mathewhe/aqua_rat huggingface dataset:
Question: If 45% of a number is 36, then the number is
(A) number is 60
(B) number is 70
(C) number is 90
(D) number is 80
(E) None of these
Rationale: Solution:
Let "a" be the number we seek. We get
45% × a = 36
2 × 45% × a = 2 × 36 = 72
90% × a = 72
10% × a = 72 : 9 = 8
100% × a = 8 × 10 = 80
a = 80
Answer D
Answer: (D) number is 80
Question: A special municipal payroll tax charges not tax on a payroll less than $200,000 and only 0.2% on a company’s payroll above $200,000. If Belfried Industries paid $400 in this special municipal payroll tax, then they must have had a payroll of
(A) $180,000
(B) $400,000
(C) $220,000
(D) $402,000
(E) $2,200,000
Rationale: ANSWER : B , ( with different approach) :
The 400 paid is 0.2% of the additional amount above 200,000. Let it be X
Now 0.2% of X = 400
Therefore X= 200,000
Total = 200,000 + X= 400,000
Answer: (B) $400,000
Question: If a * b = 2a – 3b + ab, then 5 * 7 + 7 * 5 is equal to:
(A) 34
(B) 18
(C) 72
(D) 78
(E) 82
Rationale: 5 * 7 + 7 * 5 = (2 * 5 – 5 * 7 + 5* 7) + (2 * 7 – 5 * 5 + 7 * 5)
= (10 + 14 – 25 + 35) = 34.
ANSWER:A
Answer: (A) 34
Question: The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ?
(A) Rs. 11,300
(B) Rs. 11,500
(C) Rs. 11,302
(D) Rs. 11,301
(E) Rs. 11,303
Rationale: Explanation:
Manager's monthly salary
= Rs. (1900 x 25 - 1500 x 24) = Rs. 11,500
Answer:B
Answer: (B) Rs. 11,500
Question: How many four letter words are formed using the letters of the word PROBLEM?
(A) 760
(B) 800
(C) 840
(D) 880
(E) 920
Rationale: The number of letters in the given word is seven.
The number of four letter words that can be formed using these seven letters is 7P4
= 7 * 6 * 5 * 4 = 840.
Answer: C
Answer: (C) 840
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 40%
(B) 50%
(C) 55%
(D) 65%
(E) 70%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: (B) 50%
Question: A began business with 12500 and is joined afterwards by B with 50000. When did B join, if the profits at the end of the year are divided equally?
(A) 3 months
(B) 9 months
(C) 10 months
(D) 7 months
(E) None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12500 : (12 – x) × 50000
or 12 : 4(12 – x)
Since profit is equally divided so
12 = 4(12 – x) or x = 3. Thus B joined after 8 months.
Answer A
Answer: (A) 3 months
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel eight times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/8 and W = 8S
Then we have 1/(8*S) + 1/S = 1/8 <=> 9/(8*S) = 1/8 <=> S = 9
ANS: D
Answer: (D) 9
Question: a, b are positive integers. The remainder of a to be divided by 8 is 5 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48
(A) a) 10
(B) b) 6
(C) c) 8
(D) d) 12
(E) e) 20
Rationale: Two ways to do it...
a=8x+5..
b=6y+2..
1) convenient way..
Take x and y as 0, and you will get a*b as 5*2=10
Answer : A
Answer: (A) a) 10
Question: A and B complete a work in 8 days. A alone can do it in 14 days. If both together can do the work in how many days?
(A) 5 days
(B) 8 days
(C) 6 days
(D) 3.15 days
(E) 2.75 days
Rationale: 1/8 + 1/14 = 11/56
56/11 = 5 days
Answer: A
Answer: (A) 5 days
Question: Here the sum of the series is 4+8+12+16+….. =612. find how many terms are there in the series?
(A) 15
(B) 19
(C) 17
(D) 14
(E) 13
Rationale: Solution: This is an A.P. in which a=4, d=4 and Sn=612
Then, n/2[2a+(n-1)d]=612 => n/2[2*4+(n-1)*4]=612
=> 4n/2(n+1)=612
=> n(n+1)=306
=> n^2+n-306=0
=> n^2+18n-17n-306=0
=> n(n+18)-17(n+18)=0
=> (n+18)(n-17)=0
=> n=17.
Number of terms=17.
Answer C
Answer: (C) 17
Question: If a man crosses a 600 m long street in 5 minutes. What is his speed?
(A) 7 km/hr
(B) 7.1 km/hr
(C) 7.2 km/hr
(D) 8 km/hr
(E) 9.2 km/hr
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
C
Answer: (C) 7.2 km/hr
Question: P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 40 meter/sec.
(A) 21 meter/sec
(B) 7 meter/sec
(C) 14 meter/sec
(D) 18 meter/sec
(E) 35 meter/sec
Rationale: P's speed =40 m/s
P's distance = 1000m (as it is a km race)
t = 1000/16 =25 sec
Q's distance = 1000-125= 875m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 875/25 = 35 m/s
Hence E is the answer.
Answer: (E) 35 meter/sec
Question: I have two 10 paise coins. If 4 If 4/5 of what I have is 8is 8/9 of what you have, how much do you have?
(A) 13
(B) 17
(C) 11
(D) 18
(E) 11
Rationale: D
18 paise.
Answer: (D) 18
Question: The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-seventh of its original value. How many amperes of electrical current will flow through the wire?
(A) 4/7
(B) 7
(C) 14
(D) 28
(E) 35
Rationale: Given that, I∝1/R, I*R is a constant value.
I1*R1 = I2*R2
I1*R1 = I2*R1/7
I2 = 7*I1 = 28 amperes
The answer is D.
Answer: (D) 28
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 12, the how old is B?
(A) 10 years
(B) 4 years
(C) 6 years
(D) 15 years
(E) 16 years
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 12
5x = 10
x = 2.
Hence, B's age = 2x = 4 years.
B)
Answer: (B) 4 years
Question: In how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together.
(A) W8
(B) 789
(C) 279
(D) 277
(E) 191
Rationale: Answer:D
Answer: (D) 277
Question: A car salesman earns a base salary of $800 per month plus a commission of $200 for each car he sells. If the car salesman earned $1600 in May, how many cars does he need to sell in June in order to double his May earnings?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 800+200x=3200
x=12 cars.
The answer is C.
Answer: (C) 12
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 833 1/0
(B) 833 1/3
(C) 833 1/21
(D) 833 1/2
(E) 833 1/3
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: B
Answer: (B) 833 1/3
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 9000 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
(A) 9000
(B) 98000
(C) 50000
(D) 11000
(E) 12000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 9000 ( 18 × 500 = 9000)
100% -------> 50000 votes (100 × 500 = 50000)
C
Answer: (C) 50000
Question: Reeya obtained 40, 60, 70, 80 and 80 out of 100 in different subjects, What will be the average
(A) 66
(B) 75
(C) 80
(D) 85
(E) 90
Rationale: Explanation:
(40+60+70+80+80 / 5)=66
Option A
Answer: (A) 66
Question: Convert 0.38 in to a vulgar fraction ?
(A) 18/50
(B) 16/50
(C) 17/50
(D) 19/50
(E) None
Rationale: Answer
0.38 = 38/100 = 19/50
Correct Option: D
Answer: (D) 19/50
Question: A worker is paid x rupees for painting every 25 metres of a wall and y rupees for painting every extra metre. During one week, he painted 25 metres on Monday, 50 metres on Tuesday, 25 metres on Wednesday, 45 metres on Thursday and 25 metres on Friday. What is his average daily earning rupees for the five day week?
(A) x + (8/5)y
(B) (5x + 9y)/5
(C) x + 9y
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
On Monday, the payment = Rs x
On Tuesday, the payment = Rs (x + 25y)
On Wednesday, the payment = Rs x
On Thursday, the payment = Rs (x +20y)
On Friday, the payment = Rs x
Average daily earning during the five-day week = (5x + 45y)/5
= x + 9y
Answer : C
Answer: (C) x + 9y
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
(A) 24000
(B) 23000
(C) 22000
(D) 25000
(E) 26000
Rationale: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
25 = 1/100 * x => x = 25000
ANSWER:D
Answer: (D) 25000
Question: If there are 200 questions in a 3 hr examination. Among these questions are 20 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
(A) 72 min
(B) 62 min
(C) 70 min
(D) 32.72727 min
(E) 76 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
180x+20*2x=180
x=180/220
x=0.818182
time taken for type A problem=20*2*0.818182=32.72727min
ANSWER:D
Answer: (D) 32.72727 min
Question: A runs twice as fast as B and gives B a start of 42m.How long should the racecourse be so that A and B might reach in the same time?
(A) 75 m.
(B) 80 m.
(C) 84 m.
(D) 100 m.
(E) None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 42m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 42m is 42/1=42m
so the total time taken by a and b to reach =2*42=84m
ANSWER:C
Answer: (C) 84 m.
Question: The speed of a boat in still water in 22 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 24 minutes is:
(A) 10.6
(B) 10.2
(C) 10.8
(D) 10.4
(E) 10.0
Rationale: Speed downstream = (22 + 5) = 27 kmph
Time = 24 minutes =24/60 hour = 2/5 hour
Distance travelled = Time × speed =2/5×27 = 10.8 km
Answer is C.
Answer: (C) 10.8
Question: A car that has an original value of $52,500 depricates $10000 in the first year and there original cost per year. What is its value after 8 years?
(A) $12100
(B) $13100
(C) $14100
(D) $15100
(E) $16100
Rationale: 1st year depreciation amount = 10000
next 7 year's depreciation amount = 7 * 8% original cost price
= 7*8/100 * 52500
=29400
Total depreciation amount = 39400
Value after 8 years = $13100
ANSWER:B
Answer: (B) $13100
Question: Which of the following is an integer?
I. 13! / 6!
II. 13! / 8!
III. 13! / 7!5!
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: 13!/6! = 13*12*11*10*9*8*7 which is an integer.
13!/8! = 13*12*11*10*9 which is an integer.
13!/7!5! = 13*12*11*10*9*8 / 5*4*3*2 = 13*12*11*3*2 which is an integer.
The answer is E.
Answer: (E) I, II and III
Question: If a computer program generates three-digit odd numbers using the numbers 9, 7, 0, 6, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: A
Answer: (A) 1/3
Question: Last year the range of the annual sales of the 100 lamps at Company X was $30,000. If the annual sale of each of the 100 lamps this year is 10 percent greater than it was last year, what is the range of the annual sales of the 100 lamps this year?
(A)  $27,000
(B)  $30,000
(C)  $33,000
(D)  $36,000
(E)  $63,000
Rationale: let the lowest sale be x.
Therefore, highest sale is x +30000.
Now sale of each lamp is increased by 10%.
Therefore the sale will remain arranged in the same order as before.
or Lowest sale = 1.1x and Highest = 1.1 * (x+30000)
or Range = highest - lowest = 1.1 * (x+30000) - 1.1x
= 33000, Hence, C
Answer: (C)  $33,000
Question: A sum of 1200 lent at S.I at 10% will become twice in how many years?
(A) 12 years
(B) 14 years
(C) 10 years
(D) 8 years
(E) 6 years
Rationale: Explanation:
To become twice means S.I should be as much as initial sum i.e, 1200
(1200 x 10 x T)/100 = 1200
T = 10 years
Answer: Option C
Answer: (C) 10 years
Question: If the sum of two positive integers is 12 and the difference of their squares is 48, what is the product of the two integers?
(A) 32
(B) 119
(C) 128
(D) 135
(E) 143
Rationale: Let the 2 positive numbers x and y
x+ y = 12 -- 1
x^2 - y^2 = 48
=> (x+y)(x-y)=48 -- 2
Using equation 1 in 2 , we get
=> x-y = 4 -- 3
Solving equation 1 and 3 , we get
x= 8
y= 4
Product = 8*4 = 32
Answer A
Answer: (A) 32
Question: The output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?
(A) 20%
(B) 27%
(C) 30%
(D) 32%
(E) 79%
Rationale: The original output increases by 15% and then 20%.
Total % change = a + b + ab/100
Total % change = 15 + 20 + 15*20/100 = 38%
Now, you want to change it to 0, so,
0 = 38 + x + 38x/100
x = -38(100)/138 = 27% approximately
Answer is B
Answer: (B) 27%
Question: In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 53900. How many times did he participate in the competition?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 53900 = 2*2*5*5*7*7*11
John participated 7 times.
The answer is A.
Answer: (A) 7
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is
(A) 9 years
(B) 19 years
(C) 29 years
(D) 39 years
(E) None
Rationale: Solution
Let B's present age	= x years.
Then, A's present age	‹=› (x + 9) years.
∴(x + 9) + 10 = 2 (x - 10)
‹=› x + 19 = 2x - 20
‹=› x = 39.
Answer D
Answer: (D) 39 years
Question: Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?=
(A)  y = 1.2 × 10^a, where a is a positive integer.
(B)  y = 1.5 × 10^b, where b is a positive integer.
(C)  y = 1.8 × 10^c, where c is a positive integer.
(D)  y = 2.5 × 10^d, where d is a positive integer.
(E)  y = 2.7 × 10^e, where e is a positive integer.
Rationale: Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option A is correct answer?
Answer: (A)  y = 1.2 × 10^a, where a is a positive integer.
Question: A cycle is bought for Rs.900 and sold for Rs.1170, find the gain percent?
(A) 27%
(B) 20%
(C) 80%
(D) 30%
(E) 24%
Rationale: 900 ---- 270
100 ---- ? => 30%
Answer: D
Answer: (D) 30%
Question: A person has three children with at least one boy. Find the probability of having at least two boys among the children.
(A) 3/4
(B) 1/3
(C) 2/3
(D) 1/4
(E) 1/5
Rationale: Explanation :
The event is occuring under the following situations:
Second is a boy and third is a girl OR
Second is a girl and third is a boy OR
Second is a boy and third is a boy
This will be represented by: (1/2) x (1/2) + (1/2) x (1/2) + (1/2) x (1/2) = 3/4
Answer : A
Answer: (A) 3/4
Question: 39 persons can repair a road in 24 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 13
(C) 14
(D) 15
(E) 26
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons	30	:	39	:: 12 : x
Working hours/day	6	:	5
30 x 6 x x = 39 x 5 x 24
x =	(39 x 5 x 24)/(30 x 6)
x = 26.
ANSWER:E
Answer: (E) 26
Question: P software has coding line 5% more than N, N software has coding line 4/20 more than M. M software has 80 lines of coding. find P lines.
(A) 101
(B) 107
(C) 108
(D) 109
(E) 110
Rationale: M s/w has 80 line of code
N s/w has = 80+80*4/20= 96 line of code
P s/w 5% more N' code 96+4.8=100.8
or
101 line of code
ANSWER:A
Answer: (A) 101
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 2 years
(B) 6 years
(C) 8 years
(D) 3 years
(E) 9 years
Rationale: 9261 = 8000(21/20)N
(21/20)3
= (21/20)N
=> N = 3
Answer:D
Answer: (D) 3 years
Question: The ratio of the incomes of Uma and Bala is 4:3 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $5000 then the income of Uma is?
(A) $24000
(B) $23000
(C) $22000
(D) $21000
(E) $20000
Rationale: Let the income of Uma and Bala be $4x and $3x
Let their expenditures be $3y and $2y
4x-3y = 5000-------1)
3x-2y = 5000-------2)
From 1) and 2)
x = 5000
Uma's income = 4x = 4*5000 = $20000
Answer is E
Answer: (E) $20000
Question: A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 15days, A finished the remaining work. In how many days A alone can finish the job?
(A) 10
(B) 25
(C) 60
(D) 30
(E) 20
Rationale: A+B 10days work = 10*1/40 = 1/4
Remaining work = 1-1/4 = 3/4
3/4 work is done by A in 15days
whole work will be done by A in 15*4/3 = 20days
Answer is E
Answer: (E) 20
Question: The number of years of service of the eight employees in a production department are 15, 10, 9, 19, 6, 4, 14 and 16. What is the range in the number of years of service of the eight employees?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: = 19-4
= 15
Answer E
Answer: (E) 15
Question: From the set of numbers {p, t, u, v, w, x, y, z}, how many different combinations can we have without the t or the u in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)
(A) 16
(B) 31
(C) 32
(D) 63
(E) 64
Rationale: Any letter (p, v, w, x, y, z) can be included or not.
Thus there are 2^6 combinations - 1 empty combination = 63 combinations
The answer is D.
Answer: (D) 63
Question: 650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
(A) a) 162
(B) b) 138
(C) c) 60
(D) d) 38
(E) e) 13
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 650 = 13
Answer: E
Answer: (E) e) 13
Question: Which of the following is always true for any real number 'a' and 'b'?
(A) |ab| = |a||b|
(B) |a/b| = |a|/|b|
(C) |-ab| < |a||b|
(D) |ab| > |a/b|
(E) |ab| = -|ab|
Rationale: This one is obvious if you know how absolute value works. One of the fundamental principles of absolute value is multiplicativeness, which holds that for absolute values, f(ab) = f(a) f(b). Thus the answer is A.
Answer: (A) |ab| = |a||b|
Question: The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 8981
(B) 3799
(C) 1200
(D) 2693
(E) 1732
Rationale: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer: C
Answer: (C) 1200
Question: How many ounces of a 60% salt solution must be added to 70 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?
(A) 16.67
(B) 30
(C) 50
(D) 60.33
(E) 70
Rationale: let x=ounces of 60% salt solution to be added
.2*70+.6x=.4(70+x)
x=70
Answer E
Answer: (E) 70
Question: A field is 90 metre long and 50 metre broad. A 25 metre long, 20 metre broad and 4 metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field. How much the level of field will rise?
(A) 0.5 metre
(B) 0.3 metre
(C) 0.8 metre
(D) 0.6 metre
(E) 0.7 metre
Rationale: Area of field = 90 x 50 = 4500 m2
Area of field dug out = 25 x 20 = 500 m2
Therefore, Area of remaining field = 4500 m2 - 500 m2 = 4000 m2
Volume of the earth dug out = 25 x 20 x 4 = 2000 m3
Therefore, Field will rise by 2000/4000 = 0.5 metre
Answer A
Answer: (A) 0.5 metre
Question: A shopkeeper purchased 70 kg of potatoes for Rs.420 and sold the whole lot at the rate of Rs 6.50 per kg .What will be his gain percent?
(A) 8 1/9
(B) 8 1/1
(C) 8 1/3
(D) 8 1/7
(E) 8 1/4
Rationale: Explanation:
Price per 1 kg = 4207042070 = Rs.6.
Profit per 1 kg = Rs.6.5 – Rs.6 = Rs.0.5
Profit for 70 kg = 0.5 × 70 = Rs.35
Gain % = 3542035420 × 100= 8.33% = 8 1/3
Answer: C
Answer: (C) 8 1/3
Question: Perimeter of rhombus is equal to perimeter of circle. Longest distance between two points in rhombus is 80. Area of rhombus is 2400 cm^2. Find area of circle.
Options: 10000, 62500, 2500, one more I don't Remember.
(A) 3284.28678
(B) 3184.28678
(C) 3084.28678
(D) 4184.28678
(E) 2184.28678
Rationale: Let Diagonals of Rhombus are p,q and side is a .
Let Longest side is one of the p and q, let its p=80;
Area of a Rhombus is A =p*q/2
A=2400
2400=80 *q /2
4800=80q=> q=60
4a^2 =60^2 + 80^2
4a^2=10,000=> a=>50
Given: Perimeter of R = Perimeter of Circle
4a = 2*3.14* r=> r=31.84
Area of circle = 3.14* r^2 = 3184.28678
ANSWER:B
Answer: (B) 3184.28678
Question: The simple interest at y% for y years will be $y on a sum of
(A) $ (1000)/x
(B) $(100)x^2
(C) $ x
(D) $ (100)/y
(E) $ 100x
Rationale: Principal =$(100*y)/(y*y)=$(100/y).
Answer is D
Answer: (D) $ (100)/y
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
(A) 6 2/3%
(B) 6 2/8%
(C) 6 7/3%
(D) 9 2/3%
(E) 6 2/5%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3
= 6 2/3%
Answer:A
Answer: (A) 6 2/3%
Question: If 20 men take 15 days to to complete a job, in how many days can 20 men finish that work?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Ans. 15 days
Answer: (A) 15
Question: When a number is divided by 3 &then multiply by 12 the answer is 9 what is the no.?
(A) 4.5
(B) 5
(C) 2.25
(D) 5.7
(E) 6.5
Rationale: if $x$ is the number, x/3 * 12 = 9
=> 4x = 9
=> x = 2.25
C
Answer: (C) 2.25
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
(A) 17523
(B) 2788
(C) 1750
(D) 2787
(E) 29899
Rationale: Explanation:
C.I.= Rs.[4000*(1+10/100)^2-4000]
=Rs.840
sum=Rs.(420 * 100)/3*8=Rs.1750\
Answer: C) Rs,1750
Answer: (C) 1750
Question: A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 5)%. In terms of x, how many species of bacteria will the group be able to model?
(A) x*x – 5x
(B) (x)(105 – x)
(C) (100)(105 – x)
(D) (100)(95 – x)
(E) (x-5)/100
Rationale: Let's say that x = 10
So 10% of 10,000 = 1,000 types of bacteria
After the budget cuts, this 1,000 is reduced by (10-5)% = 5%
5% of 1,000 = 50
1,000 - 50 = 950
Plug x=10 into the answers and find 950.
Answer:B
Answer: (B) (x)(105 – x)
Question: 5, -28, 2, -31....
(A) 1
(B) 3
(C) 2
(D) 4
(E) 5
Rationale: 5 - 33 = -28
-28 +30 = 2
2 - 33 =31
31 + 30 = 1
ANSWER:A
Answer: (A) 1
Question: A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 5 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
(A) 2
(B) 9
(C) 15
(D) 21
(E) 30
Rationale: Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.
Then under plan A the cost would be $0.6+0.06(t-5) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-5)=0.08t --> 60+6(t-5)=8t --> t=15.
Answer: C.
Answer: (C) 15