mathewhe/aqua_rat huggingface dataset:
Question: A train traveling at 144 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds. What is the length of the platform in meters?
(A) 240 meters
(B) 360 meters
(C) 480 meters
(D) 600 meters
(E) Cannot be determined
Rationale: Answer
Distance covered by the train when crossing a man and when crossing a platform
When a train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.
However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.
The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover. i.e., length of the platform.
Compute length of platform
Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 144 kmph * 12 seconds
Convert 144 kmph into m/sec
1 kmph = 5/18 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 144 kmph = 5/18∗144 = 40 m/sec
Therefore, length of the platform = 40 m/s * 12 sec = 480 meters.
Choice C
Answer: (C) 480 meters
Question: Difference between the length &breadth of a rectangle is 10 m. If its perimeter is 80 m, then its area is??
(A) 2000 m^2
(B) 2340 m^2
(C) 375 m^2
(D) 2556 m^2
(E) 2534 m^2
Rationale: We have: (l - b) = 10 and 2(l + b) = 80 or
(l + b) = 40
2 l = 50 => l = 25 & b = 15
Area = 25 * 15 = 375 m^2
Answer : C
Answer: (C) 375 m^2
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
(A) 23/35
(B) 23/36
(C) 23/18
(D) 23/17
(E) 23/12
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer:A
Answer: (A) 23/35
Question: What values of 'x' will be the solution to the inequality 15x - 2/x > 1?
(A) x > 0.4
(B) x < 1/3
(C) -1/3 < x < 0.4, x > 15/2
(D) -1/3 < x < 0, x > 2/5
(E) x < --1/3 or x > 2/5
Rationale: Explanatory Answer
We can rewrite the above inequality as 15x - 2/x- 1 > 0
i.e., 15x2−2−x/x> 0
i.e., 15x2−6x+5x−2/x> 0
Factorize the quadratic expression: (5x−2)(3x+1)/x > 0
The above inequality will hold good if the numerator and denominator are both positive or are both negative.
Possibility 1: When (5x - 2)(3x + 1) > 0 and x > 0
This will hold true for values of 'x' that do not lie between -1/3 and 2/5 and for x > 0.
Combining all these conditions, we get x > 2/5
Possibility 2: When (5x - 2)(3x + 1) < 0 and x < 0.
This will hold true for the following values of 'x': -1/3 < x < 2/5 and x < 0.
Combining, we get -1/3< x < 0.
Therefore, the range of values of x for which the above inequality will hold true is: -1/3 < x < 0 ∪∪ x > 2/5
Choice D
Answer: (D) -1/3 < x < 0, x > 2/5
Question: In case K is the only individual sewing on committee B, which among the following shouldserve on committee A?
(A) V and U
(B) V and T
(C) U and S
(D) L and M
(E) T and U
Rationale: L and M should serve on A
ANSWER:D
Answer: (D) L and M
Question: What is the sum of digits of (5!*4!*3!*2! - 144*120)/5!
(A) 22
(B) 4
(C) 12
(D) 3
(E) 7
Rationale: (5!*4!*3!*2! - 144*120)/5!
=(5!*4!*3!*2! - 24*6*5!)/5!
=(5!*4!*3!*2! - 4!*3!*5!)/5!
=5!*4!*3!(2!-1)/5!
=120
Sum of digits=3
Answer D
Answer: (D) 3
Question: Find the distance covered by a man walking for 42 min at a speed of 10km/hr?
(A) 7km
(B) 3km
(C) 4km
(D) 5km
(E) 6km
Rationale: Distance = 10*42/60 = 7 km
Answer is A
Answer: (A) 7km
Question: Which expression has the greatest value?
(A) 1977452/1977455
(B) 1982466/1982469
(C) 1982487/1982490
(D) 1982456/1982459
(E) 1982465/1982468
Rationale: The difference between each numerator/denominator pair is three.
The largest expression (which in this case will also be the closest to one) is the expression where '3' is the smallest fraction of the numerator (or the denominator).
The largest numerator is 1982487, or C, and this will give an expression with a value closest to one.
We can also demonstrate that this approach works with some simple logic. Taking numerator/denominator pairs that differ by three...
1/4 = 0.25
2/5 = 0.4
3/6 = 0.5
...
27/30 = 0.9
...
1982487/1982490 = 0.999998486...
ANSWER:C
Answer: (C) 1982487/1982490
Question: If positive integer k is divided by 14, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4
(A) None
(B) I
(C) II
(D) III
(E) I and II only
Rationale: k = 14m+2 = 2(7m+1)
I. k + m = 2(17m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Answer: (A) None
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 44.5 meters. How many times did the ball bounce?
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Division of total diatance travelled will be 16+16+8+4+0.5
Ans: 4
Answer: (A) 4
Question: A can do a work in 24 days and B can do it in 8 days. In how many days A and B can do the work?
(A) 20 days
(B) 10 days
(C) 6 days
(D) 8 days
(E) 7 days
Rationale: Explanation:
A's 1day's work = 1/24
B's 1day's work = 1/8
They work together = 1/24 + 1/8 = 6 days
Answer: Option C
Answer: (C) 6 days
Question: A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
(A) $4,040
(B) $4,120
(C) $1,960
(D) $4,920
(E) $1,400
Rationale: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.
Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $5,000-$880=$4,120.
Answer: B.
Answer: (B) $4,120
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
(A) 32
(B) 4/7
(C) 6/15
(D) 1/26
(E) 8/16
Rationale: Explanation:
Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) =n(E)/n(S)=2/52=1/26
Answer: D
Answer: (D) 1/26
Question: What is the ratio whose term differ by 50 and the measure of which is 2/7?
(A) A)32:23
(B) B)16:56
(C) C)71:85
(D) D)20:70
(E) E)41:52
Rationale: Let the ratio be x:(x+50)
Then, x/(x+50) = 2/7
x=20
required ratio = 20:70
Answer is D
Answer: (D) D)20:70
Question: The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 65.0. What is the quiz score of the student who dropped the class?
(A) a) 10
(B) b) 25
(C) c) 40
(D) d) 55
(E) e) 70
Rationale: Total Score of 16 students is 16*62.50 = 1000
Total Score of 15 students is 15*65 = 975
So, the score of the person who left is 25 ( 1000 - 975 )
Answer will be (B)
Answer: (B) b) 25
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 38029
(B) 38000
(C) 38028
(D) 38009
(E) 38019
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: (B) 38000
Question: If $1092 are divided between worker A and worker B in the ratio 5:8,what is the share that worker B will get?
(A) 60.32%
(B) 61.54%
(C) 62.21%
(D) 62.76%
(E) 63.87%
Rationale: Worker B will get 8/13 = 61.54%
The answer is B.
Answer: (B) 61.54%
Question: The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 1/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
(A) 1/4
(B) 9/10
(C) 5/9
(D) 9/14
(E) 5/6
Rationale: Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (2/3)*x
no of books per shelf on 2nd floor = (1/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (2/3)*x*(1/6)*y = (1/9)*xy
fraction of library books on first floor = (xy)/(xy + (1/9)*xy)
=1 / (1+(1/9))
=9/10
So B
Answer: (B) 9/10
Question: The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length E of a cube whose surface area is equal to 6z?
(A) E=16
(B) E=8√2
(C) E=8
(D) E=2√2
(E) (√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.
The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (D).
Answer: (D) E=2√2
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
(A) 52.6
(B) 52.9
(C) 52.8
(D) 52.1
(E) 52.2
Rationale: 42/360 * 22/7 * 12 * 12 = 52.8 m2
Answer: C
Answer: (C) 52.8
Question: A straight line in the xy- plane has y-intercept of 79 and slope of 6. On this line the y-coordinate of the point is 14, then what is the X-coordinate of the point?
(A) 11
(B) -10.83
(C) 71
(D) 20.83
(E) -12
Rationale: Eq of line = Y = MX +C
C= 79
M=6
Y=14
Substitute given:
X = (Y - C) / M = (14 - 79) / 6 = -65/6 = -10.83
correct option is B
Answer: (B) -10.83
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
(A) 3
(B) 3.2
(C) 3.6
(D) 3.8
(E) 3.5
Rationale: 3.6
Option 'C'
Answer: (C) 3.6
Question: A car covers a distance of 624 km in 4 hours. Find its speed?
(A) 104 kmph
(B) 126 kmph
(C) 156 kmph
(D) 174 kmph
(E) 101 kmph
Rationale: 624/4
=156 kmph
Answer:C
Answer: (C) 156 kmph
Question: 7500 + (1250 / 50)
(A) 7500
(B) 7525
(C) 7550
(D) 8000
(E) None of these
Rationale: Explanation:
As per BODMAS rule first we will solve the terms in the bracket then other.
= 7500 + (25) = 7525
Option B
Answer: (B) 7525
Question: A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p?
(A) 12
(B) 33 1/3
(C) 36
(D) 44
(E) 50
Rationale: Premium in 1997 = n;
Premium in 1998 = n(1+p/100);
Premium in 1999 = 5/6*n(1+p/100);
Premium in 2000 = 5/6*5/6*n(1+p/100).
Given that premium in 2000 = 5/6*5/6*n(1+p/100)=n --> 5/6*5/6*(1+p/100)=1 --> 1+p/100=36/25 --> p/100=11/25=44/100 --> p=44.
Answer: D.
Answer: (D) 44
Question: Which of the following is equal to the cube of a non-integer?
(A) –64
(B) –1
(C) 8
(D) 9
(E) 27
Rationale: All except 9 is cube of non integer as it is square of 3.
A. –64 = -4*-4*-4-- OUT
B. –1 = -1*-1*-1 -- OUT
C. 8 = 2*2*2 -- OUT
D. 9 -- Left One. Hence the answer
E. 27 = 3*3*3 -- OUT
ANSWER:D
Answer: (D) 9
Question: Two sides of a triangle have lengths x and e and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to e ?
(A) a) 2 : 3
(B) b) 3 : 4
(C) c) 4 : 3
(D) d) 3 : 2
(E) e) 2 : 1
Rationale: Ahhhh....my bad. Thank you, you're correct. 8x = 6e --> x/e = 3/4.
Actually B is the right answer.
Answer: (B) b) 3 : 4
Question: Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.11. How much did the meal cost without the tip?
(A) $28.98
(B) $29.91
(C) $30.40
(D) $30.60
(E) $30.85
Rationale: The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $36.11:
1.15x = 36.11
Divide both sides by 1.15:=>x=36.11/1.15=31.40
correct answer C)$31.40
Answer: (C) $30.40
Question: A amount doubles itself in 15 years. what is the rate of interest?
(A) 20/3 %
(B) 10/3 %
(C) 40/3 %
(D) 50/3 %
(E) 70/3 %
Rationale: let amount be x & rate of interest be r% annual then
(2x-x)=(x*15*r)/100
=> 15r = 100
=> r=20/3 %
ANSWER:A
Answer: (A) 20/3 %
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 15 different models of televisions, what is the minimum number of letters that must be used to make the codes?
(A) 6
(B) 7
(C) 4
(D) 9
(E) 10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥15. The smallest n which fulfills this condition is n = 4.
Answer C
Answer: (C) 4
Question: The number of stamps that P and Q had were in the ratio of 7:3 respectively. After P gave Q 13 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 5:4. As a result of the gift, P had how many more stamps than Q?
(A) 10
(B) 25
(C) 40
(D) 65
(E) 90
Rationale: P started with 7k stamps and Q started with 3k stamps.
(7k-13)/(3k+13) = 5/4
28k - 15k = 117
k = 9
P has 7(9) - 13 = 50 stamps and Q has 3(9)+13 = 40 stamps.
The answer is A.
Answer: (A) 10
Question: Solution Y is 30 percent liquid X and 70 percent water. If 3 kilograms of water evaporate from 8 kilograms of solution Y and 3 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
(A) 35%
(B) 37%
(C) 41.3%
(D) 42%
(E) 45%
Rationale: In 8 kilograms of solution Y there are 0.3*8=2.4 kilograms of solution X;
After 3 kilograms of water are replaced by 3 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*3=0.9 kilograms of solution X are added, so in the new solution of 8 kilograms there are 2.4+0.9=3.3 kilograms of solution X, which is 3.3/8*100=41.3% of this new solution.
Answer: C.
Answer: (C) 41.3%
Question: 40% of a number is added to 120, the result is the same number. Find the number?
(A) 400
(B) 288
(C) 1687
(D) 997
(E) 121
Rationale: (40/100) * X + 120 = X
2X = 400
X = 200
Answer:A
Answer: (A) 400
Question: The average of first 22 natural numbers is?
(A) 11.6
(B) 11.5
(C) 12.9
(D) 15.4
(E) 15.1
Rationale: Sum of 22 natural no. = 506/2 = 253
Average = 253/22 = 11.5
Answer:B
Answer: (B) 11.5
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
(A) 18 years
(B) 20 years
(C) 24 years
(D) 32 years
(E) 34 years
Rationale: Explanation:
Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
ANSWER IS A
Answer: (A) 18 years
Question: Pointing to a photograph, a lady tells Pramod, "I am the only daughter of this lady and her son is your maternal uncle." How is the speaker related to Pramod's father
(A) Sister-in-law
(B) Wife
(C) Either (a) or (b)
(D) Neither (a) nor (b)
(E) Either B) or (A)
Rationale: Explanation:
Clearly, the speaker's brother is Pramod's maternal uncle. So, the speaker is Pramod's mother or his father's wife
Answer: B
Answer: (B) Wife
Question: Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
(A) 29
(B) 30
(C) 30.5
(D) 31
(E) 32
Rationale: to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B
Answer: (B) 30
Question: If two letters are chosen at random (without replacement) from the word HORSEBACK, what is the probability that none of the letters are vowels?
(A) 4/9
(B) 5/9
(C) 5/12
(D) 7/24
(E) 11/36
Rationale: The number of ways to choose two letters is 9C2 = 36
The number of ways to choose two consonants is 6C2 = 15.
P(no vowels) = 15/36 = 5/12
The answer is C.
Answer: (C) 5/12
Question: You collect baseball cards. Suppose you start out with 11. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
(A) 12
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: Solution
Start with 11 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 11 + 1 which is 6,
so you're left with 11 - 6 = 5.
Peter takes 1 baseball card from you: 5 - 1 = 4 baseball cards.
Paul triples the number of baseball cards you have: 4 Ã— 3 = 12 baseball cards.
So you have 12 at the end.
Correct answer : A
Answer: (A) 12
Question: Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3.
(A) 131
(B) 197
(C) 207
(D) 219
(E) 227
Rationale: Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3.
Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131.
ANSWER:A
Answer: (A) 131
Question: A two-digit number is seven times the sum of its digits. If each digit is increased by 2, the number thus obtained is 4 more than six times the sum of its digits. Find the number.
(A) 42
(B) 24
(C) 48
(D) Data inadequate
(E) None of these
Rationale: Let the two-digit number be l0 x + y.
10x + y = 7(x + y) Þ x = 2y...(i)
10(x + 2) + y + 2 = 6(x + y + 4) +4
or 10x + y + 22 = 6x + 6y + 28 Þ 4x – 5y = 6 ... (ii)
Solving equations (i) and (ii), we get x = 4 and y = 2
Answer A
Answer: (A) 42
Question: Ross has 20 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
(A) 3 ; 5.
(B) 3 ; 6.
(C) 3 ; 7.
(D) 3 ; 8.
(E) 3 ; 9.
Rationale: Total shirts = 20
Green shirts = 3/4*20 = 15, Non green shirts = 5
Shirts without button = 1/10*20 = 2, shirts with button = 18
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 5
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 5 - 2 = 3
Hence the range would be (3, 5)
Correct Option: A
Answer: (A) 3 ; 5.
Question: Consider an equilateral triangle 4ABC with unit side length. Let M be the midpoint of side
AB. A ball is released in a straight line from M and bounces o the side BC at a point D.
Then, it bounces o the side CA at a point E and lands exactly at B. By the law of re
ection,
we have \BDM = \CDE and \CED = \AEB. Calculate MD + DE + EB, the distance
that the ball travels before reaching B.
(A) √12/2
(B) √11/2
(C) √13/2
(D) √14/2
(E) √17/2
Rationale: The solution can be obtained by re
ecting the triangle across edge CB to obtain
another equilateral triangle 4A0CB, and then across A0C to get 4A0B0C. The length of the
line MB0 is the minimum distance from M to the vertex B that hits both sides BC and CA0.
The length of the line segment BB0 is
√3/2
Thus, the length of MB =√1+3/4=√13/2
correct answer C
Answer: (C) √13/2
Question: A firm has 4 senior partners and 6 junior partners. How many different groups D of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
(A) 48
(B) 100
(C) 120
(D) 288
(E) 600
Rationale: What seems to work as well, though its tougher to come up with this solution:
(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.
Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.
Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.
Now you just need to divide the answer (600) by the number of different positions (=3!) and get D=600/6=100B
Answer: (B) 100
Question: A man's speed with the current is 30km/hr and the speed of the current is 5 km/hr. The man's speed against the current is
(A) 10 km/hr
(B) 20 km/hr
(C) 25 km/hr
(D) 30 km/hr
(E) 35 km/hr
Rationale: Explanation:
Speed of man with the current = 30 km/hr
Speed of current = 5
Since, Speed of current + speed of man = 30
5 + speed of man = 30
Speed of man = 25 km/hr
man's speed against the current is = speed of man - speed of current = 25 - 5 = 20 km/hr
Answer: Option B
Answer: (B) 20 km/hr
Question: (786×74) ÷ ? = 1211.75
(A) 4.8
(B) 48
(C) 58
(D) 68
(E) 48
Rationale: Explanation:
58164/x = 1211.75 => x = 58164/1211.75 = 48
Answer: Option B
Answer: (B) 48
Question: A store’s selling price of $2240 for a certain computer would yield a profit of 40 percent of the store’s cost for the computer. What selling price would yield a profit of 60 percent of the computer’s cost?
(A) 	$2400
(B) 	$2464
(C) 	$2560
(D) 	$2732
(E) 	$2800
Rationale: 1.4x = 2240
x=2240/1.4
so, 1.6X = 2240*1.6/1.4= 2560
Answer:- C
Answer: (C) 	$2560
Question: Using all the letters of the word "NOKIASE", how many words can be formed, which begin with N and end with A?
(A) 8
(B) 120
(C) 9
(D) 3
(E) 1
Rationale: There are five letters in the given word.
Consider 7 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 5! ways.
The number of words = 5! = 120.
Answer:B
Answer: (B) 120
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick. The thickness of the bottom is:
(A) 90 cm
(B) 6 dm
(C) 1 m
(D) 1.1 cm
(E) None of these
Rationale: Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (160 - x)] = 8000 × 1000
=> 320 × 250 × (160 - x) = 8000 × 1000
=> (160 - x) = 8000×1000/320=
100
=> x = 60 cm = 6 dm.
Answer: B
Answer: (B) 6 dm
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
(A) 290 sq cm
(B) 800 sq cm
(C) 209 sq cm
(D) Cannot be determined
(E) 200 sq cm
Rationale: Explanation:
Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: Option D
Answer: (D) Cannot be determined