mathewhe/aqua_rat huggingface dataset:
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
(A) XB < YD
(B) XB < YD
(C) AX > XB
(D) AX < XB
(E) CY < AB
Rationale: A------X--B
C--Y------D
CY < AB.
Answer: E.
Answer: (E) CY < AB
Question: In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the each share of profit?
(A) 7800
(B) 8000
(C) 8200
(D) 8400
(E) 8600
Rationale: Given A=45000 B=30000 C=22500
A:B:C= 450:300:225
As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees
But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital,
So A= 450*4+ 225*9= 1800+2025= 3825
Similarly, B= 300*13=3900
Similarly,C= 225*13= 2925
Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39
C's share=39/142(28400)=7800
ANSWER:A
Answer: (A) 7800
Question: A, B and C rents a pasture for Rs.638. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 198
(C) 676
(D) 156
(E) 122
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 638= 198
Answer: B
Answer: (B) 198
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 55, what is the compound interest on the same sum at the rate and for the same time?
(A) s. 56.37
(B) s. 53.22
(C) s. 56.219
(D) s. 51.18
(E) s. 51.11
Rationale: Explanation:
Sum = (55 * 100) / (2 * 5) = Rs. 550
Amount = [550 * (1 + 5/100)2] = Rs. 606.375
C.I. = (606.375 - 550) = Rs. 56.37
Answer:A
Answer: (A) s. 56.37
Question: If an amount of Rs 41,800 is distributed equally
amongst 22 persons, how much amount would each
person get?
(A) Rs 1900
(B) Rs 2000
(C) Rs 745
(D) Rs 765
(E) None
Rationale: Required amount =41800/22 = Rs 1900
Answer A
Answer: (A) Rs 1900
Question: The simple interest on a sum of money will be Rs.800 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 8981
(B) 3799
(C) 1200
(D) 1600
(E) 1732
Rationale: P --- 10 ---- 800
P --- 5 ----- 400
3P --- 5 ----- 1200
------
=> 1600
Answer: D
Answer: (D) 1600
Question: Find the simple interest on Rs.620 for 10 months at 10 paisa per month?
(A) 277
(B) 620
(C) 640
(D) 678
(E) 121
Rationale: I = (620*10*10)/100 = 620
Answer: B
Answer: (B) 620
Question: You collect coins. Suppose you start out with 18. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 11
Rationale: Solution
Start with 18 coins.
Sharon takes 3 coins from you: 18 - 3 = 15 coins.
Steven takes 4 coins from you: 15 - 4 = 11 coins.
So you have 11 at the end.
Correct answer : E
Answer: (E) 11
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 8 sec. What is the length of the platform?
(A) 287 m
(B) 350 m
(C) 1267 m
(D) 1287 m
(E) 1162.5 m
Rationale: Speed = 300/8 = 75/2 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 75/2
=> x = 1162.5 m.
Answer:E
Answer: (E) 1162.5 m
Question: A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:
(A) 100/17% loss
(B) 100/17% gain
(C) 20/3% loss
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Let the cost price of 1st transistor be Rs. x and the cost price of 2nd transistor be Rs. y
S.P. of 1st transistor at 20% profit = Rs. 840
=> (x + 20% of x) = 840
=> x*(120/100) = 840
=> x = 700
S.P. of 2nd transistor at 4% loss = Rs. 960
=> (y - 4% of y) = 960
=> y*(96/100) = 960
=> y = 1000
So, total C.P. = (x + y) = Rs. 1700
Total S.P. = 840 + 960 = 1800
Profit = (S.P. - C.P.) = (1800 - 1700) = Rs. 100
% Profit = (100/1700∗100)% = 100/17 %
Answer : B
Answer: (B) 100/17% gain
Question: If the simple interest on $1500 increase by $20,when the time increase by 2 years. Find the rate percent per annum.
(A) 0.6%
(B) 0.5%
(C) 0.1%
(D) 0.2%
(E) 0.7%
Rationale: Applying the above formula, we have
20=1500*r*2/100
r=20*100/1500*2=0.7%.
Answer is E
Answer: (E) 0.7%
Question: A train 175 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 22 sec
(B) 16 sec
(C) 17 sec
(D) 88 sec
(E) 10 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 175 * 2/35 = 10 sec
Answer:E
Answer: (E) 10 sec
Question: A sum of Rs. 1870 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
(A) Rs. 120
(B) Rs. 160
(C) Rs. 240
(D) Rs. 330
(E) None
Rationale: EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 1870
=> 17x/12 = 1870
=> 1870 x 12/ 17 = Rs.1320
Hence, B’s share = Rs. (1320/4) = Rs. 330.
Answer D
Answer: (D) Rs. 330
Question: A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 3 specified cars. In how many ways cars can be arranged?
(A) 720
(B) 650
(C) 1500
(D) 1640
(E) 1440
Rationale: we arranged 3 specified cars in 3 slots = 3!
remaining 5 cars in 5 slots = 5!
number of ways = 3!*5! = 720
correct option is A
Answer: (A) 720
Question: 3/4 of 1/2 of 2/5 of 5060 = ?
(A) 392
(B) 759
(C) 753
(D) 493
(E) 540
Rationale: B
759
? = 5060 * (2/5) * (1/2) * (3/4) = 759
Answer: (B) 759
Question: A rectangular grass field is 85 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) 1450
(B) 1971
(C) 9676
(D) 1679
(E) 2691
Rationale: Area = (l + b +2d) 2d
= (85 + 55 +2.5 * 2) 2*2.5 => 725
725 * 2 = Rs.1450
Answer:A
Answer: (A) 1450
Question: At a certain conference, 42% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 40% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
(A)  18.0%
(B)  62.0%
(C)  79.2%
(D)  70.0%
(E)  82.0%
Rationale: Refer to the table in the attachment:
Let x= No. of members who have paid in Full
40 % members paid in full and did not register in advance = 0.4x
42 % registerd in advance and paid in full.
So if total No. of members = 100, then 42 members paid Full and registered in advance.
Hence total members who paid full amount = 0.4x + 42 =x
0.6x =42
Hence x = 70
i.e. 80 out of 100 or 70 %
Ans. D
Answer: (D)  70.0%
Question: 2 pipes function simultaneously the reservoir will be filled in 12 hrs. One pipe fills reservoir 10 hrs faster thanthe other. How many hours does the faster pipe take to fill the reservoir?
(A) 10
(B) 20
(C) 30
(D) 34
(E) 36
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
B
Answer: (B) 20
Question: The percentage profit earned by selling an article for Rs. 1820 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) 3000
(B) 1230
(C) 2000
(D) 5600
(E) 1937.5
Rationale: C.P. be Rs. x.
Then, (1820 - x)/x * 100 = (x - 1280)/x * 100
1820 - x = x - 1280
2x = 3100 => x = 1550
Required S.P. = 125 % of Rs. 1550 = 125/100 * 1550 = Rs. 1937.5.
ANSWER E
Answer: (E) 1937.5
Question: If x - 8 = |x - 9|, then x=?
(A) 8.5
(B) 8
(C) 9
(D) 6
(E) 4
Rationale: x - 8 = |x - 9| ...(given)
x^2 - 16x + 64 = x^2 - 18 x + 81
0*x^2 + 2*x - 17 = 0 ....(by solving above eq. we get) , x = 8.5 ===> Ans - A
Answer: (A) 8.5
Question: If a*b*c=130, b*c*d = 65, c*d*e=500 and d*e*f=250 the (a*f)/(c*d) = ?
(A) 1/2
(B) 1/4
(C) 3/4
(D) 2/3
(E) 1
Rationale: Explanation :
aâˆ—bâˆ—c/bâˆ—câˆ—d= 130/65 => a/d = 2
dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/500 => f/c = 1/2
a/d* f/c = 2 * 1/2 = 1
Answer : E
Answer: (E) 1
Question: Average weight of 10 people increased by 0.5 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: Explanation:
Total weight increased is 0.5 * 10 =5.
So weight of new person is 45+5 = 50
Answer: Option A
Answer: (A) 50
Question: A coin is tossed 4 times. What is the probability of getting exactly 3 heads?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 3/16
Rationale: The number of possible outcomes is 2^4 = 16
There are 4 ways to get exactly 3 heads.
P(exactly 3 heads) = 4/16 = 1/4
The answer is B.
Answer: (B) 1/4
Question: Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations Y of classes are available?
(A) 3
(B) 6
(C) Y=7
(D) Y=9
(E) Y=12
Rationale: I think it should be E only.
No where it is given that he attends different classes on each day.
Experts please provide your views.
--- EDITED my Response. It was a typo. I meant 12 is the answer.
If only Day 1 : 3 options
If Day 1 and Day 2 : 3*3 = 9 Options
So, Total = 3+9= 12.
Answer: (D) Y=9
Question: If 20 men can build a water fountain 56 metres long in 3 days, what length of a similar water fountain can be built by 35 men in 3 days?
(A) 40 m
(B) 64 m
(C) 77 m
(D) 89 m
(E) 98 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 3: 3 : : 56 : x
Therefore (20 x 3 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/60=98
Hence, the required length is 98 m.
Answer : E
Answer: (E) 98 m
Question: What is the sum of all possible solutions to |x - 5|^2 + |x - 5| = 20 ?
(A) -1
(B) 6
(C) 7
(D) 10
(E) 14
Rationale: Denote |x - 5| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 5|, so it's an absolute value and thus cannot be negative.
y = |x - 5| = 4 --> x = 9 or x = -1. The sum =10
Answer: D.
Answer: (D) 10
Question: Approximately how many revolutions will be made by a car tire with a 10-inch diameter if the car travels 1⁄2 mile?
(A) 120
(B) 180
(C) 1003
(D) 1000
(E) 1,440
Rationale: Diameter of car tire = 10 inches
Radius of car tire = 5 inches = 5*2.54 cm = 12.7 cm
Circumference of the car tire = 2*pi * 12.7 = 2 *3.14 *12.7= 79.76 cm
Distance traveled by car = .5 mile = .5 *1.6 km = .8 km = 800 m = 8 * 10^4 cm
Number of revolutions =Distance traveled / Circumference of tire = 8 * 10^4 / 79.76 = 1003
Since the answer choices are far apart we should use estimation in this question .
Ideally ,in the GMAT the conversion between units would be provided .
Answer C
Answer: (C) 1003
Question: Robin mixes two liquids, one blue in coloUr and other red in colour in the ratio 2:3 and sells the mixture at the rate of $20 per liter, thereby making a 25% profit on his outlay. The blue liquid costs Robin $5 per litre lesser than the red liquid. How much does a liter of red liquid cost?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Let x be the required cost per litre of red paint.
Take 5 litres of this mixture.
Sold at 100 with a profit of 1/4th of total cost. So, total cost will be 1/5th less than 100; total cost = 80.
2(x-5) + 3(x) = 80
x = 14
Answer is C
Answer: (C) 14
Question: A cricketer scored 136 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
(A) 46.2%
(B) 54.54 %
(C) 55.88%
(D) 70%
(E) None of these
Rationale: Explanation :
Number of runs made by running = 136 - (12 x 4 + 2 x 6)
= 136 - (60)
= 76
Now, we need to calculate 72 is what percent of 136.
=> 76/136 * 100 = 55.88 %
Answer : C
Answer: (C) 55.88%
Question: A set of numbers has the property that for any number t in the set, 2t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -3
II. 1
III. 6
(A)  I only
(B)  II only
(C)  I and II only
(D)  II and III only
(E)  I, II, and III
Rationale: The question is which of the followingmustbe in the set, notcouldbe in the set.
If -1 is in the set so must be 2*-1+2=0, as 0 is in the set so must be 0+2=2, as 2 is in the set so must be 4+2=6 and so on.
Answer: A.
Answer: (A)  I only
Question: John has on his shelf four books of poetry, three novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
(A) 1/6
(B) 2/5
(C) 3/10
(D) 7/20
(E) 8/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 3/9*2/8 + 2/9*3/8 = 1/6.
Answer: A.
Answer: (A) 1/6
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is
(A)  587 × 108 miles
(B)  587 × 1010 miles
(C)  587 × 10-10 miles
(D)  587 × 1012 miles
(E)  587 × 10-12 miles
Rationale: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
The answer is (D)
Answer: (D)  587 × 1012 miles
Question: 3 building 3 floors how many floors are in the 3 buildings?
(A) 1
(B) 6
(C) 3
(D) 9
(E) 10
Rationale: C
Answer: (C) 3
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 3,000, how much money did investors B and C earn in total?
(A) $4,000
(B) $4,900
(C) $5,600
(D) $9,000
(E) $10,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 3000
5x = 3000=>x=600
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 15*600 = 9,000
Answer D
Answer: (D) $9,000
Question: If (x-11)(x-3) < 0, which of the following must be true?
(A) x^2 + 5x + 6 < 0
(B) x^2 + 5x + 6 > 0
(C) 5 - x < 0
(D) x - 5 < 0
(E) 11 - x > 0
Rationale: (x-11)(x-3) < 0; 3<x<11 --> Given condition
If we review options, E is always true.
Let us review others:
x^2 + 5x + 6 = (x+3)(x+2)
(x+3)(x+2)<0, then -3<x<-2 --> This will not be true with the given conditions (3<x<11). A is out
x^2 + 5x + 6 = (x+3)(x+2)
(x+3)(x+2)>0, then x> -2 and x < -3 --> This will not be true with the given conditions (3<x<11). B is out
(C)
5 - x < 0; 5<x; x> 5. But if x = 12 , then given condition is not satisfied. So C is also out.
D. x - 5 < 0
x<5
But if x = 1, (which is less than 3) then given condition is not satisfied.
E is the answer.
Answer: (E) 11 - x > 0
Question: What is the ratio G of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 3/5
(E) 2
Rationale: One side surface area of a cube = x*x = x^2
Total 6 sides = 6x^2
As for the rectangular, Height (H) and Width (W) are same as Cube, x. Only Length = 2x.
L x H = 2x * x = 2x^2 ----> 4 sides = 2x^2 * 4 = 8x^2
W * H = x * x = x^2 ------> 2 sides = x^2 * 2 = 2x^2
Total 6 sides = 8x^2 + 2x^2 = 10x^2
Ratio of cube area to rectangular area G= 6x^2 / 10x^2 ----> 6/10 ----> 3/5 (D)
Answer: (D) 3/5
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
(A) Rs.45
(B) Rs.45
(C) Rs.55
(D) Rs.60
(E) None
Rationale: Solution
A : B : C	=(10×7):(12×5):(15×3)
= 70 :60 :45
= 14 :12 :9
c's rent	=Rs.(175×9/35)
= Rs.45.
Answer A
Answer: (A) Rs.45
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
(A) 14
(B) 15
(C) 52
(D) 25
(E) 32
Rationale: Answer: Option A
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
Answer: (A) 14
Question: If 5^5 × 5^7 = (5^4)^x , then what is the value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 5^5 × 5^7 = (5^4)^x
5^(5+7) = 5^(12) With multiplying numbers with exponents it's the same as adding the exponents
5^12 = (5^4)^x
since base is same, we can equate powers:
When raising an exponent to an exponent, it's the same as multiplying them, therefore:
12=4x
x=3
Ans. B) 3
Answer: (B) 3
Question: A loan has a variable interest rate that fluctuates between 5% and 9% of the base payment per month. If base payments remain at $250 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
(A) $ 262.50
(B) $ 265.13
(C) $ 272.50
(D) $ 275.23
(E) $ 286.13
Rationale: To find the maximum amount, select the maximum rate that is 9%. Therefore the combined amount is 272.5.
To this amount add 1% extra of it, as a surcharge.
This will be something close to 275.
ANSWER:D
Answer: (D) $ 275.23
Question: 5020−(1004÷20.08)=?
(A) 4520
(B) 4350
(C) 4210
(D) 4100
(E) 4970
Rationale: Explanation:
=5020−(1004/2008×100)
=5020−50=4970
Option E
Answer: (E) 4970
Question: If a lies in the range (-4,3) then which of the following statements must be true?
(A) a^4 >a^3 > a^2 > a
(B) a > a^2 > a^3 > a^4
(C) a^4 > a^2 > a^3 >a
(D) a^2 > a^4 > a^3 >a
(E) a^2 > a^4 > a > a^3
Rationale: consider any number from the given range (-4,+3)..let a=-1/2
then a^2= 1/4
a^3=-1/8
a^4=1/16
so we have a^2>a^4>a^3>a
Ans D
Answer: (D) a^2 > a^4 > a^3 >a
Question: Half of the volume of the milk and water mixture of ratio 7:5 is converted into a mixture of ratio 3:1 by the substitution(or replacement method) the mixture of ratio 7:5 was formed from the mixture 7:3 by adding the water in it. if 240 L milk is required in the replacement method ,what it the total amount of water was added t6o prepare the mixture 7:5 ?
(A) 100 L
(B) 50 L
(C) 400 L
(D) 300 L
(E) 200 L
Rationale: 2 actions have been done on the mix...
1)7:3 is converted into 7:5 mix..
2) half of the mix of 7:5 is converted in 3:1 by adding 240l milk..
let's start with 2 action as more info is given there..
let the mix common ratio be 2x..
so total sol = milk:water=7*2x:5*2x
240 l milk is added to half of it to make it 3:1..
so (7x+240)/5x =3:1..
we get x=30 or 2x=60..
so the sol is 7*60:5*60=420:300..
now we look at the first action ..
this was created from 7:3 mix...
so say x was added to get this ratio...
so 420/(300-x)=7/3..
here x =120..
but 120 does not seem to be a choice..
now why 120 has to be correct..
initial milk:water=420:180=7:3(this is given to us)..
120 l of water is added= 420:180+120=420:300=7:5(again this confirms with what has been given)
240 l of milk is removed from half the mixture..
half the mix=210:150..
add 240 l milk...
210+240:150=450:150=3:1(satisfies the given data in Q).
ANSWER:D
Answer: (D) 300 L
Question: By selling 32 apples in a dollar, a man loses 40%. How many apples must he sell in a dollar to gain 20% profit?
(A) 16
(B) 18
(C) 20
(D) 25
(E) 28
Rationale: This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 apples for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many apples he has to sell in order to make a 20% profit, or be at 120% (100% + 20% = 120%). 120% is double 60%, meaning that we simply cut the number of apples in half to double our returns (from 60% to 120%), yielding 32/2 = 16 apples, or answer choice A.
Answer: (A) 16
Question: A and B together can do a work In 4 days. A alone can do it in 12days.what time B will take to do the work alone?
(A) 6 days
(B) 8 days
(C) 12 days
(D) 10 days
(E) 5 days
Rationale: Explanation:
A and B 1day's work = 1/4
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/4) - (1/12) = 6 Days
Answer: Option A
Answer: (A) 6 days
Question: A store owner estimates that the average price of type A products will increase by 15% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,305
(B) $15,325
(C) $16,000
(D) $16,225
(E) $17,155
Rationale: cost of type A products next year = 1.15 * 4500 = 5175
cost of type B products next year = 1.1 * 8300 = 9130
total 5175 + 9130 = 14305 option A
Answer: (A) $14,305
Question: A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred.
(A) Rs. 5750
(B) Rs. 6000
(C) Rs. 5500
(D) Rs. 5000
(E) Rs. 7000
Rationale: The price varies as the square of the weight,
P = K x W2
12250 = K x 352
K = 10
Thus, P = 10W2
When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively.
Their values should be :
10g piece: 10 x 102 = Rs. 1000;
25g piece: 10 x 252 = Rs. 6250.
Total value of stone now, = 1000 + 6250 = Rs. 7250
Loss incurred = 12250 - 7250 = Rs. 5000
ANSWER:D
Answer: (D) Rs. 5000
Question: a man and a woman, walking together start out by boyh taking a step with the left foot.in order to keep together, the man whose stride is longer,takes two steps while the woman takes three.how many steps will the woman have taken they are both about to step out on the right foot for the first time together?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: first man left and right, in that time woman has to do left,right and left. man and woman are ends with left and left.
next man left and right again, but woman has to start with right step. right,left,right. man and woman ends with right and right now.
hence solution is five.
ANSWER:B
Answer: (B) 5
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 59 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320.20$
(B) 380.20$
(C) 421.20$
(D) 451.20$
(E) 481.20$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 59 ) = 481.20
Hence answer will be (E)
Answer: (E) 481.20$
Question: If it takes Alex 20 minutes to walk from home to School and it takes him 10 minutes to walk from home to the supermarket, which of the following COULD be true?
I. The School is closer to Alex's home than the supermarket.
II. To walk to School, Alex will spend double the time it takes him to walk to the supermarket.
III. Alex will spend more time walking to the school than walking to the supermarket.
(A)  I only
(B)  I and II only
(C)  I and III only
(D)  II and III only
(E)  I, II and III
Rationale: Let’s check each statement.
Statement I:The School is closer to Alex's home than the supermarket. Alex spends 10 minutes to walk to the supermarket and spends 20 minutes to walk to school, it takes him longer time to get to school in which case Statement I can NEVER be true.
Statement II: To walk to School, Alex will spend double the time it takes him to walk to the supermarket. Alex spends 10 minutes to walk to school, double that time is 20 minutes. The time taken to walk to school is actually double the time taken to walk to the supermarket in which case Statement II is TRUE.
Statement III: Alex will spend more time walking to the school than walking to the supermarket. Alex spends 20 minutes walking to school and spends 10 minutes walking to the supermarket. Obviously more time is taken to walk to school than walking to the supermarket, in which case Statement III is TRUE.
Statement II and III are true.
So,the correct answer is D.
Answer: (D)  II and III only