divelab/Sys2Bench huggingface dataset:
Question: How many ways are there for 2 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
Options:
A)6
B)12
C)72
D)4
E)720
Rationale: So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 2 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 2! different ways, so total 2*2!=4
Answer D.
Answer: D
Question: Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for r dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs?
Options:
A)(x – s)r – sd
B)xr – (xd – sd)
C)xd – sr
D)(x – s)d – xr
E)(s – r)d – xr
Rationale: Answer D:
The amount of hotdogs she can sell is x-s. The price per pound is d, so the revenue is (x-s)d. The total costs are x time r, so the profit is (x-s)d-xr.
Answer: D
Question: What is the value of 4^6+4^8?
Options:
A) 4^12
B) 4^35
C) 17(4^6)
D) 8^12
E) 7(4^5)
Rationale: 4^6+4^8
=4^6(1+4^2)
=4^6 * 17
Answer C
Answer: C
Question: At Company X, senior sales representatives visit the home office once every 16 days, and junior sales representatives visit the home office once every 12 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
Options:
A)10%
B)25%
C)33%
D)50%
E)67%
Rationale: Each 48-day period, senior representatives visit the home office 3 times while junior representatives visit 4 times, thus 33% more.
The answer is C.
Answer: C
Question: Which of the following values of x will satisfy the in equality 2x2 – 7x < 15?
Options:
A)-3⁄2 < x < 5
B)x > 5 or x < -3⁄2
C)x< 5 and x < -3⁄2
D)x > -3⁄2 and x > 5
E)None of these
Rationale: 2x2 – 7x < 15
or, 2x2 – 7x – 15 < 0
or, 2x2 – 10x + 3x – 15 < 0
or, 2x(x – 5) + 3(x – 5) < 0
or, (x – 5)(2x + 3) < 0
----------|--------------------|--------
+ve -3⁄2 –ve 5 +ve
-3⁄2 < x < 5
Answer A
Answer: A
Question: The speed at which a man can row a boat in still water is 20 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)16 seconds
B)76 seconds
C)26 seconds
D)9.4 seconds
E)18 seconds
Rationale: Speed of the boat downstream = 20 + 3
= 23 kmph
= 23 * 5/18 = 115/18 m/s
Hence time taken to cover 60 m
= 60*18/115
= 9.4 seconds.
Answer: D
Answer: D
Question: If n is an integer greater than 6, which of the following must be divisible by 4?
Options:
A)1. n (n+1) (n-4)
B)2. n (n+2) (n-1)
C)3. n (n+3) (n-5)
D)4. n (n+4) (n-2)
E)5. n (n+5) (n-6)
Rationale: We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
B
Answer: B
Question: The average monthly expenditure of a family for the first four months is Rs 2,750, for the next three months is Rs 2,940 and for the last five months Rs 3,130. If the family saves Rs 5,330 during the whole year, find the average monthly income of the family during the year.
Options:
A)Rs 3,800
B)Rs 3,500
C)Rs 3,400
D)Rs 4,200
E)None of these
Rationale: Average monthly expenditure of 4 months
= Rs 2,700
Total expenditure for 4 months = Rs 2,700 x 4
= Rs 11,000
Average monthly expenditure of 3 months
= Rs 2,940
Total expenditure of 3 months = Rs 2,940 x 5
= Rs 8,820
Average monthly expenditure of 5 months
= Rs 3,130
Total expenditure of 5 months = Rs 31,020
= Rs 1,560
Total expenditure in the whole year
= Rs 11,000 + 8,820 - Rs 15,650 = Rs 35,470.
Saving during the whole year = Rs 5,330.
Total income of the family during the year= Rs 35,470 + Rs 5,330 = Rs 40,800.
Therefore, Average monthly income during the year 40800/12 = Rs 3,400.
ANSWER:C
Answer: C
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)27 sec
B)16 sec
C)56 sec
D)15 sec
E)12 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35
= 16 sec
AnswerB
Answer: B
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 11 men
do it ?
Options:
A)65 hours
B)82 hours
C)30 hours
D)62 hours
E)66 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
11 : 36 : : 25 : x	(11 x x) = (36 x 25)	(36 x 25)/11 = 82
Hence, 15 men can do it in 60 hours.
Answer is B.
Answer: B
Question: which number need to add to 859622 to get a no. exactly divisible by 456?
Options:
A)345466
B)465767
C)565676
D)645469
E)859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: E
Question: If c is a positive even integer, and n and m are consecutive integers, then (n - m)^c/(m - n)^c =
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: c= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^c)/((m-n)^c)= ((n-m)/(m-n))^c = (-1)^c
Since we are raising the difference of n and m to power c , which is even , the answer will be 1 .
Answer D
Answer: D
Question: P and Q started a business investing Rs 85000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
Options:
A)17:5
B)17:3
C)17:6
D)17:7
E)17:8
Rationale: Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 85000:15000
= 85:15
= 17:3
Option B
Answer: B
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price R per glass on the second day?
Options:
A) $015
B) $0.20
C) $0.30
D) $0.40
E) $0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.
Answer: D.
Answer: D
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)5500
B)6500
C)7000
D)7700
E)7500
Rationale: A : B : C
=20000×24:15000×24:20000×18
=20×4:15×4:20×3=4×4:3×4:4×3
=4:3:3
B's share = 25000×3/10=7500
Answer is E.
Answer: E
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 750 grams. Find the profit percent.
Options:
A)100/17%
B)100/23%
C)100/19%
D)100/3%
E)None of these
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 750
100 + g / 100 + 0 = 1000 / 750
100+g = 4/3*100
g = 100/3 %
ANSWER: D
Answer: D
Question: A student answered 86 problems on a test correctly and
received a grade 98%. How many problems were on the test,
if all the problems were worth the same number of points?
(Round to the nearest whole number)
Options:
A)48 problems
B)28 problems
C)68 problems
D)58 problems
E)88 problems
Rationale: 98/100=86/x
Multiply the opposites:
100 x 86 = 8600
Divide by the remaining number:
87.7/8600 .0
98
88 problems (rounded to nearest whole)
correct answer E
Answer: E
Question: A can work three times as fast as B. Together they can finish a job in 24 days. In how many days can A complete the job alone?
Options:
A)28
B)30
C)32
D)34
E)36
Rationale: B's rate is x and A's rate is 3x.
x + 3x = 1/24
x = 1/96
A's rate is 3x = 1/32
A can complete the job in 32 days.
The answer is C.
Answer: C
Question: If two numbers are in the ratio 2:3. If 5 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)A)10
B)B)18
C)C)20
D)D)24
E)E)26
Rationale: 2:3
2x + 5 : 3x + 5 = 3 : 4
4[2x + 5] = 3[3x + 5]
8x + 20 = 9x + 15
9x - 8x = 20 - 15
x = 5
Then smallest number is = 2
2x = 10
Correct Option A
Answer: A
Question: 6.513/10.02 =
Options:
A) 0.35
B) 0.3505
C) 0.3509
D) 0.65
E) 0.3527
Rationale: 6.513 / 10.02
6.513 / 1002 = 6.5
move the comma two places to the left as we have 2 decimal places from the divisor: 0.65. Answer: D
Answer: D
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.40 for every box, and if the university needs 2.16 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
Options:
A)$120
B)$180
C)$310
D)$450
E)$640
Rationale: The volume of each box is 20*20*12 = 4800 cubic inches.
Number of boxes = 2,160,000/4800 = 450 boxes
Total cost = 450×$0.4=$180
The answer is B.
Answer: B
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 3% p.a. in 5 years. What is the sum?
Options:
A)26775
B)28772
C)28821
D)89255
E)28871
Rationale: Principal = (100 * 4016.25) / (3 * 5)
= Rs.26775.
Answer:A
Answer: A
Question: A company uses 5 pizza machines to produce 500 pizzas in a day. They buy 2 more new machines that can produce 20% more. How many pizzas in all can be produced for 5 days?
Options:
A)1,100
B)4,000
C)3,000
D)5,500
E)2,500
Rationale: Old machines produce 500*5= 2,500
New machines produce 1.20*2,500= 3,000
In all 2,500 + 3,000 = 5,500 pizzas an be produced.
Answer D.
Answer: D
Question: If x and y are prime numbers, which of the following CANNOT be the sum of x and y?
Options:
A)5
B)9
C)13
D)16
E)23
Rationale: All answer choices but D are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.
Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.
Answer: E.
Answer: E
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Options:
A)23772
B)14988
C)12778
D)14000
E)27191
Rationale: Explanation:
25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Answer: D
Question: What is the area of square field whose side of length 5 m?
Options:
A)80 sq m
B)26 sq m
C)25 sq m
D)45 sq m
E)96 sq m
Rationale: 5 * 5
= 25 sq m
Answer: C
Answer: C
Question: What is the smallest positive integer K such that the product of 1575 x K is a perfect square?
Options:
A)7
B)9
C)15
D)25
E)63
Rationale: perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.
Now, 1575 = 3^2 * 5^2 * 7, so if k=7 then 1575 k = (3 * 5 * 7)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).
Answer: A.
Answer: A
Question: What will come in place of the x in the following Number series? 5,28,57,88,125,166,209
Options:
A)156
B)159
C)166
D)170
E)256
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
209=43+166
256=47+ 209
=256
E
Answer: E
Question: Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?
Options:
A)22
B)40
C)277
D)26
E)12
Rationale: We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2 = 40.
Answer:B
Answer: B
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)11
B)50
C)88
D)53
E)22
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8 = 45 ==> x
= 53 km/hr.
Answer:D
Answer: D
Question: Convert 100 inches into centimeter?
Options:
A)112cm
B)120cm
C)150cm
D)210cm
E)254cm
Rationale: 1 inch = 2.54cm
100 inches = 100*2.54 = 254cm
Answer is E
Answer: E
Question: Two trains are moving in the same direction at 50 km/hr and 30 km/hr. The faster train crosses a man in the slower train in 18 seconds. Find the length of faster train.
Options:
A)1777 meter
B)100 meter
C)1787 meter
D)1768 meter
E)8167 meter
Rationale: ANSWER: B
Answer: B
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Options:
A)65 sec
B)88 sec
C)25 sec
D)88 sec
E)55 sec
Rationale: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer: C
Answer: C
Question: Working individually, Julie can peel potatoes in 10 hours and Ted can peel potatoes in 8 hours. If Julie and Ted work together but independently at the task for 4 hours, at which point Ted leaves, how many remaining hours will it take Julie to complete the task alone?
Options:
A)3/15
B)2/11
C)1/4
D)1/3
E)1
Rationale: In first 4 hrs Ted will finish 4/8 = 1/2 of work and Julie will finish 4/10 work so total 1/2 + 2/5 = 9/10 work is finished and
1-9/10 = 1/10 work remaining. Now Julie will take (1/10)*10 = 1 hrs to finish it.
So answer is E.
Answer: E
Question: In a School, 93 percent of students like vegetarian, 95 percent of students like Non-veg, 89 percent likes fast food and 91 percent likes Chines food.
Can you find out the percentage of students who like all 4 food variety?
Options:
A)50%
B)65%
C)75%
D)88%
E)68%
Rationale: E
68% of student study all four subjects.
Answer: E
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 25 mangoes. Find the gain percent?
Options:
A)27%
B)25%
C)21%
D)20%
E)24%
Rationale: SP = CP + g
150 SP = 150 CP + 25 SP
125 SP = 150 CP
125 --- 25 CP
100 --- ? => 20%
Answer:D
Answer: D
Question: On a certain farm the ratio of horses to cows is 5:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 17:7. After the transaction, how many more horses than cows would the farm own?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Originally, there were 5k horses and k cows.
7(5k-15) = 17(k+15)
35k-17k = 255+105
18k = 360
k = 20
The difference between horses and cows is (5k-15)-(k+15) = 4k-30 = 50
The answer is C.
Answer: C
Question: If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of?
Options:
A)150
B)339
C)342
D)359
E)362
Rationale: Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer W= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
Answer: C
Question: Ashok secured average of 70 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
Options:
A)50
B)74
C)78
D)80
E)None of these
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 70
Therefore total marks in 6 subjects = 70 * 6 = 420
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 420 – 370 = 50
ANSWER A
Answer: A
Question: If the sides of a triangle are 28 cm, 26 cm and 10 cm, what is its area?
Options:
A)120
B)130
C)288
D)266
E)2848
Rationale: The triangle with sides 28 cm, 26 cm and 10 cm is right angled, where the hypotenuse is 28 cm.
Area of the triangle = 1/2 * 26 * 10 = 130 cm2
Answer: B
Answer: B
Question: How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits D equal to 28?
Options:
A)14
B)24
C)28
D)48
E)96
Rationale: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So D=24+24=48.D
Answer: D
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)Rs.1000
B)Rs.1087
C)Rs.1028
D)Rs.1029
E)Rs.1023
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: A
Question: A lady has fine gloves and hats in her closet - 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure she has a pair of each color?
Options:
A)60
B)65
C)70
D)75
E)80
Rationale: 32r+24y+1y+1b+2b=60
ANSWER:A
Answer: A
Question: A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 8 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
Options:
A)$54.00
B)$89.60
C)$90.00
D)$100.80
E)$154.80
Rationale: Correct Answer: B
The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.08 ($1120) = $89.60. The correct answer is B.
Answer: B
Question: The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number.
Options:
A)28
B)19
C)37
D)46
E)50
Rationale: a+b = 10
10a + b - 10b - a = 54
a-b = 6
a= 8, b = 2.
Reversed number is 28.
Ans A
Answer: A
Question: If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers?
Options:
A)It is a multiple of 3
B)It is a multiple of 4
C)It is a multiple of 2
D)It is a multiple of 5
E)It is a prime number
Rationale: n+14 is a positive odd integer. This means n will be an odd integer
The next 4 integers would be: n + 14, n + 15, n + 16, n + 17
Sum = 4n + 62
This sum will always be even.
Option C
Answer: C
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 24 girls Will take to construct?
Options:
A)4 days
B)14 days
C)6 days
D)8 days
E)9 days
Rationale: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
8 boys + 24 girls = 8 Ã— 6/4 + 12 = 12 + 24 = 36 girls
4 days to complete the work
Answer: Option A
Answer: A
Question: A dishonest dealer uses a scale of 92 cm instead of a metre scale and claims to sell at cost price. His profit is
Options:
A)9%
B)10%
C)12%
D)None of these
E)8.7%
Rationale: Solution
Gain%	= (8 / 92 x 100)%
= 8.7%
Answer E
Answer: E
Question: A man is 28 years older than his son. In four years, his age will be twice the age of his son. The present age of this son is
Options:
A)21 years
B)22 years
C)23 years
D)24 years
E)25 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+28.
=> 2(x+4) = (x+28+4)
=> 2x+8 = x+32
=> x = 24 years
Answer: Option D
Answer: D
Question: Reduce
368/736
to the lowest terms
Options:
A)3/5
B)2/9
C)2/8
D)1/2
E)None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 736 which is 368
Step2: Divide both by 368, we will get the answer 1/2
Answer: Option D
Answer: D
Question: From a group of 5 boys and 5 girls, 6 children are to be randomly selected. What is the probability that 3 boys and 3 girls will be selected?
Options:
A)4/15
B)6/17
C)8/19
D)10/21
E)12/23
Rationale: The total number of ways to choose 6 children from 10 is 10C6 = 210
The number of ways to choose 3 boys and 3 girls is 5C3*5C3 = 10*10 = 100
P(3 boys and 3 girls) = 100/210 = 10/21
The answer is D.
Answer: D
Question: If x and y are integers and x divided by y is 17.15, then which of the following integers is a possible value for the remainder when x is divided by y? I. 15 II. 5 III. 3
Options:
A)II only
B)I only
C)II,III only
D)III only
E)I,III only
Rationale: x=17.15y from which x = 17y + 15y/100 or x = 17y + 3y/20.
Since x and y are integers, 3y/20 must also be an integer. 3 is not divisible by 20, then y must be divisible by 20, and therefore, y/20 is an integer and 3y/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.
Answer E
Answer: E
Question: If each side of a rectangle is increased by 50% with the length being double the width, find the percentage change in its area?
Options:
A)284%
B)276%
C)265.25%
D)284.5%
E)275%
Rationale: area = 2a x a
New length = 250a / 100 = 5a /2
New width = 150a / 100 = 3a /2
New area =(5a x 3a) / (2 x 2) = (15a²/4)
increased area== (15a²/4) - a²
Increase %= [(11a²/4 ) x (1/a² ) x 100]% = 275%
answer :E
Answer: E
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.75 at the candy store. What is John’s weekly allowance?
Options:
A)$2.40
B)$2.80
C)$3.20
D)$3.60
E)$4.80
Rationale: Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.8
Therefore, X=$2.80. Answer B
Answer: B
Question: By approximately what percent is x greater than 2/5 if (3/5)(x) = 1?
Options:
A)723%
B)156%
C)316%
D)37%
E)29%
Rationale: what percent is x greater than 2/5 if (3/5)(x) = 1?
=> x = 5/3
% change =[(5/3 -2/5) /(2/5) ] * 100
= 316.5%
= 316% approx
Ans ,C
Answer: C
Question: How many positive integer solutions does the equation 2x+3y = 100 have?
Options:
A)50
B)33
C)16
D)35
E)14
Rationale: formula: (constant)/(lcm of two nos)
=100/(2*3)=15.5
ANSWER:C
Answer: C
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 five 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?
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: 2*3*5 = 30
The answer is B.
Answer: B
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is
Options:
A)48
B)22
C)56
D)27
E)67
Rationale: Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
Option A
Answer: A