divelab/Sys2Bench huggingface dataset:
Question: Java House charges $4.25 for a cup of coffee that costs a total of $3.85 to make. Cup'O'Joe charges $4.80 for a cup that costs $4.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?
Options:
A)7,858
B)8,301
C)14,667
D)63,840
E)146,667
Rationale: Java: Profit/Cup = 4.25-3.85 = 0.4
: No of Cups = 55,000
: Gross Profit = 55,000*0.4 = 22,000
Joe: Profit/Cup = 0.15
: Gross Profit = 22,000
: No of Cups = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)
Answer E
Answer: E
Question: In a forest 160 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Options:
A)150
B)750
C)1,250
D)1,600
E)2,500
Rationale: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 160 tagged deers comprise 10% of total # of deers --> total # of deers = 160*10 = 1,600.
Answer: D.
Answer: D
Question: If each term in the sum T=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12=T => 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
Hence C.
Answer: C
Question: When x + p is divided by p - 2, the quotient is n and there is no remainder. Which of the following must be the value of x?
Options:
A)n(p +1)
B)n(p − 1)
C)p(n + 1) + 2n
D)p(n - 1) + 2n
E)n(p + 1) (p − 1)
Rationale: Given in question (x+p)/p-2= n
=> x+p= n(p-2)
=>x= np+2n-p
or x= np-p+2n
Now we are good to check the options
x= p(n-1) + 2n
Answer D
Answer: D
Question: Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 2500 = D(100/4)2
D = 4
Answer: D
Answer: D
Question: What was the day of the week on, 16th July, 1776?
Options:
A)Tuesday
B)Wednesday
C)Monday
D)Saturday
E)SUNDAY
Rationale: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 2 days)
Total number of odd days = (0 + 2) = 2.
Required day was 'Tuesday'.
Answer:A
Answer: A
Question: A horse is tethered to one corner of a rectangular grassy field 45 m by 25 m with a rope 22 m long. Over how much area of the field can it graze?
Options:
A)354 cm2
B)380 m2
C)350 m2
D)407 m2
E)None of these
Rationale: Area of the shaded portion
= 1⁄4 × π × (22)2 = 380 m2
Answer B
Answer: B
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Options:
A)20 hrs
B)25 hrs
C)35 hrs
D)Cannot be determined
E)None of these
Rationale: Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/5
7/x = 1/5 => x = 35 hrs.
ANSWER:C
Answer: C
Question: If 0 < a < b < c < 1 , which of the following are positive?
I.	b-c
II.	a-b
III.	c-a
Options:
A)I only
B)II only
C)III only
D)I and II
E)I and III
Rationale: We could solve this easily using examples.
I is false since b<c and both are positive
II is false since b<c and both are positive
III is true since c>a and both are positive
So, the answer is C.
Answer: C
Question: Evaluate combination
100C97=100!/(97)!(3)!
Options:
A)161700
B)151700
C)141700
D)131700
E)None of these
Rationale: Explanation:
nCr=n!/(r)!(n−r)!
100C97=100!/(97)!(3)!
=100∗99∗98∗97!/(97)!(3)!
=100∗99∗98/3∗2∗1
=100∗99∗98/3∗2∗1=161700
Option A
Answer: A
Question: Find the area of trapezium whose parallel sides are 26 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)227
B)299
C)330
D)161
E)212
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (26 + 18) * (15)
= 330 cm2
Answer: C
Answer: C
Question: X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14080 ?
Options:
A)3200
B)4000
C)3250
D)3825
E)4096
Rationale: Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = 14080 Ã— 16/55 = Rs.4096.
Share of Z in the profit is Rs.4096.
Option E
Answer: E
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)16 seconds
B)18 seconds
C)19 seconds
D)27 seconds
E)10 seconds
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5
= 27 seconds.
Answer:D
Answer: D
Question: If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265
Options:
A)Rs. 750
B)Rs. 800
C)Rs. 850
D)Rs. 900
E)None of these
Rationale: Explanation:
Let the cost of Production = Rs. P
Then, as per question,
=>(125/100∗115/100∗110/100∗P)=1265
=>253/160P=1265
=>P=800
Option B
Answer: B
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)12
B)16
C)17
D)19
E)10
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.
Answer: A
Answer: A
Question: A meeting has to be conducted with 5 managers.Find the number of ways in which the managers may be selected from among 8 managers,if 2 managers will not attend the meeting together.
Options:
A)1.35
B)2.91
C)3.12
D)4.36
E)5.15
Rationale: 8 managers, but two of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these two managers in it. That would mean selecting 5, from the remaining 6 which is 6C5 = 6
2. Meeting with one of the two managers. select 1 manager from two, and then select 4 from the remaining 6, which is 2C1 X 6C4 = 15.
So, answer is 30 + 6 = 36.
Answer : D
Answer: D
Question: If 0.25 of a number is equal to 0.05 of another number, the ratio of the numbers is :
Options:
A)2 : 5
B)3 : 4
C)1 : 5
D)20 : 5
E)30:7
Rationale: 0.25A = 0.05B
-> A/B = 0.05/0.25 = 5/25 = 1/5
:. A : B = 1 : 5
ANSWER:C
Answer: C
Question: The average weight of A,B,C is 45 Kg. The avgwgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
Options:
A)23
B)43
C)21
D)31
E)43
Rationale: Sol. Let A,B,c represent their individual wgts.
Then,
A+B+C=(45*3)Kg=135Kg
A+B=(40*2)Kg=80Kg & B+C=(43*2)Kg=86Kg
B=(A+B)+(B+C)-(A+B+C)
=(80+86-135)Kg
=31Kg.
ANSWER D
Answer: D
Question: A family made a down payment of $20
and borrowed the balance on a set of
encyclopedias that cost $120. The
balance with interest was paid in 7
monthly payments of $15.2 each and a
final payment of $7. The amount of
interest paid was what percent of the
amount borrowed?
Options:
A) 6%
B) 12%
C) 13.4%
D) 16%
E) 20%
Rationale: interest paid = 15.2*7+7 - 100 = 13.4
% off the balance = (13.4/100) * 100 = 13.4 %
Answer is C.
Answer: C
Question: If x^2 = 161, which of the following is closest to a potential value of x?
Options:
A)-127
B)-11
C)12
D)13
E)131
Rationale: Here the thing we must not forget is that X^even has two potential solutions
=> x =+- √161 => +- 13 (approx)
this value is closer to 13
Hence D is correct.
Answer: D
Question: What least number should be subtracted from 1398 so that the remainder when divided by 7, 9, and 11 will leave in each case the same remainder 5 ?
Options:
A)6
B)7
C)8
D)10
E)11
Rationale: The LCM of 7, 9, and 11 is 693. The next multiple is 2*693 = 1386.
1386 + {remainder} = 1386 + 5 = 1391, which is 7 less than 1398.
Answer: B.
Answer: B
Question: If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ?
Options:
A)12
B)7
C)11
D)9
E)10
Rationale: E
Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1
Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)
Answer: E
Question: If 90% of A =30% of B and B=x% of A, then the value of x is?
Options:
A)800
B)300
C)700
D)400
E)None of these
Rationale: 0.9 A= 0.3 B
so b=3A means 300% of A
ANSWER:B
Answer: B
Question: During the first two weeks of May, the total rainfall in Springdale was 35 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of May?
Options:
A)12
B)15
C)18
D)21
E)24
Rationale: Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.
2.5x = 35
x = 14
The rainfall during the second week was 1.5 * 14 = 21 inches
The answer is D.
Answer: D
Question: An athlete runs 200 metres race in 25 seconds. What is his speed?
Options:
A)23
B)38
C)37
D)30
E)28.8
Rationale: Speed=Distance/Time = 200/25 = 8 m/s = 8 * 18/5 = 28.8 km/hr
Answer :E
Answer: E
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 25 to produce 100 units?
Options:
A)5
B)9
C)6
D)10
E)2
Rationale: 5 machines would produce 100 units in 50 hours. Increasing the amount of machines by 5 would mean dividing 50 hours by 5.
50/5 = 10
Answer : D
Answer: D
Question: A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work?
Options:
A)22
B)88
C)27
D)14
E)99
Rationale: Let A worked for x days.
x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18
A worked for 18 days. So, A can complete the remaining work in 18 - 4 = 14 days.
Answer: D
Answer: D
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 1440, find the total rent of the field.
Options:
A)6500
B)3550
C)4250
D)2250
E)3250
Rationale: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=1440 = x=(1440 x 325)/72 = 6500
Hence, total rent of the field is Rs. 6500.
Answer is A.
Answer: A
Question: Which of the following is equal to (x+2)!/x!?
Options:
A)x-1
B)1+(1/x)
C)1
D)x+1
E)(x+1)(x+2)
Rationale: (x + 1)! = (x + 1) (x+2)* x!
(x + 1)!/x! = (x + 1)(x+2)
Answer: E
Answer: E
Question: A can do a job in 8 days and B can do it in 20 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)21 ½ days
B)11 3/7 days
C)23 ½ days
D)12 ½ days
E)None of these
Rationale: Explanation:
1/8 + 1/20 = 7/40
40/7 = 40/7 *2 = 11 3/7 days
Answer: B
Answer: B
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Options:
A)11
B)99
C)28
D)20
E)87
Rationale: In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.
stoppage time = 20/60 hrs = 20 min.
Answer:D
Answer: D
Question: The price of 3 tables and 4 chairs is Rs. 3300. With the same money one can buy 2 tables and 10 chairs. If one wants to buy 1 table and 1 chair, how much does he need to pay?
Options:
A)Rs.940
B)Rs.1050
C)Rs.1040
D)Rs.950
E)Rs.960
Rationale: Explanation :
Let price of a table = t
and price of a chair = c
3t + 4c = 3300 ---(Equation 1)
2t + 10c = 3300
=> t + 5c = 1650 ---(Equation 2)
(Equation 2) × 3 => 3t + 15c = 4950 ---(Equation 3)
(Equation 3) - (Equation 1) => 11c = 1650
=> c = 150
Substituting the value of c in equation 1, we get
3t + (4 × 150) = 3300
=> 3t = 3300 – 600 = 2700
=>t = 2700/3 = 900
Cost of 1 table and 1 chair = c + t = 150 + 900 = 1050
Answer : B
Answer: B
Question: All the stocks on the over-the-counter market are designated by either a 6 letter or 5 letter codes that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Options:
A)2(26^5)
B)26(26^4)
C)27(26^6)
D)26(26^5)
E)27(26^5)
Rationale: with 4 letters: 26^6
with 5 letters: 26^5
26^6 + 26^5 = 27*(26^5)
C
Answer: C
Question: If (10^86) – 23 is written as a base 10 integer, which of the following options is the sum of the digits in that integer?
Options:
A)780
B)775
C)790
D)730
E)770
Rationale: We know that (10^86) is ending 00, so (10^86) – 23=9....9977
total number of digits in (10^86) – 23 is 86, or 84 digits of 9 and two digits 7 and 7.
answer choice is 84*9+14=770
Answer is E 770
Answer: E
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
Options:
A)12
B)14
C)16
D)18
E)22
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
A)
Answer: A
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 21) both lie on the line defined by the equation x = (y/7) - (2/5), what is the value of p?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x = (y/7) - (2/5), and so y = 7x + 14/5. The slope is 7.
(n+21-n) / (m+p-m) = 7
p = 3
The answer is C.
Answer: C
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)45 m
B)60 m
C)56 m
D)67 m
E)70 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B
Question: A student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 36 more than the correct answer. Find the number.
Options:
A)60
B)70
C)80
D)90
E)100
Rationale: Let the number be x.
(5/4) * x = (4/5)*x + 36
25x = 16x + 720
9x = 720
x = 80
The answer is C.
Answer: C
Question: Every year an amount increases by 1/6th of itself. How much will it be after two years if its present value is Rs.64000?
Options:
A)87111
B)81007
C)81008
D)81066
E)81022
Rationale: 64000* 7/6 * 7/6 = 87111
Answer:A
Answer: A
Question: Find the missing number: ? - 1936248 = 1635773
Options:
A)3572021
B)3572012
C)3770221
D)3570221
E)None of them
Rationale: Let x - 1936248=1635773.
Then, x = 1635773 + 1936248
=3572021.
Answer is B.
Answer: B
Question: The perimeter of one square is 40 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
Options:
A)11.2√2
B)13√2
C)23√2
D)12√4
E)13√9
Rationale: 4a = 40 4a = 20
a = 10 a = 5
a2 = 100 a2 = 25
Combined area = a2 = 125 => a = 11.2
d = 11.2√2
Answer: A
Answer: A
Question: If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 2 other contributions made before john's, what is the size of his donation?
Options:
A)$125
B)$150
C)$200
D)$250
E)$450
Rationale: Cavg = average contribution before John
Cavg*1.5 = 75, therefore the average cont is $50 before John.
If he needs to increase the average contribution by $25, he must put in $25 for each of the 2 people.
so $50.
But, he also has to put in the average for himself (the threeth person), so add $75.
So $125 is your answer.
Answer A
Answer: A
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?
Options:
A)108 sq.cm
B)112 sq.cm
C)116 sq.cm
D)120 sq.cm
E)130 sq.cm
Rationale: Explanation:
The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle =1/2 x base x height => 1/2 x 24 x 10 = 120 sq.cm
ANSWER IS D
Answer: D
Question: P sells an article to Q at 10 % profit. Q sells it to R at 25 % profit. If R pays Rs. 250 for it, What did P pay for it ?
Options:
A)Rs. 181.81
B)Rs. 181.88
C)Rs. 181.82
D)Rs. 181.89
E)Rs. 181.812
Rationale: Explanation:
Selling price of P = Cost price of Q
Selling Price of Q = Cost price of R = Rs. 250 ….. Given
Q sold it to R with 25 % profit.
Cost price of Q = 100/125 * 250/1 = Rs. 200 = Selling price of P.
P sold it to Q with 10 % profit.
Cost price of P = 100 / 110 * 200 / 1 = Rs. 181.81
ANSWER: A
Answer: A
Question: If 4 women can color 48 m long cloth in 2 days, then 6 women can color 36 m long cloth in
Options:
A)2 days
B)3 days
C)1 day
D)4 days
E)5 days
Rationale: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.
C
Answer: C
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio W of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
Options:
A)8:3
B)3:2
C)4:3
D)2:3
E)3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio W of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: B
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.840 find the share of A.
Options:
A)240
B)388
C)379
D)277
E)320
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 840 = 320
Answer: E
Answer: E
Question: 3x^2-6x+3 = 0
Find the above equation find the value of x
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: B
Question: If x#y is defined to equal x^2/y for all x and y, then (-1#2)#2 =
Options:
A)4/3
B)1/3
C)1/12
D)1/8
E)-4/3
Rationale: (-1)^2 / 2 = 1/2
(1/2)^2 / 2 = 1/8
so D is my answer
Answer: D
Question: A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability Z that the game will end after the fourth throw?
Options:
A)1/16
B)3/32
C)1/8
D)3/16
E)1/4
Rationale: Another approach:
Two likely scenarios would be : HHTH or THTH
for each of the scenarios probability would be 1/16
So Probablilty Z is 1/16 + 1/16 = 1/8.C
Answer: C
Question: A rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)s.3988
B)s.3900
C)s.3228
D)s.3922
E)s.3600
Rationale: Area = (l + b – d) d
(70 + 60 – 10)10 => 1200 m2
1200 * 3
= Rs.3600
Answer:E
Answer: E
Question: A team of eleven footballers has an average height of 170 cm. Four footballers whose average height is 140 cm, left the team and four new others whose average height is 124 cm, joined. Calculate the new average height of the footballers (in cm) is?
Options:
A)166.2 cm
B)154.2 cm
C)364.2 cm
D)124.2 cm
E)164.2 cm
Rationale: Total height = 170 * 11 = 1870 cm.
Total height of those who left = 140 * 4 = 560
Total height of those who joined = 124 * 4 = 496
New average
= [1870 - 560 + 496 ] / 11 = 1806/11 cm.
= 164.2 cm
Answer:E
Answer: E
Question: A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.
Options:
A)32 Cm2
B)16 Cm2
C)20 Cm2
D)64 Cm2
E)None of these
Rationale: Solution: Side of the first square is 4 cm.
side of second square = 2 √2 cm.
Side of third square = 2 cm.
and so on. i.e. 4, 2 √, 2, √2, 1 ......
Thus, area of these square will be,
= 16, 8, 4, 2, 1, 1/2 ....... Hence, Sum of the area of first, second, third square ......
= 16+8+4+2+1+ .....
= [16/{1-(1/2)}] = 32 Cm2.
Answer: Option A
Answer: A
Question: If f(a)=4a-6, what is the value of (f(5a)-f(a))/2 ?
Options:
A)12a-6
B)10a+5
C)5a/6
D)4a-6
E)20a+6
Rationale: f(a)=4a-6
f(5a) = 20a-6
(f(5a)-f(a))/2 = (20a-6+4a-6)/2 = 12a-6
Answer is
Answer: A
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)229
B)238
C)500
D)288
E)211
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.Answer: C
Answer: C
Question: If the time is currently 1:30pm, what time will it be in exactly 842 hours?
Options:
A)12:30am
B)3:30am
C)12:30pm
D)2:30pm
E)10:30pm
Rationale: Every 24 hours will bring us to the same 1:30pm. 840 is divisible by 24 (35*24=840), so if it were 840 hours we would have 1:30pm, but since it's 842 hours then it will be 2 hour more, so 13:30pm.
Answer: B
Answer: B
Question: n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is
Options:
A)8
B)12
C)16
D)18
E)24
Rationale: When we say k is the product of all integers from 1 to n, we mean k = n!
Now 1440 = 1.2.3.4.5.6.2
Now if k is a multiple of 1440, it has to be at least 8!. This is so because it cannot be 6! due to the extra 2 factor at the end; it cannot be 7! either, again because the extra 2 in the end will be unaccounted for.
If k = 8! = 1.2.3.4.5.6.7.8, then k = 1440*7*4 i.e. k will be a multiple of 1440.
Answer A
Answer: A
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
Options:
A)800
B)802
C)821
D)897
E)828
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: A
Answer: A
Question: If the cost price is 75% of the selling price, then what is the profit percent?
Options:
A)5%
B)11%
C)13%
D)21%
E)33%
Rationale: Let S.P. = $100
C.P. = $75
Profit = $25
Profit% = 25/75 * 100 = 25/6 = 33% approximately
Answer is E
Answer: E
Question: A small library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
Options:
A)200
B)300
C)285
D)400
E)450
Rationale: avg visitors on sundays = 510
tot visitors of 5 sundays = 510*5
avg visitors of other 25 days = 240*25
tot visitors = (510*5)+(240*25)
tot days = 30
avg no of visitors per day =(510*5)+(240*25)/30
=285
ANSWER C
Answer: C
Question: The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km?
Options:
A)300
B)400
C)250
D)350
E)450
Rationale: 50 kmph consumption is 1 lt/hr
so 400 km will take 8 hrs and the consumption is 8 lt for entire distance.
1 lt costs $30
so 8 lt costs $240
extra expenses for 1 hr - $20
8 hrs - $160
total expense - $240 + $160= $400
Answer : B
Answer: B