mathewhe/aqua_rat huggingface dataset:
Question: In how many different ways can 7 identical green shirts and 7 identical red shirts be distributed among 14 children such that each child receives a shirt?
(A) 87178291200
(B) 871782912
(C) 8717829
(D) 871782
(E) 87178
Rationale: GGG RRR
Therefore total number of ways is
14! but there are two groups of 3 identical things.
Therefore total number of "different" ways is
14!/ (7!) (7!) = 20 ANS:A
Answer: (A) 87178291200
Question: A store sells five different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: 5C2=10.
The answer is C.
Answer: (C) 10
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 228
(B) 277
(C) 342
(D) 291
(E) 112
Rationale: 400*(90/100)*(95/100) = 342
Answer: C
Answer: (C) 342
Question: In a group of 800 people, 1/5 play at least one instrument, 32 play two or more. What is the probability that one student play exactly one instrument?
(A) 2/125
(B) 4/25
(C) C)2/25
(D) 3/25
(E) 1/5
Rationale: P(playing 2 or more instruments) = 32/800 = 1/25.
Then, the probability of playing exactly one instrument is given by:
P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 1/25 = 4/25.
Answer B.
Answer: (B) 4/25
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5080. What is the average monthly balance maintained by John in his
account during the year?
(A)  2840
(B)  5680
(C)  6840
(D)  25400
(E)  28400
Rationale: bank balance is doubled with accumulation of interest tp 5080..
this means INTEREST is 5080/2=2540 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 25400..
D
Answer: (D)  25400
Question: Compound interest of Rs.2000 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.315
(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=2000[1+(5/100)]^3 - 2000=2000[(21/20)^3 -1]
=2000(9261-8000)/8000
=2*1261/8
=315
ANSWER:D
Answer: (D) Rs.315
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 170 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 55
(B) 65
(C) 75
(D) 85
(E) 95
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 170 + P
C + M = 170
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 170/2 = 85.
ANSWER:D
Answer: (D) 85
Question: There are two sections Y and Z of a class, consisting of 288 and 352 students respectively. If the average weight of sections Y is 320 kg and that of sections Z is 280 kg. Find the average weight of the whole class
(A) 297.5
(B) 298.0
(C) 298.5
(D) 299.0
(E) None
Rationale: Solution
Total weight of(288+352)Students	= (288x320+352x280)Kg
= 1,90,720 kg.
Average weight of the whole class	= (190720 / 640)
= 298.00.
Answer B
Answer: (B) 298.0
Question: In how many ways letters of the word RSCUPERATE be arranged?
(A) 275788
(B) 287578
(C) 4357809
(D) 437479
(E) 302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: (E) 302400
Question: Of the 100 athletes at a soccer club, 40 play defense and 68 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
(A) 10 to 20
(B) 10 to 40
(C) 28 to 40
(D) 30 to 70
(E) 40 to 70
Rationale: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 68 - {both} + {neither}
{both} = {neither} + 8.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20+8=28.Eliminate A and B.
Answer: C.
Answer: (C) 28 to 40
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 4 students left over. What is the sum of the two smallest possible values of n?
(A) 30
(B) 34
(C) 38
(D) 42
(E) 46
Rationale: n = 4k+1 = 5j+4
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 5j+4.
1, 5, 9 = 5(1)+ 4
The next such number is 9 + 4*5 = 29.
9+29 = 38
The answer is C.
Answer: (C) 38
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
(A) 153
(B) 150
(C) 137
(D) 120
(E) 89
Rationale: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 120
=> x = 86
Verify. 80 + 40= 120
Answer is D
Answer: (D) 120
Question: In how many seconds will a train 150 meters long pass an oak tree, if the speed of the train is 54 km/hr?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: speed = 54 * 5/18 = 15 m/s
time = 150/15 = 10 seconds
The answer is C.
Answer: (C) 10
Question: A committee has 5 men and 4 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 127
(B) 40
(C) 882
(D) 272
(E) 323
Rationale: The number of ways to select two men and three women
= ⁵C₂ * 4C₃
= (5 *4 )/(2 * 1) * (4 * 3 * 2)/(3 * 2)
= 40
Answer: B
Answer: (B) 40
Question: What do you get if you add 9 to 311 four times?
(A) 305
(B) 310
(C) 327
(D) 320
(E) 309
Rationale: D
320 , 320 , 320 , 320
Answer: (D) 320
Question: Mary's income is 60% more Than Tim's income and Tim's income is 50% less than Juan's income.What % of Juan's income is Mary's income.
(A) 124%
(B) B.120%
(C) 96%
(D) 80%
(E) 64%
Rationale: Even I got 96%
J = 100
T = 100*0.5 = 50
M = 50*1.6 = 80
If Mary's income is x percent of J
M = J*x/100
x = M*100/J = 80*100/100 = 80
Ans:D
Answer: (D) 80%
Question: What is the value of x^2yz − xyz^2, if x = 2, y = 1, and z =2?
(A)  20
(B)  24
(C)  0
(D)  32
(E)  48
Rationale: 4*1*2-(2*1*4)
=8+8 = 0
Ans: C
Answer: (C)  0
Question: Find the missing figures: 0.25% of ? = 0.04
(A) 16
(B) 20
(C) 17
(D) 12
(E) 18
Rationale: Let 0.25% of x = 0.04. Then , 0.25*x/100 = 0.04
X= [(0.04*100)/0.25] = 16.
Answer is A.
Answer: (A) 16
Question: The maximum number of girls among them 2923 bags and 3239 eyeliners can be distributed in such a way that each student gets the same number of bags and eyeliners.
(A) 80
(B) 79
(C) 78
(D) 81
(E) 82
Rationale: Max no of girls=HCF of 2923 and 3239= 79
ANSWER:B
Answer: (B) 79
Question: When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of z customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
(A) (n - 1) z
(B) n + z –1
(C) n/(z-1)
(D) z/(n-1)
(E) (n-1)/z
Rationale: E. (n - 1) / z
Answer: (E) (n-1)/z
Question: When n is divided by 19, the remainder is 6 . When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
(A) 3
(B) 7
(C) 10
(D) 13
(E) nineteen
Rationale: N = 19 q + 6
N = 11 z + 6
Equating
19 Q + 6 = 11z+6
11z=19q
11z/19 = q
since q is an integer Z must be divisible by 19.
ANSWER:E
Answer: (E) nineteen
Question: Which of the following functions does not intersect with Q = 3x^2 + 2x + 1
(A) Q= 3x^2 + 3x + 1
(B) Q = 2x^2 + 3x + 1
(C) Q = 3x^2 + 2x + 3
(D) Q = 4x^2 + 2x - 3
(E) Q = x^2 + 2x + 3
Rationale: Let’s find the actual intersecting point of given function and each choice Q
A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0
B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1
C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.
D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2
E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.
So only choice (C) has no intersecting point. The answer is (C).
Answer: (C) Q = 3x^2 + 2x + 3
Question: A bike covers a certain distance at the speed of 64km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
(A) 80 km/h
(B) 85.34 km/h
(C) 90.14 km/h
(D) 91.24 km/h
(E) 92 km/h
Rationale: Ans.(B)
Sol. Total distance = 64 × 8 = 512 km
Now speed = 512/6 = 85.34 km/h
Answer: (B) 85.34 km/h
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Four pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
(A)  5
(B)  12
(C)  24
(D)  32
(E)  120
Rationale: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.
But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.
The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 5.
Answer: option A
Answer: (A)  5
Question: 4 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 12/9 days
(B) 60/13 days
(C) 82/8 days
(D) 22/76 days
(E) 22/2 days
Rationale: 4M = 6W ---- 20 days
12M + 8W -----?
18W + 8 W = 26W ---?
6W ---- 20 26 -----?
6 * 20 = 26 * x => x = 60/13 days
Answer:B
Answer: (B) 60/13 days
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
(A) 3%
(B) 8%
(C) 9%
(D) 4%
(E) 24%
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100
=0.04 * 100
= 4%
Answer: D
Answer: (D) 4%
Question: A thief is spotted by a policeman from a distance of 200 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
(A) 350m
(B) 200m
(C) 400m
(D) 800m
(E) None of them
Rationale: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover
(200m/1000) x 1/2 hr = 1/10 hr.
In 1/10 hrs, the thief covers a distance of 8 x 1/10 km = 4/5 km = 800 m
Answer is D.
Answer: (D) 800m
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
(A) 4 3/6
(B) 4 3/9
(C) 4 3/8
(D) 4 3/4
(E) 4 3/1
Rationale: RS = 5 3/4 - 4 1/2 = 1 1/4
T = 3 1/2 h.
D = 5/4 * 7/2 = 35/8 = 4 3/8 km
Answer: C
Answer: (C) 4 3/8
Question: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
(A) 8 : 9
(B) 21 : 22
(C) 17 : 18
(D) 12 : 20
(E) Cannot be determined
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
(120/100 x 7x)	and	(110/100 x 8x)
42x/5 and 44x/5
The required ratio = (42x/5 : 44x/5)= 21 : 22.
ANSWER B
Answer: (B) 21 : 22
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
(A) 277
(B) 266
(C) 299
(D) 600
(E) 261
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer: D
Answer: (D) 600
Question: What is the perimeter of a square with area 4p^2/16 ?
(A) 3p/4
(B) 3p^2/4
(C) 2p
(D) 3p^2
(E) 4p/3
Rationale: Area of square, (side)^2 = (2p/4)^2
Therefore side of the square = 2p/4
Perimeter of square = 4*side = 4* (2p/4) = 2p
Answer is C.
Answer: (C) 2p
Question: In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximatelywhat %of the sp is the profit?
(A) 50%
(B) 70%
(C) 80%
(D) 90%
(E) 110%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
B
Answer: (B) 70%
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
(A) 2868
(B) 1718
(C) 1689
(D) 8112
(E) 1718
Rationale: A = 7500(26/25)2
= 8112
Answer:D
Answer: (D) 8112
Question: The cost of 20 pens and 12 pencils is Rs.400 and the cost of 6 pens and 4 pencils is Rs.100. Find the cost of each pen?
(A) Rs.50
(B) Rs.100
(C) Rs.150
(D) Rs.25
(E) Rs.125
Rationale: 20p + 12q = 400 --- (1)
6p + 4q = 100
8p + 8q = 192 --- (2)
(1) - (2) => 8p = 160
=> p = 50
ANSWER:A
Answer: (A) Rs.50
Question: In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks X are made of cotton?
(A) 100
(B) 80
(C) 60
(D) 50
(E) 25
Rationale: I'll prefer to solve this with plug n play method.
As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks X has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.
100 fits perfectly after relevant calculations. Hence answer A.
Answer: (A) 100
Question: For which of the following functions f is f(b) = f(1-b) for all b?
(A) f (x) = 1 - x
(B) f (b) = 1 - b^2
(C) f (b) = b^2 - (1 - b)^2
(D) f (b) = b^2*(1 - b)^2
(E) f (x) = x/(1 - x)
Rationale: I remember seeing this problem in a GMATprep test. I think choice D should be F(b)=(b^2) (1-b)^2. If that is true then substituting (1-b) for will give us the same function back and the answer choice is D, where the function is multiplicative
Answer: (D) f (b) = b^2*(1 - b)^2
Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was:
(A) 10000
(B) 12000
(C) 14000
(D) 16000
(E) 18000
Rationale: Explanation:
Purchase Price =Rs[8748 / (1- 10/100)3]=Rs.8748 x 10/9 x10/9 x10/9 = Rs.12000
ANSWER IS B
Answer: (B) 12000
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(A) 128
(B) 130
(C) 132
(D) 143
(E) 135
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: The average of 7 numbers is 20. If each number be multiplied by 5. Find the average of new set of numbers?
(A) A)100
(B) B)122
(C) C)120
(D) D)125
(E) E)145
Rationale: Explanation:
Average of new numbers = 20 * 5 = 100
Answer: Option A
Answer: (A) A)100
Question: A retailer buys 100 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?
(A) 110
(B) 175
(C) 212
(D) 218
(E) 220
Rationale: let the market price of each pen be $1
then, Cost Price of 100 pens = $ 36 Selling Price of 100 pens =99% of $100=$ 99
profit %=((63*100)/36) %=175%
Answer B
Answer: (B) 175
Question: A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds?
(A) 5/6
(B) 3/4
(C) 2/3
(D) 1/2
(E) 3/5
Rationale: The searchlight completes one revolution every 30 seconds.
The probability that the man's area will be lit up is 10/30=1/3.
The probability that he will stay in the dark is 1-1/3=2/3
The answer is C.
Answer: (C) 2/3
Question: The units digit of (35)^(87) + (3)^(45) is:
(A) 2
(B) 8
(C) 6
(D) 9
(E) 0
Rationale: any power of anything ending in 5 always has a units digit of 5. So the first term has a units digit of 5.
2nd part
3^45 has a units digit of 3
Therefore, the second term has a units digit of 3.
Of course 5 + 3 = 8, so something with a units digit of 5 plus something with a units digit of 3
Answer = B
Answer: (B) 8
Question: A light has a rating of 86 watts, it is replaced with a new light that has 18% higher wattage. How many watts does the new light have?
(A) 105
(B) 95
(C) 80
(D) 60
(E) 101
Rationale: Final number = Initial number + 18%(original number) = 86 + 18%(86) = 86 + 15= 101.
Answer E
Answer: (E) 101
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 299
(B) 277
(C) 999
(D) 255
(E) 245
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5
= 999
Answer: C
Answer: (C) 999
Question: A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 370 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
(A)  90
(B)  190
(C)  120
(D)  130
(E)  220
Rationale: Orchestra Seats - a
Balcony Seats - b
a+b = 370
and 12a + 8b = 3320
Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)
4a = 3320 - 8*370 = 3320 - 2960 = 360
i.e. a = 90
and b = 370-90 = 280
More seats in balcony than orchestra = b-a = 280 - 90 = 190
Answer: option B
Answer: (B)  190
Question: A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream,it takes 4 hour.What is the speed of the boat in still water ?
(A) 4 km/hr
(B) 6 km/hr
(C) 8 km/hr
(D) Data inadequate
(E) None of these
Rationale: Solution
Rate downstream =(16/2) kmph = 8 kmph,Rate upstream = (16/4) kmph = 4 kmph.
∴ Speed in still water =1/2(8+4) kmph = 6 kmph. Answer B
Answer: (B) 6 km/hr
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 179
(B) 367
(C) 269
(D) 177
(E) 199
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 â€“ 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x â€“ 190
x + (x - 190) = 208
2x = 398
x = 199 runs
ANSWER: E
Answer: (E) 199
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
(A) 16 6/3%
(B) 16 2/8%
(C) 16 3/3%
(D) 16 2/3%
(E) 16 2/6%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: (D) 16 2/3%
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
(A) 1017
(B) 1029
(C) 1000
(D) 1028
(E) 1026
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
Answer: C
Answer: (C) 1000
Question: Beginning in Town A, Biker Bob rides his bike 12 miles west, 6 miles north, 4 miles east, and then 12 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
(A) 18.97 miles
(B) 20 miles
(C) 22 miles
(D) 23 miles
(E) 25 miles
Rationale: Using Pythagoras we have one side i,e total distance traveled in north direction = 12+6=18m
other being the base ie distance traveled west- distance traveled eat=12- 6= 6 m
now this third side or the distance between town A and Town B=18^2+ 6^2=sq root 360=18.97 mile
Answer : A
Answer: (A) 18.97 miles
Question: The height of a triangle is decreased by 15% and its base increased by 50%. Its area will
(A) decrease by 12.5%
(B) increase by 12.5%
(C) decrease by 25%
(D) Increase by 27.5%
(E) None of these
Rationale: Explanation :
Let the initial height be 100 and the base be 200 units.
âˆ´ Area = 1/2 x 100 x 200 = 10000 sq units
Now, height = 85 units and base = 300 units
âˆ´ New area = 1/2 x 85 x 300 = 12750
âˆ´ Area is increased by (12750 - 10000)/10000 x 100
= 27.5%
Answer : Option D
Answer: (D) Increase by 27.5%
Question: The X&co having such a sales structure out of their whole sales 70% of the customers are corporate companies out of these 20% of them are related to banking sector and 60% of the corporate companies related to banking sector having their head quarters in USA. If total sales of the company X&co is 100 cr then, what is sales amount of corporate companies related to banking sector having their head quarters in USA?
(A) 8.5
(B) 7.0
(C) 6.3
(D) 3.6
(E) 8.4
Rationale: total amount of sales =100 cr; out of these 70% are corporate companies = 70 cr; out of these 20% are related to banking sector = 14 cr ; 60% of the corporate companies related to banking sector having their head quarters in USA = 8.4 cr.
Answer: (E) 8.4
Question: A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
(A) 48
(B) 99
(C) 266
(D) 28
(E) 17
Rationale: Explanation:
If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.
Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.
Answer: A) 48
Answer: (A) 48
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 25?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?
(A) 25x^2 + 4 = y^2
(B) 75x^2 = 3y^2 - 12
(C) 5x = y - 5
(D) 25x^2 = (y + 2)(y - 2)
(E) x^2 = (y^2 - 4)/25
Rationale: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 5
If we square both sides, we end up with....
(5X)^2 = (Y-5)^2
(5X)(5X) = (Y-5)(Y-5)
25X^2 = Y^2 - 10Y + 25
This is NOT a match for the original equation, so it's the answer that is NOT equivalent. C
Answer: (C) 5x = y - 5