mathewhe/aqua_rat huggingface dataset:
Question: A diner is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad?
(A) 9
(B) 11
(C) 24
(D) 48
(E) 54
Rationale: 2*3*4 = 24
The answer is C.
Answer: (C) 24
Question: How many consecutive zeros are there at the end of 100! (100 factorial) ?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: number of zeros will be 24
Reason 100/5=20
20/5=4
so the total number of 5 will be 20+4=24
ANSWER:D
Answer: (D) 24
Question: Find the area of a parallelogram with base 32 cm and height 22 cm?
(A) 281
(B) 284
(C) 704
(D) 640
(E) 920
Rationale: Area of a parallelogram = base * height
= 32 * 22
= 704 cm2
Answer: C
Answer: (C) 704
Question: The average of squares of first 11 consecutive even numbers is:
(A) 164
(B) 174
(C) 184
(D) 194
(E) 204
Rationale: 2(n+1)(2n+1)/3
(2*12*23)/3
=2*4*23
=184
ANSWER:C
Answer: (C) 184
Question: A rectangular grass field is 75 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.1 per sq m?
(A) 675, Rs.1350
(B) 575, Rs.675
(C) 1350, Rs.675
(D) 1450, Rs.775
(E) 1550, Rs.875
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 1 = Rs. 675
ANSWER:B
Answer: (B) 575, Rs.675
Question: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 35% nuts, what percent of the combined mixture is dried fruit?
(A) 48.3%
(B) 52.8%
(C) 55.5%
(D) 58.3%
(E) 61.4%
Rationale: 35% is 5%-points above 30% and 25%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 5:1.
5/6*70% = 58.3%
The answer is D.
Answer: (D) 58.3%
Question: A military commander has to choose 4 soldiers out of a company of 7 for guarding the headquarters. How many different group combinations of 4 does he have to choose from?
(A) 4
(B) 15
(C) 16
(D) 27
(E) 35
Rationale: A military commander has to choose 4 soldiers out of a company of 7.
different group combinations of 4
He can do this in 7C4 ways
7*6*5*4/4*3*2*1= 35 ways
ANSWER:E
Answer: (E) 35
Question: Line Q has the equation 5y – 3x = 30. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)
(A) 22
(B) 33
(C) 36
(D) 41
(E) 58
Rationale: 5y - 3x = 30 and so y = 3x/5 + 6
When x = 0, then y = 6.
When y = 0, then x = -10
The slope is 3/5, so the slope of line S is -5/3.
Through the point (-10, 0), 0 = -5(-10)/3 + c
The y-intercept is c = -50/3 < -16.
Thus the perpendicular line S can have y-intercepts from -16 up to 5.
The number of possible lines is 16 + 5 + 1 = 22
The answer is A.
Answer: (A) 22
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 42 more. What was his original selling price?
(A)  $770
(B)  $660
(C)  $700
(D)  $1100
(E)  $840
Rationale: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $42 more in second scenario => 1.3(0.9X) - 1.1X = 42
=> 0.07X = 42
=> X = $600
Original purchase price = $600
Hence, original selling price (at 10% of profit) = 1.1(600) = $660
Option B
Answer: (B)  $660
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 18 years. What is Deepak present age?
(A) 22
(B) 15
(C) 77
(D) 9
(E) 182
Rationale: Present age is 4x and 3x,
=> 4x + 6 = 18 => x = 3
So Deepak age is = 3(3) = 9
Answer: D
Answer: (D) 9
Question: Two men start from opposite banks of a river . They meet 340 meters away from one of the banks on forward journey. After that they meet at 170 meters from the other bank of the river on their backward journey. What will be the width of the river (in meters)?
(A) 750
(B) 850
(C) 900
(D) 980
(E) 950
Rationale: let p,q are two persons then their speeds be a,b->m/hr
x----340----------------------|---(d-340)---------y
in forward journey
time taken by p=340/a;
time taken by q=d-340/b;
in forward journey, time taken by p=time taken by q
so 340/a=d-340/b
a/b=340/d-340------------(1)
after that they continue their journeyand reach other banks
now in backward journey,
x---------------(d-170)--------------------------|-----170------y
distance travelled by p from meet 1 to meet 2 = (d-340)+170
distance travelled by p from meet 1 to meet 2 =340+(d-170)
now time taken by p= time taken by q
(d-340)+170/a=340+(d-170)/b
(d-340)+170/340+(d-170)=a/b---------(2)
from 1&2
340/(d-340)=(d-340)+170/340+(d-170)
340/(d-340)=d-170/d+170
340d+57800=d^2-340d-170d+57800
340d=d^2-510d
d^2-850d=0
d(d-850)=0
d=0 ord=850
so width of the river is 850
ANSWER:B
Answer: (B) 850
Question: The price of sugar is increased by 9%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
(A) (700/107) %
(B) (107/100) %
(C) (900/109)%
(D) (7/100)%
(E) (100/700)%
Rationale: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $109.
We want the spendings to remain at $100.
(New consumption)*109 = 100 --> (New consumption) = 100/109 kg.
Percent decrease = Change/Original *100 = (1 - 100/109)/1*100 = 900/109%.
Answer: C.
Answer: (C) (900/109)%
Question: A man buys an article for 16% less than its value and sells it for 16% more than its value. His gain or loss percent is:
(A) no profit, no loss
(B) 20% profit
(C) less than 35% profit
(D) more than 35% profit
(E) None
Rationale: Let the article be worth Rs. x.
C.P. 84% of Rs. x = Rs. 84x/100
S.P. = 116% of Rs. x = Rs. 116x/100
Gain = (116x/100 - 84x/100) = Rs. 8x/25
Gain % = 8x/25 * 100/84x * 100 = 38 2/21 % > 35%
ANSWER:D
Answer: (D) more than 35% profit
Question: Currently apples cost 60 cents/pound. Due to a disease affecting the apple trees it is expected that next month apples will cost 200% more than they do currently. How much are apples expected to cost next month?
(A) 200 cents /pound
(B) 150 cents /pound
(C) 160 cents /pound
(D) 180 cents /pound
(E) 170 cents /pound
Rationale: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 60 cents/pound + (200/100)(60 cents/pound)
= 60 cents/pound + 120 cents/pound
= 180 cents /pound
Answer : D
Answer: (D) 180 cents /pound
Question: Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Renee will win or draw?
(A) 5/6
(B) 2/3
(C) 1/2
(D) 5/12
(E) 1/3
Rationale: There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Renee winning the game or drawing is (favorable outcomes) / (total # of outcomes) = 6/9 = 2/3
Answer: B
Answer: (B) 2/3
Question: The owner of a furniture shop charges his customer 15% more than the cost price. If a customer paid Rs. 5750 for a computer table, then what was the cost price of the computer table?
(A) 2299
(B) 2699
(C) 2670
(D) 6725
(E) 5000
Rationale: CP = SP * (100/(100 + profit%))
= 5750(100/115) = Rs. 5000
Answer:E
Answer: (E) 5000
Question: Which of the following is the lowest positive integer that is divisible by 4, 5, 6, 7, 8, 9, and 10?
(A) 1680
(B) 1950
(C) 2230
(D) 2520
(E) 2870
Rationale: The number needs to be divisible by 2^2, 5, 2*3, 7, 2^3, 3^2, and 2*5.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520
The answer is D.
Answer: (D) 2520
Question: The sum of three consecutive even numbers is 60. Find the middle number of the three?
(A) 14
(B) 60
(C) 18
(D) 70
(E) 45
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 60
6P = 60 => P = 10.
The middle number is: 10P = 60.
ANSWER:B
Answer: (B) 60
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 3 Ohms and y is 5 Ohms?
(A) 15/8
(B) 3/8
(C) 5/8
(D) 7/15
(E) 8/15
Rationale: 1/R = 1/x + 1/y
1/R = 1/3+1/5 = 8/15
R = 15/8
The answer is A.
Answer: (A) 15/8
Question: sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6600 ?
(A) 5591
(B) 2477
(C) 2877
(D) 2676
(E) 1881
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6600 x 6) - 34009]
= Rs. (39600 - 34009)
= Rs. 5591
Answer: A
Answer: (A) 5591
Question: If 90 percent of 600 is 50 percent of x, then x=?
(A) 100
(B) 1000
(C) 1080
(D) 1020
(E) 1200
Rationale: 0.9 * 600 = 0.5 * x
x = 9/5 * 600 = 1080
Answer: (C) 1080
Question: A Person X started at 3 hours earlier at 40km/h from a place P, then another person Y followed him at 60km/h. Started his journey at 3 O'clock, afternoon. What is the diference in time when X was30 km ahead of Y and when Y was 30 km ahead of X?
(A) 8h
(B) 3h
(C) 6h
(D) 3h
(E) 1h
Rationale: Explanation:
Time ( when X was 30 km ahead of Y) = (120-30)/20 =4.5h
Time ( when Y was 30 km ahead of X) = (120+30)/20 = 7.5 h
Thus, required difference in time = 3h
Answer: B
Answer: (B) 3h
Question: A grocer has a sale of Rs. 5124, Rs. 5366, Rs. 5808, Rs. 5399 and Rs. 6124 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5400?
(A) 4079
(B) 4579
(C) 5579
(D) 5679
(E) 5779
Rationale: Total sale for 5 months = Rs. (5124 + 5366 + 5808 + 5399 + 6124) = Rs. 27821.
Required sale = Rs. [ (5400 x 6) - 27821 ]
= Rs. (32400 - 27821)
= Rs. 4579.
ANSWER:B
Answer: (B) 4579
Question: A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
(A) 10:12:14
(B) 12:24:28
(C) 20:22:12
(D) 20:49:64
(E) None of these
Rationale: Explanation :
Ratio in which A,B and C shared the profit = 5 : 7 : 8
Assume that the ratio of their investment = a:b:c
Then 14a : 8b : 7c = 5 : 7 : 8
Good to go, we got the equation. Now it's a matter of time to find a, b and c
14a/8b = 5/7
=> 98a = 40b
=> b = 98a/40 = 49a/20 ---(1)
14a/7c =5/8
=> 2a/c =5/8
=> 16a = 5c
=> c = 16a/5 ---(2)
a : b : c = a : 49a/20 : 16a/5 = 1 : 49/20 : 16/5 = 20 : 49 : 64. Answer : Option D
Answer: (D) 20:49:64
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 250 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
(A) 0.6
(B) 0.06
(C) 0.006
(D) 0.0006
(E) 6.0e-05
Rationale: Suppose machine A produce 1000 units
total defective = 9
Machine B then produces=1500 units
total defective=6
probability=15/2500
=0.006
C . correct
Answer: (C) 0.006
Question: The diagonals of a rhombus are 11 cm and 16 cm. Find its area?
(A) 277
(B) 266
(C) 150
(D) 88
(E) 212
Rationale: 1/2 * 11 * 16 = 88
Answer: D
Answer: (D) 88
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
B)
Answer: (B) 3
Question: The average of temperatures at noontime from Monday to Friday is 60; the lowest one is 45, what is the possible maximum range of the temperatures?
(A) 20
(B) 25
(C) 40
(D) 45
(E) 75
Rationale: there are 5 days so the sum of temperature can be 60*5=300
lowest is 45. to find the maximum range we can say the temperature was the lowest for 4 of the 5 days
so 4*45=180.
on the fifth day it is 300-180=120
range is therefore 120-45=75
answer E
Answer: (E) 75
Question: 20-3*5^2+15 = ?
(A) 287
(B) -40
(C) -73
(D) 13
(E) None
Rationale: 20-3*5^2+15=-40
B
Answer: (B) -40
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 50 sec
(C) 44 sec
(D) 49 sec
(E) 60 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer:A
Answer: (A) 40 sec
Question: I have an amount of Rs 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?
(A) 252
(B) 250
(C) 1001
(D) 1089
(E) None
Rationale: Solution:
The situation is similar to placing 10 identical balls among 5 distinguishable boxes, where a box may have zero or more balls in it.
This case can be represented as arranging ten balls and (5-1) four walls in the single row, which can be done in 14C4 ways.(The balls placed between every successive pair of walls belong to one group) 14C4 = 1001 ways.
Answer: Option C
Answer: (C) 1001
Question: Which of the following is closer to √0.5+√0.1?
(A) 0.5
(B) 0.7
(C) 0.9
(D) 1.0
(E) 1.2
Rationale: √0.5+√0.1=approximately √0.49+√0.09=0.7+0.3=1.0. Hence, the correct answer is D.
Answer: (D) 1.0
Question: How long will it take for a sum of money to grow from Rs.2000 to Rs.10,000, if it is invested at 10% p.a simple interest?
(A) 8 years
(B) 64 years
(C) 72 years
(D) 40 years
(E) None
Rationale: In this case, Rs. 2000 has become Rs.10,000.
Therefore, the interest earned = 10,000 – 2000 = 8000
Interest for Rs 2000 @ 10% for 1 year = 200
200 - 1
8000 - ? => 40 years
Answer : D
Answer: (D) 40 years
Question: A can do a work in 5 days. B is 50% more efficient than A. How many days does B alone take to do the same job?
(A) 12/7
(B) 13/3
(C) 11/2
(D) 9/4
(E) 10/3
Rationale: Ratio of times taken by A and B = 150:100 = 3:2
suppose B alone to take x days to do the work
then, 3:2::5:x
3x= 2*5
x=10/3 days
correct option is E
Answer: (E) 10/3
Question: Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?
(A) 0
(B) 1/3
(C) 1/2
(D) 2/3
(E) 1
Rationale: The only way for the 2 houses to get done in under 7 weeks is if they work together. If Mike works alone - it would take him 12 weeks to build 2 houses. If Emily works alone, it would take 16 weeks. The check for this is below.
Together, they have a rate of 6∗86+86∗86+8 per house. Knowing that they'll need 2, we get 2∗(6∗86+8)=6672∗(6∗86+8)=667
Knowing this - the only way to complete in under 7 weeks is to work together - we can move on to the probability. This is very simple: 2 sides of the dice (a 5 or a 6) out of 6 possible outcomes is 2/6, which reduces to 1/3.. The Answer is B.
Answer: (B) 1/3
Question: Micky has 10 different letters and 5 different envelopes with him. If he can only put one letter in an envelope, in how many ways can the letters be put in the envelopes?
(A) 5!
(B) 5555
(C) 10C5 * 5!
(D) 10C5∗5510C5∗55
(E) 510
Rationale: The Q basically wants us to choose 5 letters from the 10 and then place it in envelopes..
choosing 5 letters out of 10 =10C5..
these 5 letters can be placed in 5! ways in 5 envelope..
total ways = 10C5*5!
ANSWER:C
Answer: (C) 10C5 * 5!
Question: A cube of edge 15cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 14cm , find the rise in water level?
(A) 6cm
(B) 12.05cm
(C) 11.25cm
(D) 15.12cm
(E) 20.62cm
Rationale: Increase in volume = volume of the cube = 15*15*15 cm^3
Rise in water level = volume / area = 15*15*15/20*14 = 12.05cm
Answer is B
Answer: (B) 12.05cm
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) 255
(B) 267
(C) 245
(D) 277
(E) 211
Rationale: 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:C
Answer: (C) 245
Question: How many arrangements of the letters of the word SPECIAL can be made, without changing the place of the vowels in the word?
(A) 24
(B) 26
(C) 28
(D) 32
(E) 34
Rationale: E,I,A fixed. Consonants can be arrangements in 4P4 = 4! = 24 ways
Option 'A'
Answer: (A) 24
Question: Juan is a gold medalist in athletics. In the month of May, if Juan takes 9 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 10x/y
(B) 11x/y
(C) 9x/y
(D) 12x/y
(E) 13x/y
Rationale: velocity=distance/time;
since he ran at same rate both d tyms,
y/9=x/t
so t=9x/y
ANSWER:C
Answer: (C) 9x/y
Question: The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.69 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?
(A) $1.59
(B) $1.64
(C) $1.68
(D) $1.72
(E) $1.76
Rationale: Average price = (550*1.69)+(270*1.38)/550+270=1.59 (Approx)
Answer A
Answer: (A) $1.59
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 15 sec
(B) 22 sec
(C) 18 sec
(D) 10 sec
(E) 12 sec
Rationale: Explanation:
Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
ANSWER IS D
Answer: (D) 10 sec
Question: If a, b, r are integers, 33 = abr, and a < b < r, what is the smallest possible value of a?
(A) -33
(B) -3
(C) 1
(D) 3
(E) 11
Rationale: Given : a * b * r = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.
Correct answer is A
Answer: (A) -33
Question: 15.06 * 0.00001 = ?
(A) 15060000
(B) 0.0001506
(C) 0.01506
(D) 0.1506
(E) None of these
Rationale: Explanation:
Clearly after decimal 7 digits should be there.
Option B
Answer: (B) 0.0001506
Question: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/6, then what is the value of abc/def ?
(A)  27/4
(B)  27/8
(C)  3/4
(D)  3/8
(E)  1/4
Rationale: Say a = 2. Then:
a/b = 1/3 --> b = 6;
b/c = 2 --> c = 3;
c/d = 1/2 --> d = 6;
d/e = 3 --> e = 2;
e/f = 1/6 --> f = 12.
abc/def = (2*6*3)/(6*2*12) = 1/4.
Answer: E.
Answer: (E)  1/4
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
(A) 11 1/7%
(B) 11 7/7%
(C) 11 1/9%
(D) 71 1/9%
(E) 11 1/2%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer:C
Answer: (C) 11 1/9%
Question: If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
(A) 333
(B) 2877
(C) 278
(D) 480
(E) 288
Rationale: Explanation:
Let the sum be Rs. P. Then,
[P(1 + 25/(2 * 100))2 - P] = 510
P[(9/8)2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480
Answer: D
Answer: (D) 480
Question: There are 3 red chips and 3 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?
(A) A)10
(B) B)12
(C) C)24
(D) D)60
(E) E)200
Rationale: Using anagram method:
@NL6_ 5_4_3_2_1
R_R_R_B_B_B
so..
6!/Number of repeated letters (3!)(3!) = 20
ANS:E
Answer: (E) E)200
Question: If a: b :: 3 : 7, then what is (5a+6b): (a-b)?
(A) 57:11
(B) -57:4
(C) 11 : 10
(D) -11 : 10
(E) -1 : 10
Rationale: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-1]= [5*(3/7)+6]/[(3/7)-1]= -57/4
B
Answer: (B) -57:4
Question: Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (a,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?
(A)  2x + y = ax + 7
(B)  2x + y = –ax
(C)  x + 2y = ax + 7
(D)  y – 7 = x ÷ (a – 2)
(E)  2x + y = 7 – ax
Rationale: we need m=a-2, so we should gety=mx+bform in answer choices
(A) 2x+y=ax+7 => y=ax-2x+7 => y=x(a-2)+7. It is what we need
(B) 2x + y = –ax => y=-px-2x => y=x(-a-2). Wrong
(C) x + 2y = ax + 7 => y=x(a-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (a – 2) => y=(1/a-2)x+7. Wrong
(E) 2x + y = 7 – ax => y=-ax-2x+7 => y=x(-a-2)+7. Wrong
A=answer
Answer: (A)  2x + y = ax + 7
Question: Seven children — A, B, C, D, E,— are going to sit in seven chairs in a row. The children CE have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 48
(D) 4320
(E) 4800
Rationale: for such questions , we can treat both as one then total person=4..
these 4 can be arranged in 4! ways.. but within these 4, one consists of two people who can be arranged in 2 ways CF or FC.. so ans =4!*2=48
ans C
Answer: (C) 48
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
(A) 3:9
(B) 3:3
(C) 3:4
(D) 3:1
(E) 3:2
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y = 80
Ratio of speeds = 60:80 = 3:4
Answer: C
Answer: (C) 3:4
Question: A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $120,000 and variables costs averaging $8 per item. If the manufacturer’s selling price per item is $12, how many items the manufacturer produce and sell to earn an annual profit of $140,000?
(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 65,000
Rationale: Let the items manufactured or sold bex
120000+8x = 12x-140000
4x = 260000
x = 65000
Ans:E
Answer: (E) 65,000
Question: A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before is
(A) 20 min
(B) 35 min
(C) 50 min
(D) 70 min
(E) none
Rationale: Solution
Let original diameter be d metres. Then, its circumference = (Πd)metres.
Time taken to cover (8Πd)m = 40 min.
New diameter = (10d)m. Then, its circumference = (Π x 10d)m.
Time taken to go round it once
‹=› [40 / 8Πd x 10Πd]m
‹=›50 min.
Answer C
Answer: (C) 50 min