A.
Answer: (A) (−2, 30)
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
(A) 1 hr
(B) 2 hrs
(C) 6 hrs
(D) 8 hrs
(E) 10 hrs
Rationale: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0 => x = 6.
ANSWER:C
Answer: (C) 6 hrs
Question: what will be the highest no. of students in which 1001 pen and 910 pencil should be distributed so that everyone get equal no. of pen and pencils?
(A) 91
(B) 910
(C) 1011
(D) 1911
(E) 825
Rationale: h.c.f of 910 and 1001=91
answer A
Answer: (A) 91
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
(A) 8 months
(B) 4 months
(C) 7 months
(D) 9 months
(E) 2 months
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer:C
Answer: (C) 7 months
Question: Two cans A & B contain 25% & 30 % of milk. If 6 parts of can A and 4 parts of can B acre mixed in a can C. What is the proportion of milk in can C.
(A) 25%
(B) 26%
(C) 27%
(D) 28%
(E) 29%
Rationale: suppose we take 10 lits of solution in tank A and B then
25% of in A is 2.5 lits and 30% in B is 3 lits milk
6 parts of A can have 1.5 lits of milk and 4 parts of B have 1.2 lts of milk so
totally 2.7 lits of milk in c i.e 27%.
ANSWER:C
Answer: (C) 27%
Question: If n and k are integers whose product is 900, which of the following statements must be true?
(A) n+k>0
(B) n does not equal k
(C) Either n or k is a multiple of 10
(D) If n is even, then k is odd
(E) If n is odd, then k is even
Rationale: If n is odd and k is odd, then the product is odd.
The answer is E.
Answer: (E) If n is odd, then k is even
Question: A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is
(A) 85
(B) 80
(C) 75
(D) 70
(E) 65
Rationale: Explanation:
Clearly, out of every 16 persons, there is one captain. So, number of captains (1200/16) = 75.
Answer: C
Answer: (C) 75
Question: A train 820 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 510
(B) 540
(C) 480
(D) 520
(E) 589
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (820 + x)/60 = 65/3
x = 480 m.
Answer: Option C
Answer: (C) 480
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 12 sec, then the speed of each train is?
(A) 11
(B) 90
(C) 36
(D) 99
(E) 27
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/12 => x = 25
Speed of each train = 25 m/sec.
= 25 * 18/5 =- 90 km/hr.
Answer: B
Answer: (B) 90
Question: Side of a square is 10 cm. after joining the mid point of all sides makes a another inner square and this process goes to infinite.Find the sum of perimeter of all squares.
(A) 333
(B) 278
(C) 27
(D) 8
(E) 81
Rationale: You can calculate the side of the small square in two ways. Take half of the side which is equal to 5 cm. Using Pythagorean theorem, x2=52+52x2=52+52 ⇒x2=50⇒x2=50 ⇒x=50−−√=52–√=102–√⇒x=50=52=102
In another way, we can equate the squares of the sides of the small square to square of the side which is equal to 10. ⇒x2+x2=102⇒x2+x2=102
⇒2x2=100⇒2x2=100⇒x=50−−√=52–√=102–√⇒x=50=52=102
So if you observe carefully, the side of the small square is 12–√12 part of the side of the bigger square.
So the side of the square inside the small square = 102–√×12–√=102=5102×12=102=5 and so on...
So areas of the perimeters = 4(10+102–√+102+...)4(10+102+102+...)
= 40(1+12–√+12+...)40(1+12+12+...)
The terms in the bracket are in GP withe common ratio of 12–√12
So Sum of the perimeters = 40⎛⎝⎜11−12–√⎞⎠⎟40(11−12) = 40(2–√2–√−1)
Answer:B
Answer: (B) 278
Question: If x = 55 + 2q and y = 4q + 41, then for what value of q, x is equal to y ?
(A) -14
(B) 14
(C) -7
(D) 7
(E) 0
Rationale: Explanation:
x = y <=> 55 + 2q = 4q + 41 <=> 2q = 14 <=> q = 7.
Answer: D
Answer: (D) 7
Question: Which of the following numbers is a perfect square?
(A) 1266
(B) 1444
(C) 2022
(D) 4034
(E) 8122
Rationale: perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.
38*38 = 1444
ANSWER:B
Answer: (B) 1444
Question: The area of a parallelogram is 72 cm^2 and its altitude is twice the corresponding base. What is the length of the base?
(A) 1 cm
(B) 3 cm
(C) 6 cm
(D) 4 cm
(E) 2 cm
Rationale: let base= x cm
height = 2x cm
area = x Ã— 2x=2x^2
area=x Ã— 2x=2x^2
Area is given as 72 cm^2
2x^2=72
x^2=36
x=6 cm
ANSWER:C
Answer: (C) 6 cm
Question: If 2 dice as rolled, what is the probability of the total score being 2?
(A) 1/12
(B) 5/12
(C) 2/3
(D) 1/3
(E) 1/6
Rationale: Using the rules of probability, the likelihood of rolling a 2 would be 1/12, as the total score of rolling a 2 is 1 and 1. Answer: A
Answer: (A) 1/12
Question: Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.
(A) 3082
(B) 2887
(C) 3087
(D) 2887
(E) 2812
Rationale: Explanation:
Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11
Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400
Therefore Shyam's share = (441/841) * 5887 = 3087
Answer: C) 3087
Answer: (C) 3087
Question: If q and r are negative integers, which of the following statements must be true?
I. (-q)^r is positive.
II. (-q)^(-r) is positive.
III. q^(-r) is positive.
(A) None
(B) II only
(C) I and II
(D) I and III
(E) I, II and III
Rationale: Let's q = -2 and r = -3
I. (-q)^r = (2)^(-3) = 1/(2^3) --> Positive
II. (-q)^(-r) is positive. = 2^3 --> Positive
III. q^(-r) is positive. = -2^3 --> Negative
Answer: C
Answer: (C) I and II
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.4
(C) 1.2
(D) 1.5
(E) 1.1
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: (D) 1.5
Question: The sum of three consecutive odd numbers is always divisible by:
I. 2 II. 3 III. 5 IV. 6
(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and IV
(E) none of these
Rationale: Let the three consecutive odd numbers be (2x+1), (2x+3) and (2x+5).
Their sum = (6x=9)= 3 (2x+3), which is always divisible by 3.
ANSWER:B
Answer: (B) Only II
Question: What is the positive difference between the sum of the squares of the first 7 positive integers and the sum of the prime numbers between the first square and fourth square?
(A) 11
(B) 52
(C) 83
(D) 94
(E) 99
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +...+7^2 = 140
the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13=41.
So the difference between 41 and 140 is 99.
So the answer is (E).
Answer: (E) 99
Question: Radha bought a watch for Rs. 144 and got a percentage of profit equal to the cost price of the watch. What is the cost price of the watch?
(A) Rs. 72
(B) Rs. 78
(C) Rs. 80
(D) Rs. 90
(E) Rs. 92
Rationale: SP=144
CP=x
profit %=x
C.P.= (100/(100+gain%))*S.P.
x=(100/100+x) *144
x^2+100x=14400
x^2+180x-80x-14400=0
(x+180) (x-80)=0
x=-180
x=80
ANSWER:D
Answer: (D) Rs. 90
Question: The average of first ten prime numbers which are odd is?
(A) 15.9
(B) 15.7
(C) 15.1
(D) 15.8
(E) 15.3
Rationale: Sum of first 10 prime no. which are odd = 158
Average
= 158/10
= 15.8
Answer:D
Answer: (D) 15.8
Question: In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by?
(A) 16
(B) 8
(C) 4
(D) 1/8
(E) 1/64
Rationale: Say r=6 => V1 = 1/144
when r=3; V2 = 1/36
V2 = 36*V1.
Answer : C
Answer: (C) 4
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
(A) 12.8
(B) 12.6
(C) 12.5
(D) 12.2
(E) 12.1
Rationale: 1000*15 = 1200*x
x = 12.5.Answer: C
Answer: (C) 12.5
Question: The value of x is to be randomly selected from the integers from 1 to 9, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?
(A) 1/9
(B) 2/9
(C) 1/3
(D) 4/9
(E) 1/2
Rationale: y will only be negative for x=2.
(We can check the values from 1 to 9 to be certain.)
P(y is negative) = 1/9
The answer is A.
Answer: (A) 1/9
Question: Mangala completes a piece of work in 15 days, Raju completes the same work in 35 days. If both of them work together, then the number of days required to complete the work is
(A) 6 days
(B) 10 1/2 days
(C) 8 1/2 days
(D) 9 days
(E) 11 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 15 Ã— 35/50 = 10 1/2 days.
B
Answer: (B) 10 1/2 days
Question: 476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:
(A) 8 and 8
(B) 8 and 5
(C) 8 and 7
(D) 7 and 5
(E) 8 and 3
Rationale: Explanation:
Let the number be 476ab0
476ab0 is divisible by 3
=> 4 + 7 + 6 + a + b + 0 is divisible by 3
=> 17 + a + b is divisible by 3 ------------------------(i)
476ab0 is divisible by 11
[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11
=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)
Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.
if a=6 and b=2,
17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer
if a=8 and b=2,
17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)
[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer
if a=6 and b=5,
17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer
if a=8 and b=5,
17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1
[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2
Since these values satisfies both equation 1 and equation 2, this is the answer
Answer: D) 8 and 5
Answer: (D) 7 and 5
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission for each sale made. If each of her sales is for $2,000, what is the least number of sales she must make per year if she is not to lose money because of the job change?
(A) 57
(B) 133
(C) 178
(D) 377
(E) 378
Rationale: Lets say she sales x items so her commission will be : x * 2000*15/100 = 300x
Salary difference is: 85000 - 45000 = 40000
So commission must at least be equal to salary difference i.e. x = 40000/300= 133 (Approx).
Hence answer is B
Answer: (B) 133
Question: A train 80 m in length crosses a telegraph post in 6 seconds. The speed of the train is?
(A) 16 kmph
(B) 88 kmph
(C) 54 kmph
(D) 48 kmph
(E) 19 kmph
Rationale: S = 80/6 * 18/5
= 48 kmph
Answer: D
Answer: (D) 48 kmph
Question: At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 14th highest price and the 21st lowest price among the prices of the items sold, how many items were sold at the garage sale?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: There were 13 items sold at a higher price than the radio and 20 items sold at a lower price than the radio. Including the radio, there were 13 + 20 + 1 = 34 items sold.
The answer is B.
Answer: (B) 34
Question: Roger can read a book in k minutes. What part of the book can he read in 5 minutes? (k>8)
(A) 8+k
(B) 8/k
(C) k/8
(D) (k+ 8)/k
(E) (k-8) / k
Rationale: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer: E
Answer: (E) (k-8) / k
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 399 km
(B) 162 km
(C) 277 km
(D) 887 km
(E) 668 km
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.Answer: B
Answer: (B) 162 km
Question: Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 10:00 am and Pipe B at 11:00 am, at what time will the pool be full?
(A) 22:00
(B) 20:00
(C) 21:00
(D) 18:00
(E) 17:00
Rationale: Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 10:00 a.m and Pipe B at 11:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 11:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12
Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1
Therefore, it takes 10 hrs to fill the pool
As Pipe A started at 10:00 a.m, pool is full at 20:00 hrs
Answer : B
Answer: (B) 20:00
Question: Tarun got 30% concession on the labelled price of an article and sold it for Rs. 8750 with 25% profit on the price he bought. What was the labelled price ?
(A) 10000
(B) 22438
(C) 28789
(D) 10002
(E) 27910
Rationale: Explanation:
Cost Price = = Rs. 7000. Let the labelled price be Rs. x.
Then,
= Rs.10000
Answer: A) 10000
Answer: (A) 10000
Question: A basketball player succeeds with 50% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
(A) 0.585
(B) 0.625
(C) 0.75
(D) 0.875
(E) 0.925
Rationale: P(missing all 3 free throws) = 0.5^3 = 0.125
P(succeeding at least once) = 1 - 0.125 = 0.875
The answer is D.
Answer: (D) 0.875
Question: Commodious means ‘spacious’, large, voluminous and extensive.
(A) 22
(B) 28
(C) 277
(D) 199
(E) 11
Rationale: Answer:A
Answer: (A) 22
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4070. What is the difference between Rose ’s and Tom ’s share in the profit?
(A) s.340
(B) s.362
(C) s.370
(D) s.382
(E) s.390
Rationale: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 4070 × 1/11 = Rs.370.
C)
Answer: (C) s.370
Question: How many box's of length 40 Cm, width 30 Cm and height 10 Cm can be formed from a box of 6 m length, 4 m width and 2 m height.
(A) 2000
(B) 5000
(C) 7000
(D) 4000
(E) 8000
Rationale: (600×400×200)/(40×30×10) = 4000
Answer is D
Answer: (D) 4000
Question: One copy machine can make 30 copies a minute, and a second copy machine makes 15 copies a minute. If the two copiers work together, how long would it take them to make 900 copies?
(A) 15 minutes
(B) 20 minutes
(C) 25 minutes
(D) 30 minutes
(E) 35 minutes
Rationale: Total work done by both machines in a minute = 30 + 15 = 45 copies
Total number of copies required = 900
Time = 900/45 = 20 mins
Answer B
Answer: (B) 20 minutes
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 41 kmph. For how many minutes does the bus stop per hour?
(A) 7 min
(B) 8 min
(C) 14.4 min
(D) 10 min
(E) 11 min
Rationale: Due to stoppages, it covers 13 km less.
Time taken to cover 13 km =(13/54)x60 = 14.4 min
answer : C
Answer: (C) 14.4 min
Question: 50 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.
(A) 190
(B) 200
(C) 1225
(D) 220
(E) 230
Rationale: total no. of handshakes = 49+48+47+...+3+2+1 = 19*(19+1)/2 = 1225
or, if there are n persons then no. of shakehands = nC2 = 50C2 = 1225
Answer : C
Answer: (C) 1225
Question: 385, 462, 572, 396, 421, 671, 264
(A) 385
(B) 421
(C) 671
(D) 264
(E) None of these
Rationale: Solution
In each number except 421,the middle digit is the sum of the other two. Answer B
Answer: (B) 421
Question: An express traveled at an average speed of 120 km/hr, stopping for 4 min after every 85 kn. How long did it take to reach its destination 8400 km from the starting point?
(A) 5 hrs 21 min
(B) 4 hrs 21 min
(C) 6 hrs 41 min
(D) 7 hrs 32 min
(E) 4 hrs 34 min
Rationale: D
7 hrs 32 min
Time taken to cover 840 km = 840/120 = 7 hrs.
Number of stoppages = 840/85 - 1 = 8
Total time of stoppages = 4 * 8= 32 min
Hence, total time taken = 7 hrs 32 min.
Answer: (D) 7 hrs 32 min
Question: There are three leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
(A) 7 leopard and 3 sheep
(B) 4 leopard and 7 sheep
(C) 6 leopard and 4 sheep
(D) 5 leopard and 1 sheep
(E) 2 leopard and 1 sheep
Rationale: E
2 leopard and 1 sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: (E) 2 leopard and 1 sheep
Question: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =
(A)  3^7
(B)  3^8
(C)  3^14
(D)  3^28
(E)  3^30
Rationale: We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*3^7 we would have: sum=9*(2*3^7)=2*3^9=~3^10, so the actual sum is less than 3^10 and more than 3^7 (option A) as the last term is already more than that. So the answer is clearly B.
Answer: B.
Answer: (B)  3^8
Question: Find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 15 cm and 5 cm?
(A) 100 cm2
(B) 150 cm2
(C) 200 cm2
(D) 250 cm2
(E) 500 cm2
Rationale: 1/2 * 50(15 + 5)
= 500 cm2
Answer: E
Answer: (E) 500 cm2
Question: If (a-4)(b-2) =0, which of the following must be true ?
I. a=4 and b=2
II. if a is not = 4, then b=2
III. if a=4, then b is not=2
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: (a-4)(b-2)=0
So either a=4 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.
The answer is B.
Answer: (B) II only
Question: A clock shows the time as 10 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?
(A) 45 minutes
(B) 55 minutes
(C) 35 minutes
(D) 25 minutes
(E) 40 minutes
Rationale: there are 8 hours in between 10 a.m. to 6 p.m.
8*5=40 minutes.
ANSWER:E
Answer: (E) 40 minutes
Question: Working alone, machine X can manufacture 1,200 nails in 12 hours. Working together, machines X and Y can manufacture 1,200 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
(A) 3 9/17
(B) 5 1/3
(C) 7
(D) 7 1/7
(E) 8 4/7
Rationale: rate of machine x = 1200/12
(1200/12 + y)5=1200
y=700/5
700/5 * t = 1000
t=7 1/7
D.
Answer: (D) 7 1/7
Question: A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 11 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
(A) $54.00
(B) $64.80
(C) $90.00
(D) $100.80
(E) $123.20
Rationale: Correct Answer: E
The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.11 ($1120) = $123.20. The correct answer is E.
Answer: (E) $123.20
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 33 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 6 books, how many shelves does the bookcase have?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let x be the number of shelves.
11x - 33 = 7(x-1) + 6
4x = 32
x = 8
The answer is C.
Answer: (C) 8
Question: There are two numbers. If 70% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) 5/9
(B) 5/7
(C) 5/3
(D) 5/8
(E) 5/14
Rationale: Let the two numbers be x and y.
70/100 * x + y = 5/4y
=> 7/10 x = 1/4 y => x/y
= 5/14
Answer: E
Answer: (E) 5/14
Question: Find the one which does not belong to that group?
(A) 16
(B) 36
(C) 21
(D) 64
(E) 4
Rationale: Explanation:
16, 36, 64 and 4 are perfect squares but not 21.
Answer:C
Answer: (C) 21
Question: How many kg of pure salt must be added to 30kg of 2% solution of salt and water to increase it to a 10% solution?
(A) 8/3
(B) 9/7
(C) 7/4
(D) 5/2
(E) 6/7
Rationale: Amount salt in 30kg solution = 2*30/100 = 0.6 kg
Let x kg of pure salt be added
then(0.6+x)/(30+x)=10/100
60+100x=300+10x
90x = 240
x = 8/3
Answer is A
Answer: (A) 8/3
Question: The dimensions of a field are 10 m by 10 m. A pit 10 m long, 5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
(A) 2 m
(B) 3 m
(C) 4 m
(D) 5 m
(E) 1.5 m
Rationale: The volume of the earth removed is 10*5*4 = 200 m^3.
The remaining area of the field is 10*10 - 10*5 = 50 m^2.
200 m^3 of the earth evenly spread over the area of 50 m^2 will rise the height by (height) = (volume)/(area) = 200/50 = 4 m.
Answer: C
Answer: (C) 4 m
Question: One half of the staffs in a software company are programmers,quarter are testers,one-fifth are administrative and the other 50 are HR. How many workers total are there in the software company?
(A) 250
(B) 366
(C) 400
(D) 500
(E) 1000
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 50
x= 50*20= 1000
E is the answer.
Answer: (E) 1000
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 6000, the number of valid votes that the other candidate got, was:
(A) 2800
(B) 2700
(C) 2160
(D) 2200
(E) 2300
Rationale: C
Number of valid votes = 80% of 6000 = 4800.
Valid votes polled by other candidate = 45% of 4800
= (45/100 x 4800) = 2160.
Answer: (C) 2160
Question: Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit
(A) Rs. 8510
(B) Rs. 8620
(C) Rs. 8730
(D) Rs. 8820
(E) None of these
Rationale: Explanation:
=>(8000×(1+5/100)2)
=>8000×21/20×21/20
=>8820
Option D
Answer: (D) Rs. 8820
Question: The Speed of a boat in still water is 25 kmph. If it can travel 10 km upstream in 1 hr, What time it would take to travel the same distance downstream?
(A) 26 minutes
(B) 23 minutes
(C) 15 minutes
(D) 19 minutes
(E) 28 minutes
Rationale: Speed of boat in still water = 25 km/hr
Speed upstream = 10⁄1 = 10 km/hr
Speed of the stream = (25-10) = 15 km/hr
Speed downstream = (25+15) = 40 km/hr
Time taken to travel 10 km downstream = 10/40 hours=(10×60)/40= 15 minutes
Answer is C
Answer: (C) 15 minutes