mathewhe/aqua_rat huggingface dataset:
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is
(A) 5780 litres
(B) 5770 litres
(C) 5760 litres
(D) 5750 litres
(E) 5740 litres
Rationale: Explanation:
Work done by the inlet in 1 hour =
1/6−1/8=1/24
Work done by inlet in 1 min=1/24∗1/60=1/1440
=>Volume of 1/1440 part = 4 liters
Volume of whole = (1440 * 4) litres = 5760 litres.
Option C
Answer: (C) 5760 litres
Question: Find the term next in series ....
1, 1/2,3/2,2,5,1/3,16/3,15,12,1/4,25/4,?
(A) next number is 48
(B) 58
(C) 40
(D) 43
(E) 44
Rationale: [1,1/2,3/2,2], [5,1/3/16/3,15] ,[12,1/4,25/4,x]
1+1/2=3/2......1/1/2= 2
5+1/3=16/3.....5/1/3= 15
12+1/4=25/4....12/1/4=48
ANSWER:A
Answer: (A) next number is 48
Question: If the product of two numbers is 17820 and their H.C.F. is 12, find their L.C.M.
(A) 2574
(B) 2500
(C) 1485
(D) 1574
(E) None of these
Rationale: Explanation:
HCF * LCM = 17820, because we know
Product of two numbers = Product of HCF and LCM
LCM = 17820/12 = 1485
Option C
Answer: (C) 1485
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 9
(B) 9.6
(C) 10
(D) 8
(E) 12
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
ANSWER:D
Answer: (D) 8
Question: The length of a rectangle is increased by 20% and its breadth is decreased by 20%. What is the effect on its area?
(A) 1288
(B) 9600
(C) 1000
(D) 10000
(E) 2887
Rationale: 100 * 100 = 10000
120 * 80 = 9600
Answer: B
Answer: (B) 9600
Question: The sum of two numbers is 16. The difference is 0. What are the two numbers?
(A) 10-6
(B) 8-8
(C) 9-7
(D) 11-5
(E) 13-3
Rationale: 8+8 = 16
8 - 8 = 0
The Answer is B
Answer: (B) 8-8
Question: How many tiems do the hands of a clock coincide in day?
(A) 11
(B) 12
(C) 22
(D) 24
(E) None
Rationale: Sol.
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e. at 12 o’clock).
∴ The hands coincide 22 times in a day.
Answer C
Answer: (C) 22
Question: Which of the following is closer to √0.8+√0.05?
(A) 0.5
(B) 0.7
(C) 0.9
(D) 1.1
(E) 1.2
Rationale: √0.8+√0.05=approximately √0.81+√0.04=0.9+0.2=1.1. Hence, the correct answer is D.
Answer: (D) 1.1
Question: If Henry were to add 9 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
(A) 25
(B) 40
(C) 64
(D) 72
(E) 96
Rationale: 7/8x-3/4x=9galls
1/8*x=9gallons
x=72 gallons
Answer D
Answer: (D) 72
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 445 km
(B) 415 km
(C) 420 km
(D) 480 km
(E) 490 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420
ANSWER:C
Answer: (C) 420 km
Question: If the ratio of the ages of two friends A and B is in the ratio 3 : 5 and that of B and C is 3 : 5 and the sum of their ages is 147, then how old is B?
(A) 27 Years
(B) 75 Years
(C) 45 Years
(D) 49 Years
(E) 59 Years
Rationale: Explanation:
The ratio of the ages of A and B is 3 : 5.
The ratio of the ages of B and C is 3 : 5.
B's age is the common link to both these ratio. Therefore, if we make the numerical value of the ratio of B's age in both the ratios same, then we can compare the ages of all 3 in a single ratio.
The can be done by getting the value of B in both ratios to be the LCM of 3 and 5 i.e., 15.
The first ratio between A and B will therefore be 9 : 15 and
the second ratio between B and C will be 15 : 25.
Now combining the two ratios, we get A : B : C = 9 : 15 : 25.
Let their ages be 9x, 15x and 25x.
Then, the sum of their ages will be 9x + 15x + 25x = 49x
The question states that the sum of their ages is 147.
i.e., 49x = 147 or x = 3.
Therefore, B's age = 15x = 15 × 3 = 45
Answer: C
Answer: (C) 45 Years
Question: How many seconds will a 600 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) 11 sec
(B) 36 sec
(C) 77 sec
(D) 14 sec
(E) 12
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 = 600 * 3/50
= 36 sec.
Answer: B
Answer: (B) 36 sec
Question: Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took P.E. as an elective, 1/3 of the students took Theatre as an elective, and all of the other students took Music. In this year, 1/3 of the students who took P.E. and 1/4 of the students who took Theatre left school, other students did not leave, and no fresh student come in. What fraction of all students took P.E. or Music?
(A) 2/3
(B) 1/4
(C) 7/9
(D) 1/5
(E) 8/11
Rationale: Lets pick smart numbers. Total number of students: 12
P.E. (1/2): 6
Theatre (1/3): 4
Music (1/6): 2
After leaving school
P.E.: 4
Theatre: 3
Music: 2
New Total number of students: 9
P.E. and Music: 6
Answer 2/3 or A
Answer: (A) 2/3
Question: The events A and B are independent. The probability that event A occurs is a and the probability that event B occurs is b. Which of the following is equal to the probability that exactly one of the events A and B occurs?
(A) a − 2ab
(B) b − ab
(C) a + b − 2ab
(D) a + b −ab
(E) a + b
Rationale: Probability of A occuring = a , Probability of A NOT occuring = 1-a
Probability of B occuring = b , Probability of B not occurring = 1-b
Probability of atleast of one of A and B occuring = 1-(1-a)(1-b) =a+b -ab
D
Answer: (D) a + b −ab
Question: If 7/10 of a pencil is green, 4/5 of the remaining is gold and the remaining 1/2 is white, what is the total length of the pencil?
(A) 5
(B) 3
(C) 1
(D) 4
(E) 2
Rationale: Green is 7/10 Gold is 4/5 which can also be written as 8/10White is 1/2 which can also be written as 5/107/10 + 8/10 + 5/10= 2Answer is E) 2
Answer: (E) 2
Question: Vikram borrowed rupees 6450 at 5% simple interest repayable in 4 equal installments. what will be the annual installment payable by him?
(A) 1710
(B) 1810
(C) 1910
(D) 1860
(E) 1850
Rationale: Let the annual instalment be Rs. P.
Amount of ₹ 100 after 4 yr = 100 + (100 x 5 x 4)/100 = ₹ 120
∴ Present Value (PV) of ₹ 120 due after 4 yr = ₹ 100
Present Value (PV) of ₹ due after 4 yr = 100P/120 = 5P/6
Similary, PV of ₹ P due after 3 yr = 20P/23
PV of ₹ P due after 2 yr = 10P/11
PV of ₹ P due after 1 yr = 20P/21
∴ 5P/6 + 20P/23 + 10P/11 + 20P/11 = 6450
⇒ P = ₹ 1810
ANSWER:B
Answer: (B) 1810
Question: Which is odd one
10, 25, 45, 54, 60, 75, 80
(A) 10
(B) 45
(C) 54
(D) 60
(E) 75
Rationale: All numbers except 54 is multiple of 5.
answer :C
Answer: (C) 54
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 388
(B) 375
(C) 288
(D) 266
(E) 269
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer:B
Answer: (B) 375
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/29
(B) 2/28
(C) 2/21
(D) 2/22
(E) 2/26
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: (C) 2/21
Question: A trader has 30 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
(A) 3 and 27 kg
(B) 10 and 40 kg
(C) 15 and 27 kg
(D) 20 and 30 kg
(E) 40 and 30 kg
Rationale: Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 30/1+9 *1 = 3 kg
Quantity sold at 6% loss = 30/1+9 *9 = 27 kg
ANSWER:A
Answer: (A) 3 and 27 kg
Question: The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
(A) P(1 - 0.03x + 0.02x^2)
(B) P(1 - 0.03x + 0.0002x^2)
(C) P(1 - 0.03x + 0.002x^2)
(D) P(1 - 2x^2)
(E) P(1 - 3x + 2x^2)
Rationale: Let us say that P = 100 $ and x = 10 %
Now if there are two successive discounts of 10 % and 20 % then the effective discount percentage will be -10 - 20 + (-10) (-20)/100 = -30 + 2 = 28 %
Hence the new price will be 100 - 28 = 72
Hence by plugging in P = 100 and x = 10 the answer should be 72
A: P(1 - 0.03x + 0.02x^2) = 100 (1 - 0.3 + 2) = 100(2.7)
B: P(1 - 0.03x + 0.0002x^2) = 100 (1 - 0.3 + 0.02) = 100 (1 - 0.28) = 72 (BINGO!) (Let's still eliminate all other answer options - what if another one gives me 72)
C: P(1 - 0.03x + 0.002x^2) = 100 (1 - 0.3 + 0.2)
D: P(1 - 2x^2) = 100 ( 1 - 200)
E: P(1 - 3x + 2x^2) = 100 ( 1 - 0.2 + 200)
Hence the answer is B
Answer: (B) P(1 - 0.03x + 0.0002x^2)
Question: The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $22. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?
(A) 347.6
(B) 987.6
(C) 941.6
(D) 637.6
(E) 667.6
Rationale: Let the costs of each kg of mangos and each kg of rice be $a and $r respectively.
10a = 24r and 6 * 22 = 2r
a = 12/5 r and r = 66
a = 158.4
Required total cost = 4 * 158.4 + 3 * 66 + 5 * 22
= 633.6 + 198 + 110 = $941.60
C
Answer: (C) 941.6
Question: A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/7 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?
(A) x/3
(B) 5x/2
(C) 2x/3
(D) 3x/2
(E) 2x
Rationale: x/(x+y) = 2/7
7x = 2x+2y
5x = 2y
y = 5x/2
Answer B
Answer: (B) 5x/2
Question: The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 180 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 99
(C) 88
(D) 40
(E) 23
Rationale: Speed of the boat in still water = (100+180)/2 = 70 kmph. Speed of the stream = (180-100)/2 = 40 kmph. Answer:D
Answer: (D) 40
Question: At Joel’s bookstore, the current inventory is 30% historical fiction. Of the historical fiction books, 30% are new releases, while 40% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
(A) 4/25
(B) 9/37
(C) 2/5
(D) 8/15
(E) 2/3
Rationale: let there be 100 books in all
Historic fiction books = 30% of total = 30
Other books = 70
New historic fiction = 30% of 30 = 9
Other new books = 40% of 70 = 28
total new books = 37
fraction = 9/37
Ans: B
Answer: (B) 9/37
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 35150. What percentage of profit did he make?
(A) 22
(B) 27
(C) 58
(D) 26
(E) 11
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 35150
Profit(%) = (35150 - 22250)/22250 * 100 = 58%.Answer:C
Answer: (C) 58
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 288
(B) 2667
(C) 288
(D) 150
(E) 812
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time)
= (50/3 * 9) m = 150 m.
Answer: D
Answer: (D) 150
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 50
(B) 52.5
(C) 60
(D) 62.5
(E) 65
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80 = 52.5
ANSWER B
Answer: (B) 52.5
Question: Machine W can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A)  1/2
(B)  1/3
(C)  4/13
(D)  8/29
(E)  6/33
Rationale: Let the following be true:
W makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Answer: (C)  4/13
Question: Two trains 140 meters and 160 meters long are running in the same direction with speeds of 92 km/hr, 56km/hr. In how much time will the first train cross the second
(A) 37 sec
(B) 25 sec
(C) 30 sec
(D) 28 sec
(E) 32 sec
Rationale: Explanation:
Relative speed of the trains = (92 - 56) km/hr = 36 km/hr
= (36Ã— 5/18) m/sec = 10 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (140 + 160) m at 10 m /sec = (300/10) sec = 30 sec.
Answer: Option C
Answer: (C) 30 sec
Question: What is the are of an equilateral triangle of side 24 cm?
(A) 66âˆš3 cm2
(B) 74âˆš3 cm2
(C) 64âˆš3 cm2
(D) 64âˆš5 cm2
(E) 144âˆš3 cm2
Rationale: Area of an equilateral triangle = âˆš3/4 S2
If S = 24, Area of triangle = âˆš3/4 * 24 * 24 = 144âˆš3 cm2;
Answer:E
Answer: (E) 144âˆš3 cm2
Question: If m ≠ 1 and if nm/(n - m) = 1, what is the value of n in terms of m?
(A) m/(m+1)
(B) (m - 1)/m
(C) m/(1-m)
(D) (m + 1)/m
(E) (1 - m)/m
Rationale: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
C
Answer: (C) m/(1-m)
Question: If the L.C.M of two numbers is 450 and their product is 22500, find the H.C.F of the numbers.
(A) 50
(B) 30
(C) 125
(D) 25
(E) None of these
Rationale: H.C.F = (Product of the numbers) / (Their L.C.M) = 22500/450 = 50.
ANSWER:A
Answer: (A) 50
Question: The diagonals of a rhombus are 11 cm and 20 cm. Find its area?
(A) 329
(B) 288
(C) 150
(D) 238
(E) 110
Rationale: 1/2 * 11 * 20 = 110
Answer: E
Answer: (E) 110
Question: A and B working together could mow a field in 28days and with the help of C they could have mowed it in 21 days. How long would C take by himself?
(A) 68days
(B) 84days
(C) 90days
(D) 72days
(E) 50days
Rationale: Required answer = 28*21 / 28-21 = 84days
Answer is B
Answer: (B) 84days
Question: (2^2+4^2+6^2+.....+22^2)=?
(A) 5578
(B) 7996
(C) 9964
(D) 2024
(E) 1346
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x11)^2
=2^2 x (1^2+2^2+3^2+.......+11^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x11x12x23)
=(4x506)=2024
Answer is D
Answer: (D) 2024
Question: In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together?
(A) 120
(B) 360
(C) 1440
(D) 13440
(E) 4320
Rationale: The word 'SOFTWARE' contains 8 different letters.
when the vowels OAE are always together, they can be supposed to form one letter.
Thus, we have to arrange the letters SFTWR (OAE)
Now, 5 letters can be arranged in 6!=720 ways.
The vowels (OAE) can be arranged among themselves in 3!=6 ways.
Required number of ways =(720*6)=4320.
Answer is E
Answer: (E) 4320
Question: Which of the following ratios is greatest?
(A) 7 : 15
(B) 15 : 23
(C) 17 : 25
(D) 21 : 29
(E) None
Rationale: Sol.
7/15 = 0.466,
15/23 = 0.652,
17/25 = 0.68<,br/> 21/29 = 0.724,
Clearly, 0.724 is greatest and therefore, 21 : 29 is greatest.
Answer D
Answer: (D) 21 : 29
Question: In an examination 60% failed in Math and 40% failed in French. If 15% failed in both. What % of students passed in both.
(A) 25%
(B) 15%
(C) 20%
(D) 30%
(E) 10%
Rationale: Passed in Math = 100 - 60 = 40%
Passed in French = 100 - 40 = 60%
Students who passed Math or French = 100 -15 = 85%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-85 =15%
ANSWER:B
Answer: (B) 15%
Question: A towel, when bleached, lost 10% of its length and 20% of its breadth. What is the percentage decrease in area?
(A) 28%
(B) 30 %
(C) 44%
(D) 54%
(E) 64%
Rationale: percentage change in area
=(−10−20+(10×20)/100)%=−28%
i.e., area is decreased by 28%
ANSWER:A
Answer: (A) 28%
Question: A snooker tournament charges $40.00 for VIP seats and $10.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
(A) 190
(B) 180
(C) 170
(D) 160
(E) 148
Rationale: let no of sits in vip enclosure is x then x*40 +10( 320-x) =7500 or 25x = 7500 -3200 , x = 4300/25 =172
vip =172 general =320-172= 148
E
Answer: (E) 148
Question: A ladder 100 feet long is leaning against a vertical wall Its lower end is 60 foot from the bottom of the wall The side of the largest cubical box that can be placed between the wall and the ladder without disturbing the ladder is (to the nearest foot).
(A) 26
(B) 34
(C) 21
(D) 40
(E) 30
Rationale: if we consider the 2d image then the ladder , the wall and base making a triangle ,which height =80 foot
now we have to calculate the largest square inside the triangle.
let x be the side of square.
then,there are two triange of one height=x ,base=(60-x) and the other of height=(80-x) and base=x and a squre
by condition
(60-x)*x/2+x*(80-x)/2+x^2=80*60/2
x=34.2
ANSWER:B
Answer: (B) 34
Question: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders T will be:[/b]
(A) 3, 3, 2
(B) 3, 4, 2
(C) 5, 4, 3
(D) T=5, 5, 2
(E) 6, 4, 3
Rationale: Let the original number be X. Then by the successive dividing we have followings :
X=5A+2
A=7B+3
B=8C+4.
So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.
Now by dividing X by 8, 7, 5 successively we have followings :
X=8*(5*7C+19)+5
5*7C+19=7*(5C+2) + 5
5C+2=5C+2.
The remainders are, therefore, 5, 5, 2.
The answer is (D).
Answer: (D) T=5, 5, 2
Question: The true discount on a bill of Rs.2160 is Rs.360.The banker's discount is
(A) 430
(B) 431
(C) 432
(D) 433
(E) None of these
Rationale: Solution
P.W	= Rs.(2160 - 360)
= Rs. 1800
S.I on Rs. 2160	=Rs.(360/900 x 2160)
= Rs. 432.
Answer C
Answer: (C) 432
Question: Salesperson A's compensation for any week is $280 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?
(A) $5000
(B) $7000
(C) $9000
(D) $11,000
(E) $13,000
Rationale: 280+0.06(x-1000) = 0.08x
0.02x = 220
x = $11,000
The answer is D.
Answer: (D) $11,000
Question: In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 550. What is the sum of the last 5 integers in the sequence?
(A)  585
(B)  580
(C)  575
(D)  570
(E)  565
Rationale: All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+550=575
C
Answer: (C)  575
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
(A) 700
(B) 720
(C) 740
(D) 750
(E) 760
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
B
Answer: (B) 720
Question: Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 8% 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) 5:1
(B) 5:5
(C) 5:8
(D) 5:4
(E) 5:2
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 8% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 8/100 (6000 - x) = 480 - x/100
=> 480 - 1/100 x = 450 => x = 3000
Amount lent at 10% = 3000
Required ratio = 3000 : 3000 = 5:5
Answer:B
Answer: (B) 5:5
Question: In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?
(A) 225m
(B) 120m
(C) 220m
(D) 160m
(E) 180m
Rationale: Explanation:
Let X be the length of the course
according to the question,
A beats B by 15 metres and C by 29 metres
Applying this,
If A runs X metres, B runs (X-15) and C runs ( X-29) metres.
B and C together run, B runs X metres and C runs (X-15)
=> If B runs 1 metre, C runs X-15/X
=> B runs X-15 m, C runs (X-15/x) * (X-15)
APPLYING THIS,
X-29 = (X-15)(X-15) / X
Solving,
X2 -29X= X2 – 30 X + 225
X = 225
Thus, length of the course is 225 metres.
ANSWER A
Answer: (A) 225m
Question: Marketing executives for a certain chewing gum company projected a 30 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ?
(A) 53%
(B) 57.7%
(C) 62.5%
(D) 64%
(E) 75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 75;
Projected revenue = 130.
Actual/Projected*100=75/130*100 = 57.7%.
Answer: B.
Answer: (B) 57.7%
Question: one train has crossing a bridge of length 340 m in 42 sec and same train has crossing a another bridge of 500 m in 50 sec. what is the approximate speed of the train in km/hr?
(A) 60
(B) 64.8
(C) 72
(D) 76
(E) 78
Rationale: length of train = l m
speed of train = v m/s then
340+l = 42v
500+l = 50v
subtract, 8v = 160
=> v = 20m/s = 72 kmph
ANSWER:C
Answer: (C) 72
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 10 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
(A) 1 : 4 : 400
(B) 1 : 4 : 100
(C) 20 : 4 : 1
(D) 1:4:800
(E) 400 : 4 : 1
Rationale: millionaire 10 cents = 1/10 dollar ..therefore 1 dollar M = 200 dollar of B
therefore 4 dollar M = 800 dollar of B also 1 dollar Y
Y:M:B = 1:4:800
= 1:4:800
D
Answer: (D) 1:4:800
Question: Eshan and Mary each wrote two or three poem every day over a period of time eshan wrote 43 poems while Mary wrote 61. The number of days in this period is.....
(A) 19
(B) 21
(C) 20
(D) 19
(E) 18
Rationale: suppose, Eshan writes 2poems in first 18days 18*2=36.
2poems in next 2 days 2*2=4, 36+4=40
and 3poems in next 1day 1*3=3, 40+3=43
So, Ultimately he takes (18+2+1) = 21days to write 43 poems.
now suppose, Marry writes 3poems in 1st 18days 18*3=54
2poems in next 2days 2*2=4, 54+4=58
3poems in next 1 day 1*3=3, 58+3=61
So ultimately marry takes (18+2+1)= 21days to write 61poems.
ANSWER:B
Answer: (B) 21