divelab/Sys2Bench huggingface dataset:
Question: The average weight of 16 students in a class is 50.25 kg and that of the remaining 8 students is 45.15 kg. Find the average weights of all the students in the class.
Options:
A)A)48.55
B)B)49
C)C)51
D)D)61
E)E)62
Rationale: Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55kg
Answer is A
Answer: A
Question: A cylinder of radius R and height H is reshaped. Which of the following changes results in the cylinder of greatest volume?
Options:
A)a 20% decrease in H and a 50% increase in R.
B)a 500% increase in H and a 50% decrease in R.
C)a 300% increase in H and a 30% decrease in R
D)a 70% decrease in H and a 100% increase in R
E)a 100% increase in H and a 10% decrease in R
Rationale: Volume of a cylinder = Pi. R^2.H
Check for options as per given Q.
A. (1.5)^2 * (0.8) = 2.25 * 0.8 = 1.8 (Since 20% decrease in H and a 50% increase in R.)
B. (0.5)^2 * (6) = 0.25 * 6 = 1.5 (Since 500% increase in H and a 50% decrease in R)
C. (0.7)^2 * (4) = 0.49 * 4 = 1.96 (Since 300% increase in H and a 30% decrease in R )
D. (2)^2 * (0.3) = 4 * 0.3 = 1.2 (Since 70% decrease in H and a 100% increase in R. )
E. (0.9)^2 * (2) = 0.81 * 2 = 1.62 (Since 100% increase in H and a 10% decrease in R. )
Maximum value is 1.96
Option C
Answer: C
Question: A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 4 hours. How many hours i total will it take the crow to finish a quarter of the nuts?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: In one hour, the crow eats 1/24 of the nuts.
(1/4) / (1/24) = 6 hours
The answer is A.
Answer: A
Question: A computer program produces a sequence a1, a2, a3, ... such that a1=a2=1 and ak=a(k-1)*3-1 for 2 < k < n for some n. If n=9, what is a6?
Options:
A)35
B)37
C)39
D)41
E)43
Rationale: a1=1
a2=1
a3=1*3-1=2
a4=2*3-1=5
a5=5*3-1=14
a6=14*3-1=42-1=41
41
Answer: D
Question: Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "DOG"?
Options:
A)72
B)75
C)78
D)81
E)84
Rationale: "DOG" = (4+15+7)*3=78.
The answer is C.
Answer: C
Question: All of the students of Music High School are in the band, the orchestra, or both. 60 percent of the students are in only one group. There are 106 students in the band. If 10 percent of the students are in the band only, how many students are in the orchestra only?
Options:
A)120
B)110
C)116
D)106
E)112
Rationale: % of students in one group only = 60%
% of students in both groups = 100 - 60 = 40%
% of students in the band only = 10%
Number of students who are in band = 106
40% + 10% = 50% = 106 Students
Finding total students:
x = (106 x 100)/50
x = 212
Students in orchestra only = 212 - 106 = 106
Answer:D
Answer: D
Question: There are 500 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
Options:
A)150
B)200
C)250
D)350
E)400
Rationale: There are 495 managers and 5 others. The 5 others would compose 2% of the total number of people if there were 250 people in the room. Thus 250 managers must leave.
The answer is C.
Answer: C
Question: A shirt goes on sale for 60% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?
Options:
A)72%
B)70%
C)52%
D)50%
E)28%
Rationale: Just assume original price is 100.
Sale price = 60
Then it is marked down by 10% = 60-6=52.
Hence it is 52% od the original price. Hence answer is C.
Answer: C
Question: The third proportional to 1 and 5 is?
Options:
A)8
B)27
C)24
D)25
E)3
Rationale: (5*5)/1 = 25
Answer:D
Answer: D
Question: A man covers a certain distance Q in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?
Options:
A)200 km
B)50 km
C)20 km
D)60 km
E)80 km
Rationale: Not really. When you solve the 2 equation above, you get,
6T-4/3 = 5R/6 from simplifying equation 1
4T-2=R/2 from simplifying equation 2
You can now multiply equation 2 by 5 to get
5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance Q = R*T=20*3=60 km.D
Answer: D
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 40 ps per meter is?
Options:
A)287
B)369
C)100
D)279
E)361
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 0.40
= Rs.100
Answer:C
Answer: C
Question: Dana borrows 5000 pounds annually for her college education. If Dana gives her parents 4% of that amount back each month, how much will she still owe her parents after four years of college?
Options:
A)9800
B)10000
C)10200
D)10400
E)10600
Rationale: dana borrows 5000 and returns 4% per month.
so returns 200 per month. and 2400 per year.
so dana owes 5000-2400=2600 per year.
after 4 years she will owe 10400.
Ans (C)
Answer: C
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 12 such machines produce in 4 minutes ?
Options:
A)648
B)1800
C)2700
D)2160
E)None of these
Rationale: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
âˆ´ 6 Ã— 1 Ã— x = 12 Ã— 4 Ã— 270 â‡” x = 12x4x270/6= 2160 . Answer D
Answer: D
Question: If 7125¸1.25= 5700< the value of 712.5÷12.5 is:
Options:
A)5.7
B)57
C)570
D)0.57
E)0.057
Rationale: Given 7125/1.25 = 5700
712.5/12.5 =71.25/1.25 = 7125*1/1.25*100 = 5700/100 = 57
ANSWER:B
Answer: B
Question: Find the percentage gain if a shop owner sells 10 mtr of fabric and gains Cost Price of 2 meters?
Options:
A)10%
B)12%
C)19%
D)25%
E)20%
Rationale: Let cost of each metre be Rs. 100.
Therefore, cost price of 2m cloth = 2*100 = 200
cost price of 10m cloth = 10*100 = 1000
Since the trader made the CP of 2m from the sale of 10m therefore
Profit on sale of 10m = cost price of 2 m cloth = 200
Selling price of 10m = 1000+200 = 1200
Profit % = 20%
E
Answer: E
Question: A sum is invested at compounded interest payable annually. The interest in the first two successive years was Rs. 400 and Rs. 420. The sum is
Options:
A)Rs. 8000
B)Rs. 8200
C)Rs.7500
D)Rs. 8500
E)Rs. 9000
Rationale: Explanation:
his means that, simple Interest on Rs.400 for 1 year = 420 - 400 = 20
Rate = (100 Ã—SI)/PT = (100 Ã— 20)/(400Ã—1) = 5%
Rs.400 is the interest on the sum for 1st year
Hence, sum = (100 Ã— SI)/RT = (100 Ã— 400)/(5 Ã— 1) = Rs. 8000
ANSWER IS A
Answer: A
Question: A chocolate has 12 equal piece. Monju gave 1/4th of it to Anju, 1/3rd of it to Sujata and 1/6th of it to Fiza. The number of piece of chocolate left with Manju is?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Answer
The number of pieces of chocolate left with Manju
= 1- [(1/4) + (1/3) + (1/6)
= 1 - (3 + 4 + 2)/12
= 1 - 9/12 = (12 - 9) / 12
= 3/12
Option: C
Answer: C
Question: A certain manufacturer sells its products	to stores in 110 different	regions worldwide, with an average (arithmetic mean) of 181 stores per region. If last year these stores sold an	average of 51,752 units of the manufacturer’s product per store, which of the following is closest to the total number of units of manufacturer’s product	sold	worldwide last	year?
Options:
A)10^5
B)10^6
C)10^7
D)10^8
E)10^9
Rationale: 51752*181*110 or
51000*180*110 or
50000*200*100
=10^9
E
Answer: E
Question: If 4x + 3y = 8 and y-3x = 8, then what is the value of x + 4y?
Options:
A)1/7
B)16
C)15
D)52/7
E)60/7
Rationale: 4x+3y=8 ...equation 1
-3x+y=8 ...equation 2
adding both the equations
x+4y=16
correct answer option B
Answer: B
Question: The total of company C's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)10
E)20
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 100% GREATER than they were in 1993, which means 1993 PLUS 100% of 1993:
$500 + 1x$500 = $500 + $500 =$1000
This is 10 times the 1992 number, so the correct answer is 10N.
D
Answer: D
Question: z is a positive integer and multiple of 2; p = 4^z, what is the remainder when p is divided by 10?
Options:
A)10
B)6
C)4
D)0
E)It Cannot Be Determined
Rationale: Given: z is an even Integer
The cyclicity of Unit Digit of 4 is 2 i.e. Unit digit of powers of 4 repeat after every two powers in the pattern {4, 6, 4, 6, 4, ....}
4^1=4
4^2=16
4^3=64
4^4=256
i.e. Every Even Power of 4 gives the Unit digit = 6 = Remainder
Answer: Option B
Answer: B
Question: How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?
Options:
A)5
B)6
C)8
D)10
E)50
Rationale: The no will be of the form 2^n to achieve this. Since any other form will have odd no in the prime factorization.
Hence we need to find solution of n for equation - 1< 2^n < 101.
2^6 = 64, 2^7 - 128
Hence n can take values from 1 to 6.
Hence Answer : B
Answer: B
Question: If q and r are both odd numbers C , which of the following must also be odd?
Options:
A)q – r
B)(q + r)^2
C)q(q + r)
D)(qr)^2
E)q/r
Rationale: We're told that q and r are both ODD numbers C. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
Answer: D
Question: 23, 25, 53, 163, 657, 3291, ?
Options:
A)19853
B)18753
C)17753
D)19753
E)17532
Rationale: 23*1+2=25
25*2+3=53
53*3+4=163
163*4+5=657
657*5+6=3291
3291*6+7=19753
ANSWER:D
Answer: D
Question: If you have 5 New Year greeting cards and you want to send them to 3 of your friends, in how many ways can this be done?
Options:
A)60
B)720
C)20
D)70
E)None
Rationale: Solution
We have to find number of permutations of 3 objects out of 5 objects. This number is 5P3=5(5-1)(5-2)=5*4*3=60
Answer A
Answer: A
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 6 years the amount to be paid is?
Options:
A)3377
B)2688
C)2688
D)9490
E)1268
Rationale: A = 7500(26/25)^6 = 9490
Answer: D
Answer: D
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Options:
A)7.1
B)7.2
C)7.5
D)7.4
E)7.3
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr
Answer is B.
Answer: B
Question: If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)189km
B)195km
C)197km
D)200km
E)205km
Rationale: 14 m/s = 14 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 14 * 18/5 * 15/4 km = 189 km.
Answer:A
Answer: A
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
Options:
A)Rs. 7000
B)Rs. 8000
C)Rs. 9000
D)Rs. 9900
E)Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: E
Question: 1!+2!+3!+4!+5!+.......100! is divided by 24. Find the remainder?
Options:
A)5
B)7
C)9
D)11
E)14
Rationale: By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.
So the remainder = 1 + 2 + 6 + 0 + 0....... = 9
C
Answer: C
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 50. He was allowed to drop his lowest score. After doing so, his average test score improved to 55. What is the lowest test score that was dropped?
Options:
A)20
B)35
C)55
D)65
E)80
Rationale: The arithmetic mean of 4 equally weighted tests was 50. So what we can assume is that we have 4 test scores, each 50.
He dropped his lowest score and the avg went to 55. This means that the lowest score was not 50 and other three scores had given the lowest score 5 each to make it up to 50 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 50.
So the lowest score =50 - 15 = 35
Answer (B)
Answer: B
Question: A 18% stock yielding 8% is quoted at?
Options:
A)165
B)170
C)175
D)180
E)225
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.18, money invested = 100×18/8 = Rs.225
ie, market value of the stock = Rs.175
Answer is E.
Answer: E
Question: What is the sum of all consecutive multiples of 8 between 400 and 600, inclusive?
Options:
A)8000
B)10,400
C)12,500
D)13,000
E)15,000
Rationale: 400 is 8*50 and 600 is 8*75...
Average of 400 and 600= 500, extreme multiples of 8..
# of multiples of 8 =75-50+1=26..
Sum =#*avg= 26*500=13000
ANSWER:D
Answer: D
Question: P and Q can complete a work in 40 days and 24 days respectively. P alone started the work and Q joined him after 8 days till the completion of the work. How long did the work last?
Options:
A)5 days
B)10 days
C)14 days
D)20 days
E)26 days
Rationale: Explanation :
Work done by P in 1 day = 1/40
Work done by Q in 1 day = 1/24
Work done by P in 8 days = 8 Ã— (1/40) = 1/5
Remaining work = 1 â€“ 1/5 = 4/5
Work done by P and Q in 1 day = 1/40 + 1/24 = 1/15
Number of days P and Q take to complete the remaining work = (4/5) / (1/15) = 12
Total days = 8 + 12 = 20
Answer : Option D
Answer: D
Question: A certain quantity is measured on two different scales, the B-scale and the S-scale, that are related linearly. Measurements on the B-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the B-scale corresponds to a measurement of 100 on the S-scale?
Options:
A) 20
B) 36
C) 48
D) 60
E) 84
Rationale: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that B increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, B will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Answer: C
Question: Which one of the following is not a prime number?
Options:
A)31
B)61
C)71
D)91
E)93
Rationale: 91 is divisible by 7. So, it is not a prime number.
D)
Answer: D
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 2 1/2 percent?
Options:
A)337
B)500
C)700
D)288
E)211
Rationale: 70 = (P*4*5/2)/100
P = 700
Answer: C
Answer: C
Question: There are 7 executives, including the CEO and CFO, that are asked to form a small team of 4 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
Options:
A)25
B)28
C)30
D)32
E)35
Rationale: The total number of ways to form a team of 4 is 7C4=35.
We need to subtract the number of teams that have both the CEO and the CFO.
The number of teams with both the CEO and CFO is 5C2=10.
The number of ways to form an acceptable team is 35-10=25.
The answer is A.
Answer: A
Question: The third proportional to 0.24 and 0.36 is :
Options:
A)48
B)64
C)54
D)58
E)66
Rationale: Explanation :
Solution: Let the third proportion to 0.24 and 0.36 be x.
Then, 0.24 : 0.36 : : 0.36 : x
=> x = 0.36*0.36/0.24 = 0.54
Answer : C
Answer: C
Question: What is the number of different committees of 9 people that can be selected from a group of 10 people?
Options:
A)a) 20
B)b) 40
C)c) 80
D)d) 10
E)e)1
Rationale: 10c9 = 10
Answer is D.
Answer: D
Question: What are the last two digits of 35*37*82*71*41?
Options:
A) 10
B) 30
C) 50
D) 70
E) 80
Rationale: We know that to find the last two digits, we need to find the remainder we get when we divide the product by 100.
Remainder of (63*35*37*82*71*41)/ 100
Note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator. But before we do that, here is an important note:
Note: We cannot just cancel off the common terms in the numerator and denominator to get the remainder. But, if we want to cancel off to simplify the question, we can do it, provided we remember to multiply it back again.
So say, we want to find the remainder when 14 is divided by 10 i.e. 14/10 (remainder 4). But we cancel off the common 2 to get 7/5. The remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10. But if we multiply 2 back by 2 (the number we canceled off), the remainder will become 2*2 = 4 which is correct.
Take another example to reinforce this – what is the remainder when 85 is divided by 20? It is 5.
We might rephrase it as – what is the remainder when 17 is divided by 4 (cancel off 5 from the numerator and the denominator). The remainder in this case is 1. We multiply the 5 back to 1 to get the remainder as 5 which is correct.
So keeping this very important point in mind, let’s go ahead and cancel the common 5 and 2.
We need the
Remainder of (63*7*37*41*71*41*5*2)/10*5*2
Remainder of (63*7*37*41*71*41)/10
Now using concept 2, let’s write the numbers in form of multiples of 10
Remainder of (60+3)*7*(30+7)*(40+1)*(70+1)*(40+1)/10
Remainder of 3*7*7*1*1*1/10
Remainder of 147/10 = 7
Now remember, we had canceled off 10 so to get the actual remainder so we need to multiply by 10: 7*10 = 70.
When 63*35*37*82*71*41 is divided by 100, the remainder is 70. So the last two digits of 63*35*37*82*71*41 must be 50.
Answer (C)
Answer: C
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.630 find the share of A.
Options:
A)240
B)288
C)277
D)877
E)361
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Answer: A
Question: If k is an integer and 2 < k < 8, for how many different values of k is there a triangle with sides of lengths 3, 6, and k?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: (6-3) < k < (6+3)
3 < k < 9
Thus k = 4, 5, 6, 7, 8
Since 2 < k < 8, then k can be 4, 5, 6, or 7.
The answer is E.
Answer: E
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 150 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
Options:
A)280
B)320
C)360
D)400
E)480
Rationale: Easy 400 is the answer.
3/4 ( x/2) = 150
x = 150 * 8 /3 = 400.
Answer D
Answer: D
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs.4576 , then what was the price of the article initially?
Options:
A)Rs.5000
B)Rs.3000
C)Rs.4000
D)Rs.2000
E)Rs.6000
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 4576
for 114.4 ---> 100 ; 4576 ---> ?
Required price = (4576 * 100)/114.4 = 40 * 100 = Rs.4000.
Answer:C
Answer: C
Question: At the Boonsoft Museum, 1 out of every 3 paintings are abstract. If 1 out of every 4 abstract paintings are by Van Heymoe, and there are 20 paintings by Van Heymoe in the museum, how many paintings total are there in the museum?
Options:
A)40
B)250
C)240
D)300
E)350
Rationale: Proportions: Let P = hats, and Pa = abstract paintings, and Pav = abstract paintings by Van Heymoe.
20Pav/xPa = 1Pav/4Pa
xPa = 80Pa
80Pa/yP = 1Pa/3P
yP = 240P
Answer: C
Answer: C
Question: If a certain sample of data has a mean of 11.0 and the value 20.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
Options:
A)14.75
B)3.55
C)4.25
D)4.0
E)2.75
Rationale: 20.0 is more than 2.5 standard deviations from 11 --> 20 > 11 + 2.5*{SD} --> 2.5*{SD} < 9 --> {SD} < 3.6. Only option B offers the standard deviation less than 3.6.
Answer: B
Answer: B
Question: A man buys 10 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 15 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
Options:
A)74
B)84
C)94
D)49
E)47
Rationale: 20% in 10 lts is 2. So water = 10-2 = 8 lts. 30% of 15 lts = 4.5. So water in 2nd mixture = 15-4.5 = 10.5 lts. Now total quantity = 10 + 15 = 25 lts. Total water in it will be 8 + 10.5 = 18.5 lts. % of water = (100*18.5)/25 = 74
ANSWER:A
Answer: A
Question: The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is?
Options:
A)Rs. 400
B)Rs. 500
C)Rs. 600
D)Rs. 800
E)Rs. 900
Rationale: Let the sum be Rs. P. Then,
[P(1 + 10/100)2 - p] = 525
P[(11/10)2 - 1] = 525
P = (525 * 100) / 21 = 2500
Sum = Rs. 2500
So, S.I. = (2500 * 5 * 4)/100 = Rs. 500
ANSWER:B
Answer: B
Question: In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
Options:
A)70%
B)80%
C)58%
D)50%
E)53%
Rationale: Number of students passed
= 60% of 140 = 60/100 * 140 = 84
Number of students failed
= 140 - 84 = 56.
Required percentage
= 28/56 * 100 = 50%.
Answer:D
Answer: D
Question: If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be
Options:
A)2
B)5
C)6
D)7
E)14
Rationale: i just tried plugging in the numbers and found out that
5*8820 = 44, 100, which is a square of 210
B
Answer: B
Question: If 20 men take 15 days to to complete a job, in how many days can 25 men finish that work?
Options:
A)12
B)66
C)77
D)8
E)6
Rationale: Ans. 12 days
Answer: A
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
Options:
A)8000
B)2277
C)2678
D)1276
E)1871
Rationale: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
Answer:A
Answer: A
Question: If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ?
Options:
A)0
B)m
C)n
D)mn
E)None of these
Rationale: Explanation :
Here's the solution :
mth term of an A.P.
Am = a + (m-1)d-------------------------------(1)
nth term of an A.P.
An = a + (n+1)d--------------------------------(2)
[Here a= First term of an A.P
d= difference between two consecutive terms ]
Now , According to the question;
m*Am = n*An
m(a + (m-1)d)= n(a + (n-1)d)
m(a + md - d)= n(a + nd - d)
am + m2d-md = an + n2d - nd
a(m-n)+ (m2-n2)d -(m-n)d = 0
a(m-n)+ (m-n)(m+n)d -(m-n)d= 0
(m-n)[a + (m+n)d - d ]= 0
[a + (m+n)d - d ]= 0
[a + (m+n-1)d ]= 0-------------------------------------(3)
Hence , According to equation (3)
Am+n = 0
Hence (A) is the correct answer
Answer : A
Answer: A