divelab/Sys2Bench huggingface dataset:
Question: Marc wants to make a minimum net profit of 20% on a his headphones, which he bought for $500. If originally, he was selling the pair at 25% gain, what is the largest discount he can allow?
Options:
A)10%
B)0%
C)5%
D)3%
E)4%
Rationale: E
If he bought the headphones at $500, he is currently selling them at (115/100)*500 = $625.
He wants to make a profit of 20%, which means he needs to sell them at (120/100)*500 = $600
The max discount he can allow is thus ((625-600)/625)*100 = 4%
Answer: E
Question: 1!+2!+3!+......+50!=?
Options:
A)3.1035*10^64
B)2.1021*10^65
C)3.1035*10^63
D)3.1035*10^62
E)3.1035*10^61
Rationale: 3.1035*10^64 should be the Ans.
ANSWER:A
Answer: A
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations Q are there for the children?
Options:
A)240
B)480
C)720
D)1440
E)3600
Rationale: MAGOOSHOFFICIAL SOLUTION:
First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats?
X X X _ _ _ _
_ X X X _ _ _
_ _ X X X _ _
_ _ _ X X X _
_ _ _ _ X X X
There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2 = 10.
Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats.
Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations Q of 24*10 = 240.
Answer = A
Answer: A
Question: In a 1000 m race, A beats B by 320 meters or 25 seconds. Find the speed of B?
Options:
A)8
B)9
C)12.8
D)5
E)2
Rationale: Since A beats B by 320 m or 25 seconds, i
t implies that B covers 320 m in 25 seconds.
Hence speed of B = 320/25 = 12.8 m/s.
Answer: C
Answer: C
Question: There are 6 red balls and 4 blue balls in a jar. If 3 balls are selected from the jar, what is the probability that all 3 balls selected are red balls?
Options:
A)1/3
B)1/6
C)5/12
D)5/24
E)7/24
Rationale: The number of ways of choosing 3 balls from the jar is 10C3 = 120.
The number of ways of choosing 3 red balls is 6C3 = 20.
P(3 red balls) = 20/120=1/6.
The answer is B.
Answer: B
Question: If n is a positive integer, which one of the following numbers must have a remainder of 2 when
divided by any of the numbers 4, 5, and 6?
Options:
A)12n + 2
B)24n + 2
C)80n + 2
D)90n + 2
E)120n + 2
Rationale: The numbers 4, 5, and 6 all divide 120 so they all divide 120n.
When we divide (120n + 2) by 4, 5, or 6, the remainder must be 2.
The answer is E.
Answer: E
Question: Out of 12 students in a class, 6 are wearing blue shirts, 4 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?
Options:
A)25/33
B)35/44
C)65/77
D)75/88
E)85/99
Rationale: Total possible ways to choose 4 students out of 12 = 12C4 = 495
The number of ways to choose 4 students with no green shirts = 8C4 = 70
P(no green shirts) = 70/495 = 14/99
P(at least 1 green shirt) = 1 - 14/99 = 85/99
The answer is E.
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)150
B)200
C)180
D)250
E)230
Rationale: speed = (60*5/18) = 50/3
length = (speed*time)
length = (50/3*9) = 150 m
ANSWER A
Answer: A
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 67 kg. What is the weight of the new person?
Options:
A)75
B)65
C)87
D)95
E)80
Rationale: Total increase in weight = 8 × 2.5 = 20
If x is the weight of the new person, total increase in weight = x−67
=> 20 = x - 67
=> x = 20 + 67 = 87
Answer is C.
Answer: C
Question: If p/4 = r/2 and r = 0.75s, what is the ratio of p to r to s?
Options:
A)2 : 3 : 4
B)8 : 12 : 9
C)12 : 6 : 8
D)6 : 4 : 3
E)12 : 8 : 3
Rationale: p/4=r/2, r=0.75s, what is p:r:s?
we get p/r=4/2 and r/s=3/4, so
4/3*3/2 and 2/2*3/4
12/6 and 6/8
C
Answer: C
Question: Adam is 40% more efficient than Blanc. How much time will they, working together, take to complete a job which Adam alone could have done in 20 days?
Options:
A)35 days
B)11 1â„3 days
C)11 2â„3 days
D)20 days
E)11 3â„5 days
Rationale: Ratio of times taken by Adam and Blanc = 100 : 140 = 5 : 7.
Suppose Blanc takes x days to do the work.
Then, 5 : 7 : : 20 : x â‡’ x = (20Ã—7)/5 â‡’ x = 28
Adamsâ€™s 1 dayâ€™s work = 1â„20; Blancâ€™s 1 days work = 1â„28
(Adam + Blanc)â€™s 1 dayâ€™s work = (1â„20 + 1â„28) = 3â„35
âˆ´ Adam and Blanc together can complete the job in 35â„3 days or 11 2â„3 days.
Answer C
Answer: C
Question: X and Y are both integers. If X/Y = 59.80, then what is the sum of all the possible two digit remainders of X/Y?
Options:
A)560
B)616
C)672
D)200
E)1024
Rationale: Remainder = 0.80= --> 80/100 --> Can be written as (80/4) / (100/4) = 20/25
So remainders can be 20, 40, 60, 80
We need the sum of only 2 digit remainders --> 20 + 40 + 60 + 80 = 200
Answer: D
Answer: D
Question: The last time Rohit bought Diwali cards, he found that the four types of cards that he liked were priced Rs.9.00, Rs.7.00, Rs.4.50 and Rs.5.50 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rohit give?
Options:
A)15
B)10
C)22
D)20
E)18
Rationale: Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=> 5a + 5b + 10c + 10d = 10*x.
=> a + b + 2(c+d) = 2 * x . -----------------------------(i)
Since, a + b = 9+7 = 16
And,
=> c + d = 4.50+5.50= 10 .
Putting these values in (i), we get :-
=> 16 + 2 *10 = 2 * x.
=> x = 18.
Answer :E
Answer: E
Question: 2/3rd of the boys and 3/4th of the girls of a school participate in a function. If the no.of participating students is 550, out of which 150 are girls, what is the total no.of students in the school?
Options:
A)500
B)600
C)800
D)900
E)1000
Rationale: Let total number of boys be x and total number of girls be y. y=400=>x = 600and^= I50=>y = 200 Now, x + y = 800
C
Answer: C
Question: When x is divided by y, the quotient is t with remainder r. What is x in terms of r, y, and t?
Options:
A)y + r + t
B)yt + r
C)x/y+r
D)y/t+r
E)rt + y
Rationale: (x/y) = t + r
solve for x
x=(t*y)+r
Ans B.
Answer: B
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
Options:
A)288
B)744
C)788
D)298
E)177
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
Answer: B
Answer: B
Question: A group of 12 girl scouts had enough food to last for 8 days when they arrived in camp. However, 4 more scouts joined them without the amount of food being increased. How long will the food last if each scout is given the same daily ration as originally planned?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: (M1*D1)/W1 = (M2*D2)/W2
here W1 = W2 (food)
M1 = 12
D1 = 8
M2 = 12+4 = 16
so (12*8)= (16*D2)
D2 = 6
ANSWER:E
Answer: E
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.
Options:
A)1/166
B)1/129
C)1/526
D)1/121
E)1/126
Rationale: Out of nine, five are good and four are defective. Required probability = 4C4/9C4 = 1/126.Answer: E
Answer: E
Question: The value for S=(0.889 × 55)/9.97 to the nearest tenth is
Options:
A)0.5
B)4.63
C)4.9
D)7.7
E)49.1
Rationale: if we read the Q, we can easily home on to the answer,,
the numerator is clearly between 40 and 50..
denomiator is close to 10..
so S=(0.889 × 55)/9.97 is between 4 and 5..
It may tempt us to solve it since ther are two values between 4 and 5..
but the catch is innearest tenth
4.63 can be called nearest to hundreth and no tenth, so can be eliminated..
4.9 is our answer...
C
Answer: C
Question: In a class of 20 students, 2 students did not borrow any books from the library, 10 students each borrowed 1 book, 5 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: The total number of books the students borrowed is 20*2=40.
The students who borrowed zero, one, or two books borrowed 10*1+5*2=20 books.
The 3 students who borrowed at least three books borrowed 40-20=20 books.
If 2 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 20-6= 14 books.
The answer is C.
Answer: C
Question: 20^10 / 120^5=?
Options:
A)6^5
B)5^6
C)(10/3)^5
D)6^3
E)15^3
Rationale: 20^10 / 120^5=?
A. 6^5
B. 5^6
C. (10/3)^5
D. 6^3
E. 15^3
-> 20^10 / 120^5=(20^10)/(6^5)(20^5)=(20^5)/(6^5)=(2^5)(10^5)/(2^5)(3^5)=(10/3)^5.
Thus, C is the answer.
Answer: C
Question: A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 20 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the level of the field will raise by nearly?
Options:
A)1390
B)2887
C)2667
D)1898
E)1671
Rationale: 2(25 * 15 + 15 * 8 + 25 * 8)
2(375 + 120 + 200) => 1390
Answer: A
Answer: A
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
5, 25, 325, 4325, ?
Options:
A)29816
B)38291
C)54325
D)38290
E)55291
Rationale: C
54325
Consider 1 = 5
2 = 25
3 = 325
4 = 4325
Then 5 = 54325
See the pattern. With every digit, the previous numbers are added after that digit
So the next number in the series is 54325
Answer: C
Question: Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21
Options:
A)-1
B)-9
C)-7
D)-2
E)-4
Rationale: Explanation:
19x + 19y + 17 = -19x + 19y - 21
38x = -38 => x = -1
Answer:A
Answer: A
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Options:
A)12 Years
B)12.6 Years
C)13 Years
D)13.5 Years
E)None
Rationale: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
B
Answer: B
Question: Carl is facing very difficult financial times and can only pay the interest on a $30,000 loan he has taken. The bank charges him a quarterly compound rate of 10%. What is the approximate interest he pays annually?
Options:
A)$1200
B)$2000
C)$2150
D)$2500
E)$12000
Rationale: Usually, you are given the annual rate of interest and it is mentioned that it is annual rate.
The bank charges him a quarterly compounded ANNUAL rate of 40%.
Here you find per quarter rate as (40/4)% = 10%
I have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5% annual rate of interest, it is apparent that the intent was a 10% quarterly rate. So the bank charges 10% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 10% of 30,000 = $12000 as our answer.
But since, the interest is compounded, it will be a bit more than $12000. Option (E) looks correct.
Answer: E
Question: Someone on a skateboard is traveling 13 miles per hour. How many feet does she travel in 25 seconds? (1 mile = 5280 feet)
Options:
A)476.75 ft
B)450 ft
C)480 ft
D)490 ft
E)500 ft
Rationale: per second => 13*5280 ft/60*60 =19.07 ft
25 seconds => 19.07 * 25 = 476.75 ft
Answer : A
Answer: A
Question: If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?
I. c - a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: E.
Answer: E
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
A)6
B)2
C)3
D)4
E)98
Rationale: Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 day
Answer: B
Answer: B
Question: A student missed 6% of the questions on a test. If the student missed 12 questions, how many questions were on the test?
Options:
A)100
B)150
C)200
D)250
E)300
Rationale: 12 is 6% of the total answers on the test.
If the total number of answers on the test is X then
6/100 = 12/X
100/6 * 12 = X
1200/6 = X
200 = X
C)
Answer: C
Question: There are two clocks that are set at 8 0'clock in the morning. One clock is correct and the other clock gains 5 minutes per hour. When the faster clock shows the time 12:20 in the afternoon, what does the correct clock show?
Options:
A)12:00:00
B)11:45
C)12:26
D)11:50
E)11:56
Rationale: Faster clock gains 5 minutes per hour
At 8 0'clock both the clocks are set
At 9 0'clock -
The correct clock shows 9:00:00
The faster clock is at 9:05:00 (1 hour + gained 5 minutes)
At 10 0'clock
The correct clock is at 10:00:00
The faster clock is at 10:10:00 (2 hours + gains 10 minutes)
At 11 0'clock -
The correct clock is at 11:00:00
The faster clock is at 11:15:00 (3 hours + gains 15 minutes)
In 4 hours the faster clock would gain 20 minutes and shows 12:20:00 at that point which is 12 0'clock in the correct clock.
The answer is A
Answer: A
Question: 80% of a number is added to 120, the result is the same number. Find the number?
Options:
A)600
B)288
C)1687
D)997
E)121
Rationale: (80/100) * X + 120 = X
2X = 1200
X = 600
Answer:A
Answer: A
Question: Mr. Srinivas saves one coin of 5 on first day of the
week, three coins of 5 on the second day of the week.
Five coins of 5 on third day and so on. How much money will he has at the end of the week?
Options:
A)238
B)245
C)2867
D)987
E)111
Rationale: Number of
5 coins with him at the end of week = 5 × (1 + 3 + 5 + 7 + 9 + 11 + 13) = 5 × (sum of first 7 odd numbers) (By using the formula discussed earlier). ∴ Sum of all numbers = 5 × 72 = 245.
Answer:B
Answer: B
Question: A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7}. If no digit may be repeated and each password must be at least 6 digits long, how many passwords are possible?
Options:
A)6! + 7!
B)2 x 7!
C)6! x 7!
D)13!
E)14!
Rationale: If we choose the 7 different digits then they can be arranged in 7! ways.
The number of possible 6-digit passwords is 7*6*5*4*3*2 = 7!
The total number of passwords is 7! + 7! = 2*7!
The answer is B.
Answer: B
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)30
B)80
C)40
D)70
E)60
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: Option C
Answer: C
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?
Options:
A)8 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 = 9. Thus B joined after 9 months.
Answer B
Answer: B
Question: How many words can be formed by using all letters of the word 'BIHAR' ?
Options:
A)112
B)120
C)157
D)136
E)142
Rationale: The word BIHAR contains 5 different letters
Required number of words = 5P5 = 5! = 5*4*3*2*1 = 120
Answer is B
Answer: B
Question: In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 27, find the number?
Options:
A)867
B)1179
C)1196
D)1098
E)1197
Rationale: E
1197
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b - 2
a + b + c = 3b = 27=> b = 9
So a = 11 and b = 7
Hence the three digit number is: 1197
Answer: E
Question: Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1.15, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?
Options:
A)$22
B)$27.6
C)$30
D)$36
E)$40
Rationale: B its is.
Let price = X
(x-1.15)8 = 6X
X= 4.6
hence total money = 6*4.6 = 27.6
Answer: B
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)100
B)180
C)110
D)120
E)130
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: Option B
Answer: B
Question: If a and b are multiples of 3 then which are all the multiples of 3
1) a/b
2) a^b
3) a+b
4) a-b
5) a*b
Options:
A)1,3
B)1,2,4,5
C)1,2,5
D)all of these
E)1,2,3,5
Rationale: a*b a^b a+b a-b are multiples of 3 except a/b
ANSWER:E
Answer: E
Question: Three hundred students at College Q study a foreign language. Of these, 130 of those students study French, and 190 study Spanish. If at least 50 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from
Options:
A)10 to 40
B)40 to 100
C)60 to 100
D)60 to 120
E)70 to 110
Rationale: 130 students study French
170 students do not study French
190 students study Spanish
110 students do not study Spanish
50 students study neither French nor Spanish
170-110=60
170-50=120
D. 60 to 120
Answer: D
Question: In how many different ways can the letters of the word MISSISSIPPI be arranged?
Options:
A)11!/(4!4!2!)
B)11!/4!
C)11!/2!
D)11!
E)2×11!
Rationale: Number of ways 11 letter can be arranged = 11!
The 11! arrangement will also contain duplicates because of the characters
that are repeated
We have 4 S's =4! repeats
We have 4 I's =4! repeats
We have 2 P's =2! repeats
So the total possible arrangement will be 11!/4!4!2!
Ans A
Answer: A
Question: Find a a prime number from the options below.
Options:
A)58
B)59
C)60
D)62
E)64
Rationale: Clearly, 59 is a prime number.
B
Answer: B
Question: One water pump can fill half of a certain empty tank in 7 hours. Another pump can fill half of the same tank in 7.5 hours. Working together, how long will it take these two pumps to fill the entire tank?
Options:
A)7 7/13
B)1 5/8
C)3 1/4
D)7 7/29
E)3 1/2
Rationale: One pump can fill a tank in 7 hours and another in 7.5 hours
so the rate at which both can half fill the tank is (1/7+1/7.5) => 29/105
Thus half of the tank can be filled in 105/29
so for filling the complete tank => 105/29*2 = 210/29 =7 7/29
ANSWER:D
Answer: D
Question: If the annual interest on a principal is 4%, how many years before the amount is double?
Options:
A)22
B)25
C)12
D)13
E)17
Rationale: P = (P*4*R)/100
R = 20%
Answer: B
Answer: B
Question: A and B started a business with an investment of Rs.26000 and Rs.28000. After two months C joined in the business with an investment of Rs.32000, what is share of C in the half year profit of Rs.9040 ?
Options:
A)3360
B)3120
C)2940
D)2560
E)3550
Rationale: Investment x Time.
A = 26000 x 6 = 156000.
B = 28000 x 6 = 168000.
C = 32000 x 4 = 128000.
Ratio of shares A : B : C = 39 : 42 : 32 = [ Total 113 units ]
Share of C in the profit = 9040 × 32 / 113 = 2560
Option D
Answer: D
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?
Options:
A)22377
B)27782
C)27891
D)25000
E)18771
Rationale: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
25 = 1/100 * x => x = 25000
Answer: D
Answer: D
Question: A,B,C together can do a work in 10 days. A alone can do the work in 50days and B alone can do the same work in 60 days. Find in what time C alone can do that work?
Options:
A)15.8days
B)17days
C)19.5days
D)20.6days
E)25.4days
Rationale: The required answer is = 10*50*60 / 50*60-10(50+60)
= 30000/1900 = 15.8days
Answer is A
Answer: A
Question: The cash difference between the selling prices of an book at a profit of 4% and 6% is $ 3. The ratio of the two selling prices is:
Options:
A)50:53
B)58:53
C)52:53
D)42:36
E)38:53
Rationale: C
52:53
Let C.P. of the book be $ x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Answer: C
Question: The speed at which a man can row a boat in still water is 26 kmph. If he rows downstream, where the speed of current is 4 kmph, what time will he take to cover 150 metres?
Options:
A)18
B)27
C)28
D)12
E)25
Rationale: Speed of the boat downstream = 26 + 4 = 30 kmph= 30 * 5/18 = 8.33 m/sHence time taken to cover 150 m = 150/8.33= 18 seconds.Answer:A
Answer: A
Question: What is the unit digit of (8!*4! / 8!*3!)?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: (8!*4! /8!*3!)
=(4! / 3!)
=24/6
=4
Units digit of the above product will be equal to 4
Answer E
Answer: E
Question: A T.V was sold at a loss of 10%. If it was sold for Rs.3500 more, there would have been a gain of 10%. What is the cost price?
Options:
A)Rs. 17000
B)Rs. 18500
C)Rs.17500
D)Rs. 15500
E)Rs.15000
Rationale: 90%
110%
--------
20% ---- 3500
100% ---- ? => Rs.17500
Answer:C
Answer: C
Question: If 625^(-x) + 25^(-x) + 5^(-4x) = 15, what is the value of x?
Options:
A)-4
B)-1/4
C)0
D)1/4
E)4
Rationale: We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.
Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....
With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.
With Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.
With Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.
With Answer C, anything to the '0 power' is 1, so we'd have 1+1+1 = 3. This is not 15. Eliminate C.
E
Answer: E
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
Options:
A)6620
B)6628
C)6629
D)6624
E)6622
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)230
B)240
C)250
D)260
E)270
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer: Option B
Answer: B