mathewhe/aqua_rat huggingface dataset:
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3600. With the help of C, they completed the work in 3 days. How much is to be paid to C?
(A) s. 375
(B) s. 450
(C) s. 600
(D) s. 800
(E) s. 850
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1
C's share (for 3 days) = Rs.	(3 * 1/24 * 3600) =Rs.450
Answer = B
Answer: (B) s. 450
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 24 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: # of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D.
Bag A:
R:W:B = 2:6:9
Bag B
R:W = 1:4
6X + 4Y = 24 i.e 3X + 2Y = 12
X has to be odd to make an odd sum from the eq.
X = 2 , Y = 3 OR X = 4, Y = 0
So R can be 2X i.e 4 or 8.
Answer C
Answer: (C) 4
Question: A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain percentage.
(A) 4
(B) 2
(C) 1
(D) 3
(E) None of them
Rationale: cost price=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%
Answer is A.
Answer: (A) 4
Question: How many different ways are possible to arrange the letters of the word “MACHINE” so that the vowels may occupy only the odd positions?
(A) 800
(B) 125
(C) 348
(D) 576
(E) None of these
Rationale: Solution
MACHINE has 4 consonants and 3 vowels.The vowels can be placed in position no. 1, 3, 5, 7
⇒ Total number of ways possible = 4P3 = 24.
For each of these 24 ways the 4 consonants can occupy the other 4 places in 4P4 ways
⇒ Total = 24 × 24 = 576. Answer D
Answer: (D) 576
Question: The distance between a book store and a coffee shop is approximately 5.3 x 10^4 inches. Which of the following is closest to the distance between the book store and a coffee shop, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
(A) 1.4
(B) 2.2
(C) 1.9
(D) 2.5
(E) 2.9
Rationale: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the book store and a coffee shop is approximately 5.3 x 10^4 inches. To convert inches to kilometers, we need to multiply 5.3 x 10^4 inches by the ratio we just found out.
kilometers = 5.3 x 10^4 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 5.3x10^5/3.9x10^4 km
km = 1.36 = 1.4 km
Therefore, we can see that the closest answer is A.
Answer: (A) 1.4
Question: John's Ice Cream Shop sells ice cream at m cents a scoop. For an additional n cents, a customer can add 5 toppings to his or her sundae. How much would a sundae with 5 scoops and 5 toppings cost, in terms of m and n?
(A) 5m+5n
(B) 5m+2n
(C) 4m+n
(D) 5m+n
(E) 6m+n
Rationale: Answer D 5m+n
Answer: (D) 5m+n
Question: A watch was sold at a loss of 10%. If the watch was sold for $32 more, there would have been a gain of 6%. What is the cost price?
(A) $180
(B) $200
(C) $220
(D) $240
(E) $260
Rationale: 0.9x + 32 = 1.06x
0.16x = 32
x = 200
The answer is B.
Answer: (B) $200
Question: An error 17% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?
(A) 6.64%
(B) 36.89%
(C) 15.64%
(D) 26.64%
(E) 10.64%
Rationale: Percentage error in calculated area
=(17+17+(17Ã—17)/100)%=36.89%
ANSWER:B
Answer: (B) 36.89%
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $27. What is the cost of the carpet, in dollars per square yard? (1 square yard = 6 square feet)
(A) xy/297
(B) 11xy/3
(C) 3xy/11
(D) 297/(xy)
(E) 162/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 6.
The price per square yard is 27 / (xy/6) = 162/(xy).
The answer is E.
Answer: (E) 162/(xy)
Question: The fourth proportional to 12, 14 and 6 is?
(A) 2
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: (14*6)/12 = 7
Answer: C
Answer: (C) 7
Question: In the City ,there are 40% of the population lived in the North side at the Beginning of the Year and the rest lived in the South side. During the Same Year, the population grew by 6%. If the population in the North grew by 2%, by how much did the population grow in the South side?
(A) 8.6%
(B) 7.28%
(C) 9.2%
(D) 10.0%
(E) 8%
Rationale: Ratio of population in City = North:South :: 40%:60% = 2:3
Mean growth = 6%
North side: 2%
South side = ??
North-------------Average--------------South
2 __(3n)_____6.0%_____(2n)_____??
Since:
2+3n=6
n=4/3
Therefore:
South=6+2n
South=6+2(4/3)
The population increased in the south grew by 8.6%
Answer: (A) 8.6%
Question: In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?
(A) 4236
(B) 4306
(C) 4336
(D) 5336
(E) 4510
Rationale: Divisor = (5 x 46) = 230
10 x Quotient = 230 =	230	= 23
10
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
Option D
Answer: (D) 5336
Question: Pipe P can drain the liquid from a tank in 4/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?
(A) 9/29
(B) 8/23
(C) 3/4
(D) 17/29
(E) 3/8
Rationale: Suppose Q can drain in 1 hr. So, rQ = 1/1 = 1
So, rP = 1/[(4/4)rQ] = 4/4 =1
Also, rP = rR/(2/3) => 1 = rR/(2/3) => rR = 2/3
Let H is the time it takes to drain by running all 3 pipes simultaneously
So combined rate = rC = 1/H = 1 + 1 + 2/3 = 8/3 = 1/(3/8)
Thus running simultaneously, Pipe Q will drain 3/8 of the liquid.
Thus answer = E.
Answer: (E) 3/8
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 10%?
(A) 282
(B) 229
(C) 277
(D) 285
(E) 261.25
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 10)/100] = Rs. 261.25.
Answer:E
Answer: (E) 261.25
Question: Among the employees of a certain company, 53 percent of the employees are male and 47 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
(A)  0.3
(B)  0.4
(C)  0.5
(D)  0.6
(E)  0.7
Rationale: Much faster: draw 4 quadrants
______________Male (53%)_____Female (47%)
Married :__________70%____________50%
Not Married:_______30%____________50%
Therefore: the probability of picking one random person Not Married (he or she) is: 0,53 x 0,30 + 0,50 x 0,50 = 0,15 + 0,25 (approx.)
Solution: approx. 0,4 (answer B)
Answer: (B)  0.4
Question: (1/5)^r * (1/4)^18 = 1/(2(10)^35). What is r?
(A) 17
(B) 18
(C) 34
(D) 35
(E) 36
Rationale: We need to arrive at a common base. -->
(5)^(-r) * 2^(-36) = 2^(-36)*5^(-35)
5^(-r)=5^(-35)
-r=-35
r=35=D
Answer: (D) 35
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) 0.965D
(B) 0.760D
(C) 0.765D
(D) 0.865D
(E) 4.765D
Rationale: Explanation:
If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D
Answer: C
Answer: (C) 0.765D
Question: What is the least number which should be added to 5432 so that the sum is exactly divisible by 5, 6, 4, and 3?
(A) 16
(B) 22
(C) 28
(D) 34
(E) 40
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
When dividing 5432 by 60, the remainder is 32.
The number to be added = 60 - 32 = 28.
The answer is C.
Answer: (C) 28
Question: A , B , and C started a partnership business by investing $27,000 , $72,000 , and $81,000 respectively. At the end of the year , the profit was distributed among them. If C's share of profit is $27,000, what is the total profit?
(A) $80,000
(B) $90,000
(C) $60,000
(D) $120,000
(E) $40,000
Rationale: A:B:C = 27000:72000:81000 which is a ratio of 3:8:9.
Let the total profit be x.
x * 9/20 = 27000
x = 27000*20/9 = 60,000.
The answer is C.
Answer: (C) $60,000
Question: What is the square root of 400, divided by 2?
(A) 9
(B) 36
(C) 122
(D) 6
(E) 10
Rationale: Square root is a number times itself
Square root of 400=20, 20/2=10
(E)1
Answer: (E) 10
Question: A child buy 18 pencil and pay 100 rs. He pay 1 rs more for white pencil than brown pencil. How many white pencil He buy? and what is price of one white pencil
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: LET white pencil be x and brown be 18-x
let 1 brown pencil be y rs.
so, x(y+1)+(18-x)y=100
=>xy+x+18y-xy=100
=>x+18y=100
x=10 y=5
ans : 6
ANSWER:C
Answer: (C) 6
Question: If 1/(b – 2) = 1/(b + 2) + 1/(b – 1), which of the following is a possible value of b?
(A) 1
(B) 0
(C) -1
(D) -2
(E) 2
Rationale: Multiply by (b-2)*(b+2)*(b-1) throughout to get:
(b+2)*(b-1) = (b-2)*(b-1) + (b+2)(b-2)
Of the given options, only b=0 satisfies this.
Answer : B
Answer: (B) 0
Question: A wheel that has 2 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 49
(B) 4
(C) 12
(D) 3
(E) 27
Rationale: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 2 :: 21 : x 14 * x = 2 x 21
x =	(2 x 21)/14
x = 3.
Answer is D.
Answer: (D) 3
Question: From below option 27 is divisible by which one?
(A) A)4
(B) B)8
(C) C)9
(D) D)10
(E) E)911
Rationale: 27/9 = 3
C
Answer: (C) C)9
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes T of the competition are possible?
(A) 18
(B) 20
(C) 54
(D) 84
(E) 120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total T=84 outcomes
D
Answer: (D) 84
Question: 30 pens and 75 pencils were purchased for 570. If the average price of a pencil was 2.00, find the average price of a pen.
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (570 – 150) = 360
∴ Average price of a pen = 420⁄60 = 14
Answer E
Answer: (E) 14
Question: A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subjects has the same maximum marks, in how many subjects did he pass the exam?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: take the maximum mark in each sub as 100. qualify mark is 50.On a total dt fellow gets 60 x 5= 100.
We can write (10+9+8+7+6)a=300 => a=15/2
In 5 subjects he gets 75,67.5,60,52.5,45.
He passes in 4 subjects...
ANSWER:C
Answer: (C) 4
Question: The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people V who purchased only book A?
(A) 250
(B) 500
(C) 750
(D) 1000
(E) 1500
Rationale: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both,V= 1000 purchased A only. (This is much simpler to solve using the Venn diagram).
Correct answer is D. 1000
Answer: (D) 1000
Question: Rs. 6000 is lent out in two parts. IN that One part is lent at 7% p.a simple interest and the second one is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 5 : 7
(B) 5 : 1
(C) 6: 1
(D) 7 : 1
(E) 5 : 3
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 5000
Amount lent at 10% = 1000
Required ratio = 5000 : 1000 = 5 : 1
ANSWER:B
Answer: (B) 5 : 1
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
(A) 1/6
(B) 1/9
(C) 1/3
(D) 1/7
(E) 1/1
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: D
Answer: (D) 1/7
Question: If 0.5 : x :: 5 : 8, then x is equal to:
(A) A)1.12
(B) B)1.2
(C) C)1.25
(D) D)0.9
(E) E)0.8
Rationale: (x * 5) = (0.5 * 8)
x = 4/5
x = 0.8
Answer = E
Answer: (E) E)0.8
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
(A) 1.44% loss
(B) 14.4% profit
(C) 14.4% loss
(D) 0%
(E) None of these
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
ANSWER:A
Answer: (A) 1.44% loss
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) 0998
(B) 2899
(C) 1889
(D) 1500
(E) 2881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
Answer: D
Answer: (D) 1500
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
(A) 5
(B) 8
(C) 4
(D) 9
(E) 2
Rationale: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer:A
Answer: (A) 5
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 40.5 meters. How many times did the ball bounce?
(A) 3
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Division of total distance travelled will be 16+16+8+0.5
Ans:A
Answer: (A) 3
Question: In a particular state, 70% of the counties received some rain on Monday, and 50% of the counties received some rain on Tuesday. No rain fell either day in 20% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 70%
Rationale: 70 + 50 + 20 = 140%
The number is 40% above 100% because 40% of the counties were counted twice.
The answer is B.
Answer: (B) 40%
Question: Find the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectively
(A) 125
(B) 127
(C) 129
(D) 131
(E) 141
Rationale: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (1661 - 10) and (2045 -13)
= HCF (1651, 2032) = 127
Option B
Answer: (B) 127
Question: The price of a car is marked at $10,000. If the car has successive discounts of 25%, 20% and 5%, then at what price does a customer buy the car?
(A) $5100
(B) $5300
(C) $5500
(D) $5700
(E) $5900
Rationale: 0.95*0.8*0.75*10000 = $5700
The answer is D.
Answer: (D) $5700
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
(A) s. Rs.10,500, Rs. 13,500, Rs. 16,500
(B) s. 10,600, Rs. 13,500, Rs. 96,500
(C) s. 10,500, Rs. 73,500, Rs. 16,500
(D) s. 10,500, Rs. 18,500, Rs. 16,500
(E) s. 40,500, Rs. 13,500, Rs. 16,500
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer:A
Answer: (A) s. Rs.10,500, Rs. 13,500, Rs. 16,500
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140
(B) 287
(C) 1267
(D) 127
(E) 212
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: A
Answer: (A) 140
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 24
(B) 35
(C) 64
(D) 68
(E) 90
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: If 10% of x = 20% of y, then x:y is equal to?
(A) 2:6
(B) 2:1
(C) 7:1
(D) 2:8
(E) 2:2
Rationale: 10% of x = 20% of y
10x/100 = 20y/100 => x/10 = y/5
x/y = 10/5 = 2/1
x:y = 2:1.
Answer:B
Answer: (B) 2:1
Question: What is x if x + 2y = 10 and y = 3?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Substitute y by 3 in x + 2y = 10
x + 2(3) = 10
x + 6 = 10
If we substitute x by 4 in x + 6 = 10, we have 4 + 6 = 10. Hence
x = 4 correct answer B
Answer: (B) 4
Question: What is the total number of integers between 2 and 38 that are divisible by 4?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 11
Rationale: 4, 6, 8, ..., 32,36
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (36 - 4) / (4)+ 1 = 32/4 + 1 = 8 + 1 = 9
Answer is B
Answer: (B) 9
Question: There are 18 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
(A) 800
(B) 380
(C) 360
(D) 478
(E) 566
Rationale: The total number of stations= 20
From 20 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 20P2 ways.
20P2= 20*19= 380
ANSWER:B
Answer: (B) 380
Question: Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 30 machines produce in 6 minutes?
(A) 1344
(B) 3360
(C) 8400
(D) 12600
(E) 67200
Rationale: 8 machines produce 560 in 1 min
8 machines produce 560* 6 in 6 min
30 machine produce 560*6*(30/8) in 6 minutes
560*6*30/8=12600 answer is D.
Answer: (D) 12600
Question: The side of a square is increased by 5% then how much % does its area increases?
(A) 15.00 %
(B) 10.25 %
(C) 10.00 %
(D) 12.25 %
(E) 12.50 %
Rationale: a = 100 a2 = 10000
a = 105 a2 = 11025
----------------
10000 --------- 1025
100 -------? => 10.25 %
Answer:B
Answer: (B) 10.25 %
Question: The value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4)
(A) 8/(1-x^8)
(B) 4x/(1+x^2)
(C) 4/(1-x^6)
(D) 4/(1+x^4)
(E) 4x/(1-x^4)
Rationale: Highlighted part has mistake as the exponent of x must be 4 in last term
CORRECT QUESTION ISThe value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) = ?
Solution is as mentioned below...
one more way that could get the answer in the type of eqn and choices given is to substitute some value for x...
0 would be better as the eq has constant term free of term 'x'..
the Eq gives us 8 as the ans , as also only choice A..
Answer: (A) 8/(1-x^8)
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 7 sec
(B) 5 sec
(C) 9 sec
(D) 6 sec
(E) 1 sec
Rationale: T = 60/36 * 18/5
= 6 sec
Answer:D
Answer: (D) 6 sec
Question: 987.650 - ? + 56.98 = 126.654
(A) A)899.015
(B) B)752.804
(C) C)714.642
(D) D)629.906
(E) 917.976
Rationale: Explanation:
917.976
Answer: Option E
Answer: (E) 917.976
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
(A) 1 13/17 hours
(B) 2 8/11 hours
(C) 3 9/17 hours
(D) 4 1/2 hours
(E) NONE
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
ANSWER:C
Answer: (C) 3 9/17 hours
Question: What percent of 5 letter combinations that can be made from the letters of the word SERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?
(A) 20%
(B) 23.8%
(C) 25%
(D) 30.2%
(E) 35%
Rationale: a) noof combinations when all 5 letters are different = 7*6*5*4*3
b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3
b/a = 5/21= 0.238
B
Answer: (B) 23.8%
Question: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 4x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: The big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 2, and 4x – 2 are ALLintegers
For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.
Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers
When x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 2, and 3(3) – 2.
When we evaluate these terms we get: 4, 6, 3, 5 and 10
Rearrange to get: 3, 4, 5, 6, 10. So, when x = 3, we getconsecutive integers.
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)
Answer:
C
Answer: (C) 5
Question: 1/2+[(2/6*6/32)+1]-9/16=
(A) 29/16
(B) 19/16
(C) 15/16
(D) 9/13
(E) 0
Rationale: 1/2 - [(2/6*6/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: (E) 0
Question: A baseball card decreased in value 20% in its first year and 30% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 28%
(B) 30%
(C) 32%
(D) 36%
(E) 44%
Rationale: consider the initial value of the baseball card as $100
After first year price = 100*0.8 = 80
After second year price = 80 *0.7 = 56
final decrease = [(100 - 56)/100] * 100 = 44%
correct answer - E
Answer: (E) 44%
Question: If A got 70 marks and B got 80 marks, then what percent of A's mark is B's mark?
(A) A)60%
(B) B)80%
(C) C)65%
(D) D)87.5%
(E) of these
Rationale: A's marks =80 ; B's marks = 70.
Let x% of A = B => x/100 * 80 = 70
=> x = (70 * 100)/80 =87.5
B's marks is 87.5% of A's marks.
ANSWER:D
Answer: (D) D)87.5%
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xz is even
2. (z-x)(y-x+1) = 4
3. xy is odd
(A) I only
(B) II only
(C) II only
(D) I and II only
(E) I, II, and III
Rationale: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1can not be ascertain as is not related to y directly ---not true
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.
So, II are always true and hence answer is
C
Answer: (C) II only