mathewhe/aqua_rat huggingface dataset:
Question: A librarian has a set of eleven books, including four different books about Abraham Lincoln. The librarian wants to put the eleven books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other seven books. How many different arrangements of the eleven books are possible?
(A) (11!)/(4!)
(B) (4!)(7!)
(C) (4!)(8!)
(D) (4!)(11!)
(E) (4!)(7!)(11!)
Rationale: You can club the four Lincoln books as one, which leaves us with seven other books plus this one to think about. So, these eight items can be arranged in 8! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 8!*4!, which is C.
Answer: (C) (4!)(8!)
Question: If the cost price of 26 apples is equal to the selling price of 20 apples, the gain percent is
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Let C.P. of each apple be Re. 1.
Then, C.P. of 20 apples = Rs. 20; S.P. of 20 apples = Rs. 26.
Gain % = 6/20 * 100 = 30%
Answer:B
Answer: (B) 30
Question: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?
(A) 600
(B) 720
(C) 1080
(D) 1200
(E) 1440
Rationale: $120 for 2 years = $60 per year.
Extra $6 yearned with the compound interest is the percent yearned on percent. So, $6 is yearned on $60, which means that the interest = 10%.
This on the other hand means that half of the savings = 60*10 = $600. Twice of that = $1,200.
Answer: D.
Answer: (D) 1200
Question: Weights of two friends Ram and Shyam are in the ratio 2:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
(A) 17%
(B) 10%
(C) 21%
(D) 16%
(E) None
Rationale: Solution:
given ratio of Ram and Shayam's weight = 2:5
Hence, (x-15)/(15-10) = 2/5
Or, x = 17%.
Answer: Option A
Answer: (A) 17%
Question: A cubical block of metal weighs 8 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
(A) 48
(B) 32
(C) 24
(D) 18
(E) 64
Rationale: For example our cube have a side 1 meter, so we have 1 cubical meter in this cube
and this cubical meter weigth 6 pounds
If we take cube with side 2 meters we will have 8 cubical meters in this cube
8 meters * 8 pounds = 64 pounds
So answer is E
And similar but more theoretical approach:
if we have sides a and b than they have equal ration with their areas:
a/b = a^2/b^2
and they have equal ration with their volumes:
a/b = a^3/b^3
we have two sides 1/2 so their volume will be in ratio 1/8
weight of one cube * volume of another cube
8 * 8 = 64
So answer is E
Answer: (E) 64
Question: Of the 500 people attending a conference, 240 have signed up for the Marketing workshop and 400 have signed up for the Accounting workshop. If 80 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:
(A) 170
(B) 220
(C) 250
(D) 275
(E) 300
Rationale: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:
Total = Gp.1 + Gp.2 - Both + Neither
500 = 240 + 400 - Both + 80
500 = 720 - Both
Both = 220
Final Answer:
B
Answer: (B) 220
Question: If each data point in a certain set Q is increased by a factor of 9, what happens with the set's standard deviation?
(A) Doesn't Change
(B) Increases by Factor 9
(C) Decreases by Factor 9
(D) Increases by 9
(E) Can't be determined
Rationale: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 9, the standard deviation will increase proportionately, giving us answer choice B
Answer: (B) Increases by Factor 9
Question: Each truck from Rubins Removal Company can haul 1500 pounds of trash at a time.
On Wednesday the company has jobs to remove 10,500 pounds of trash from one
site, 500 from another site, and 4,000 from a third site. How many total pounds of
trash will be moved by Jones Company that day? How many trips will it take for the
Jones Company to remove all of the trash?
(A) 5500 lbs.-2 Trips
(B) 4500 lbs.-9 Trips
(C) 15000 lbs.-10 Trips
(D) 3500 lbs.-7 Trips
(E) 6500 lbs.-8 Trips
Rationale: Total trash = 10500+500+4000 =15000
No. of trips = 15000/1500 = 10
Answer : C
Answer: (C) 15000 lbs.-10 Trips
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) Rs.1261
(B) Rs.1440
(C) Rs.1185
(D) Rs.1346
(E) Rs.1400
Rationale: Explanation:
A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer IS A
Answer: (A) Rs.1261
Question: A shirt goes on sale for 90% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?
(A) 72%
(B) 81%
(C) 52%
(D) 50%
(E) 28%
Rationale: Just assume original price is 100.
Sale price = 90
Then it is marked down by 10% = 90-9=81.
Hence it is 81% od the original price. Hence answer is B.
Answer: (B) 81%
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4202. What is the difference between Rose ’s and Tom ’s share in the profit?
(A) s.340
(B) s.362
(C) s.370
(D) s.382
(E) s.390
Rationale: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 4202 × 1/11 = Rs.382.
D)
Answer: (D) s.382
Question: A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 20% less than B, and C costs 25% less than A,and D costs 20% less than C what percent of B's cost is D?
(A) 40%
(B) 38%
(C) 44%
(D) 36%
(E) 48%
Rationale: Soln:-
B=100
A 20% less than B = 80
C 25% less than A = 60
D 20% less than C = 48
D is what percent of B = D/B * 100
= 48/100 * 100 = 48%
ANSWER:E
Answer: (E) 48%
Question: The average expenditure of a labourer for 7 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is
(A) 70.11
(B) 72.02
(C) 86.5
(D) 78.2
(E) None of the above
Rationale: Income of 7 months = (7 × 85) – debt
= 595 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 865
Average monthly income = 865 ÷ 10 = 86.5
Answer C
Answer: (C) 86.5
Question: A is a set containing 8 different numbers. B is a set containing 7 different numbers, all of which are members of A . Which of the following statements CANNOT be true?
(A)  The range of A is less than the range of B.
(B)  The mean of A is greater than the mean of B .
(C)  The range of A is equal to the range of B.
(D)  The mean of A is less than the mean of B.
(E)  The mean of A is equal to the mean of B.
Rationale: The range of a set is the difference between the largest and smallest elements of a set.
So, the answer is straight A: the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset bemorethan the difference between the largest and smallest elements of a whole set.
As for D:
Consider set A to be {-3, -2, -1, 0, 1, 2, 3, 4} --> mean=0.5.
(D) The mean of R is less than the mean of B--> remove the smallest term -3, then the mean of Bwill be 1, so more than 0.5. ANSWER IS A
Answer: (A)  The range of A is less than the range of B.
Question: How many figures are required to number the pages the pages of a book containing 365 pages?
(A) 987
(B) 977
(C) 967
(D) 897
(E) 997
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 365 = 266 * 3 = 798
-----------
987
ANSWER:A
Answer: (A) 987
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 4 hours?
(A) 240X/Y.
(B) 120X/Y.
(C) 60Y/X.
(D) 120Y/X.
(E) (X + Y)/60.
Rationale: Kramer can pack X boxes per min.
Therefore in 4 hrs(240mins)he can pack 240X boxes.
If there are Y boxes in one case then then the total number of cases packed by Krame (ANSWER A)
Answer: (A) 240X/Y.
Question: The perimeters of two squares are 40 cm and 36 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
(A) 17.6 cm
(B) 24 cm
(C) 26 cm
(D) 28 cm
(E) 29 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 36/4 = 9 cm
Area of third Square = 10*10 - 9*9
= 19 cm
So side of third square = 4.4 [because area of square = side*side]
Perimeter = 4*Side = 4*4.4 = 17.6 cm
Answer: Option A
Answer: (A) 17.6 cm
Question: A group of 10 representatives is to be selected out of 14 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
(A) 14C₅ * 10
(B) 14C₇ * 10
(C) 14C9 * ¹⁰C₅
(D) 12 * ¹⁰C₅
(E) None of these
Rationale: Here, five seniors out of 14 seniors can be selected in 14C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 14C₅ * ¹⁰C₅ = 14C9 * ¹⁰C₅
since 14C₅ = 14C9
ANSWER:C
Answer: (C) 14C9 * ¹⁰C₅
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office?
(A) 8km/h
(B) 9km/h
(C) 10km/h
(D) 12km/h
(E) 14km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=12
\inline \Rightarrow 1.5k = 12
\inline \Rightarrow k=8km/h
A
Answer: (A) 8km/h
Question: In how many ways can you sit 8 people on a bench if 3 of them must sit together?
(A) 720
(B) 2,160
(C) 2,400
(D) 4,320
(E) 40,320
Rationale: Say 8 people are {A, B, C, D, E, F, G, H} and A, B and C must sit together. Consider them as one unit {ABC}, so we'll have total of 6 units: {ABC}, {D}, {E}, {F}, {G}, {H}, which can be arranged in 6! ways. Now, A, B and C within their unit can be arranged in 3! ways, which gives total of 6!*3!=4,320 different arrangements.
Answer: D.
Answer: (D) 4,320
Question: By investing in 16 % stock at 64, one earns Rs. 1500. The investment made is?
(A) 2288
(B) 2877
(C) 5760
(D) 7636
(E) 5728
Rationale: To earn Rs., investment = Rs. 64.
To earn Rs. 1500, investment = = Rs. 5760.
Answer: C
Answer: (C) 5760
Question: Find the area of circle whose radius is 5.5m?
(A) 138
(B) 95.1
(C) 288
(D) 280
(E) 371
Rationale: 22/7 * 5.5 * 5.5
= 95.1
Answer:B
Answer: (B) 95.1
Question: How many positive integers less than 25 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
(A) 27
(B) 25
(C) 24
(D) 22
(E) 20
Rationale: 9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}
2 odd multiples of 5: {5, 15}
10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 9+2+10-1=20.
Answer: E.
Answer: (E) 20
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) 1055
(B) 1075
(C) 1065
(D) 1070
(E) 1080
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055.
A)
Answer: (A) 1055
Question: In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
(A) 400
(B) 625
(C) 1250
(D) 2500
(E) 1000
Rationale: If x is total number of fish in the pond :
4 = 40/x * 100
=> x = 1000
So answer is E
Answer: (E) 1000
Question: Compound interest of Rs.1000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).
(A) Rs.473
(B) Rs.374
(C) Rs.495
(D) Rs.157
(E) None of the above
Rationale: 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)
So compound interest=3000[1+(5/100)]^3 - 1000=1000[(21/20)^3 -1]
=1000(9261-8000)/8000
=1*1261/8
=157
ANSWER:D
Answer: (D) Rs.157
Question: Sripad has scored average of 67 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?
(A) 85
(B) 28
(C) 38
(D) 27
(E) 21
Rationale: Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 67.
i.e (58+58+x)/3 = 67
116 + x = 201
x = 85 marks.
Therefore, the maximum marks he can score in maths is 85.
Answer: A
Answer: (A) 85
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Seven years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) Can't be determined
(B) 56
(C) 27
(D) 24
(E) None of these
Rationale: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+7)/(4x+7)=11/9
⇒ 45x + 63 = 44x + 77⇒ 9(5x + 7) = 11(4x + 7)
⇒ 45x - 44x = 77 - 63
⇒ x = 14.
Anand's present age = 4x = 56 years.
Answer: B
Answer: (B) 56
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.4 m and its walls are 5 cm thick. The thickness of the bottom is:
(A) 90 cm
(B) 4 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) × (140 - x)] = 8000 × 1000
=> 320 × 250 × (140 - x) = 8000 × 1000
=> (140 - x) = 8000×1000/320=
100
=> x = 40 cm = 4 dm.
Answer: B
Answer: (B) 4 dm
Question: If x≠5 and (x^2 - 25)/(2y) = (x - 5)/4, then in terms of y, x = ?
(A) (y - 6)/2
(B) (y - 10)/2
(C) y - 3
(D) y - 6
(E) (y + 6)/2
Rationale: Since (x^2 – 25)=(x-5)(x+5) the original equation can be changed into 4*(x-5)(x+5) = 2y *(x-5).
By cancelling 2(x-5) (we can do it because x≠5) we get :
2*(x+5)=y.
So x=(y-10)/2. So the answer is B).
Answer: (B) (y - 10)/2
Question: A, B and C started a business with a total investment of Rs. 90000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find C's share.
(A) Rs. 3240
(B) Rs. 2520
(C) Rs. 2880
(D) Rs. 3360
(E) None of these
Rationale: Explanation:
Let C's investment = Rs. x
B's investment = Rs. (x - 3000)
A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)
Now, (A + B + C)'s investment = Rs. 90000
=> x + (x - 3000) + (x + 3000) = 90000
=> 3x = 90000
=> x = 30000
Hence, A's investment = Rs. 33000
B's investment = Rs. 27000
C's investment = Rs. 30000
Ratio of the capitals of A, B and C
= 33000 : 27000 : 30000
= 11 : 9 : 10
A's share = Rs. [(10/30) Ã— 8640] = Rs. 2880
Answer: Option C
Answer: (C) Rs. 2880
Question: How many three digit numbers that do not contain the digit 2 are there?
(A) 100
(B) 200
(C) 512
(D) 648
(E) 729
Rationale: 8*9*9 = 648: 8 options for the first digit (no 0, no 2) and 9 options for each of the remaining digits (no 2 there).
Answer: D
Answer: (D) 648
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
(A) 23
(B) 19
(C) 22
(D) 35
(E) 21
Rationale: Let the total number of workers be x. Then,
8000x = (16000 * 7) + 6000(x - 7)
= 2000x = 70000
= x = 35.
ANSWER:D
Answer: (D) 35
Question: For how many integers n is 2^x = n^x ?
(A) None
(B) One
(C) Three
(D) Two
(E) More than Three
Rationale: draw a graph with x^2 and 2^x, you'll see 3 intercepts between the 2 curves, but one is in the 2nd quadrant, so it can't be an integer (for integer values of x, 2^x can be an integer only for x>0). Thus 2 are valid, and the answer is D
Answer: (D) Two
Question: What is the dividend. divisor 14, the quotient is 12 and the remainder is 8
(A) 175
(B) 176
(C) 177
(D) 178
(E) 179
Rationale: B = d * Q + R
B = 14 * 12 + 8
B = 168 + 8
B = 176
Answer: (B) 176
Question: When n is divided by 25, the remainder is 4. What is the remainder when n + 15 is divided by 5?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Assume n = 29
Remainder (n/24) = 4
n+15 = 44
Remainder (44/5) = 4
Option C
Answer: (C) 4
Question: A train 140 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 13 km/hr
(B) 55.4 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) 12 km/hr
Rationale: Speed of the train relative to man = (140/10) m/sec
= (14 m/sec. [(14
) * (18/5)] km/hr
= 50.4 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 50.4 ==> x
= 55.4 km/hr.
Answer:B
Answer: (B) 55.4 km/hr
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 10m
(B) 245m
(C) 25m
(D) 18m
(E) 12m
Rationale: Explanation:
Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer: B) 245m
Answer: (B) 245m
Question: A train is 700 meter long is running at a speed of 21 km/hour. In what time will it pass a bridge of 130 meter length?
(A) 142.286
(B) 251.228
(C) 34
(D) 200
(E) 150.627
Rationale: Speed = 21 Km/hr = 21*(5/18) m/sec = 35/6 m/sec
Total distance = 700+130 = 830 meter
Time = Distance/speed
= 830 * (6/35) = 142.286 seconds.
Answer: A
Answer: (A) 142.286
Question: Find large number from below question The difference of two numbers is 1000. On dividing the larger number by the smaller, we get 10 as quotient and the 10 as remainder
(A) 1234
(B) 1110
(C) 1456
(D) 1200
(E) 1600
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1000 = 10x + 10
9x = 990
x = 110
Large number = 110+1000=1110
B
Answer: (B) 1110
Question: Of the science books in a certain supply room, 30 are on botany, 45 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science?
(A) 125
(B) 180
(C) 236
(D) 284
(E) 311
Rationale: The worst case scenario is to remove all the books on botany, zoology, and geology.
Also we can remove 79 books each from physics and chemistry.
The total is 30 + 45 + 50 + 79 + 79 = 283.
The next book removed must either be physics or chemistry, ensuring 80 books in that subject.
The answer is D.
Answer: (D) 284
Question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 360 feet in circumference.After how many minutes are the three of them together again?
(A) 6 mins
(B) 10 mins
(C) 15 mins
(D) 3 mins
(E) 7 mins
Rationale: The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of =360/60= 6 mins.
A
Answer: (A) 6 mins
Question: A fair coin is tossed 5 times. What is the probability of getting more heads than tails in 5 tosses?
(A) 1/2
(B) 63/128
(C) 4/7
(D) 61/256
(E) 63/64
Rationale: On each toss, the probability of getting a head is 1/2 and the probability of getting a tail is 1/2.
There is no way to get the same number of heads and tails on an odd number of tosses.
There will either be more heads or more tails.
Then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes.
P(more heads) = 1/2
The answer is A.
Answer: (A) 1/2
Question: Gary drove from point A to point B at 60 Km/h. On his way back he took a train travelling at 110 Km/h and therefore his trip back lasted 5 hours less. What is the distance (in Km) between A and B?
(A) 600.
(B) 630.
(C) 660.
(D) 690.
(E) 720.
Rationale: distance=speed*time
d1=s1t1
d2=s2t2
The distance from point A to point B is the same for each trip so,
d1=d2 and
t2=t1-5
thus,
s1t1=s2t2
60t1=s2(t1-5)
t1=11
60*11=660
Answer: C
Answer: (C) 660.
Question: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (14,0), respectively. Points X, Y, and Z have xy-coordinates (6,0), (8,4), and (10,0), respectively. What fraction D of the area of triangle ABC is the area of triangle XYZ?
(A)  1/9
(B)  1/8
(C)  1/6
(D)  1/5
(E)  1/3
Rationale: If you notice, both triangles ABC and XYZ have a side on X axis. we can take these sides as bases for each triangle, therefore
Area of ABC is 1/2*12*12 (Height of ABC is the y coordinate of the third point (8,12))
similarly Area of XYZ is 1/2*4*4
dividing area of XYZ with that of ABC gives D=1/9.A
Answer: (A)  1/9
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 229
(B) 240
(C) 288
(D) 277
(E) 221
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: (B) 240
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is?
(A) 24 kg
(B) 62 kg
(C) 34 kg
(D) 31 kg
(E) 37 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have:
A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.
Answer:D
Answer: (D) 31 kg
Question: A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 1/3, and the probability of selecting a blue paper clip is 3/5. What is the probability of selecting a silver paper clip?
(A)  1/12
(B)  2/15
(C)  7/15
(D)  3/4
(E)  11/15
Rationale: Prob of Red = 1/3
Prob of Blue = 3/5
Prob of Silver = ?
P(Silver) = 1 - P(Red) - P(Blue) ==> 1-1/3-3/5 = 1/15
Ans: B
Answer: (B)  2/15