divelab/Sys2Bench huggingface dataset:
Question: The average of seven numbers is 26. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)25
B)83
C)29
D)32
E)34
Rationale: The total of seven numbers = 7X26 = 182
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (182 - 99 ) = 83
B
Answer: B
Question: How many figures are required to number the pages the pages of a book containing 709 pages?
Options:
A)2020
B)2019
C)1019
D)2029
E)2039
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 709 = 610 * 3 = 1830
-----------
2019
ANSWER:B
Answer: B
Question: If k is an integer, which of the following must be an even integer?
Options:
A)k^2-k-1
B)k^2-4k+6
C)k^2-5k+5
D)k^2+3k+8
E)k^2+2k+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: k^2-k-1 = -1 { If k = 1 }
B: k^2-4k+6 = 3 { If k = 1 }
C: k^2-5k+5 = 1 { If k = 1 }
D: k^2+3k+8 = 12 { If k = 1 }k^2+3k+8 = 18 { If k = 2 }
E: k^2+2k+10 = 13 { If k = 1 }
Thus the only possible answer is (D)
Answer: D
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
Options:
A)22
B)99
C)24
D)66
E)887
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: C
Answer: C
Question: Three unbiased coins are tossed. What is the probability of getting 2 Tails?
Options:
A)3/4
B)1/4
C)3/8
D)7/8
E)1/8
Rationale: Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 2 Tails
Then E = {TTH, THT, HTT}
P(E) = n(E)/n(S) =3/8
Answer is C
Answer: C
Question: The average age of a group of n people is 15 years old. One more person aged 37 joins the group and the new average is 17 years old. What is the value of n?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 15n + 37 = 17(n+1)
2n = 20
n = 10
The answer is A.
Answer: A
Question: The sum of ages of 5 children born at the intervals of 2 years each is 55 years. What is the age of the youngest child?
Options:
A)4
B)7
C)6
D)9
E)8
Rationale: Let the ages of children be x, (x + 2), (x + 4), (x + 6) and (x + 8) years.
Then, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 50
5x = 55-20=35
x = 7.
Age of the youngest child = x = 7 years.
Answer:B
Answer: B
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is ?
Options:
A)10/17
B)10/19
C)46/105
D)11/15
E)Cannot be determined
Rationale: Explanation:
There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.
E)
Answer: E
Question: 3,5,9,15,23,__
Options:
A)30
B)33
C)36
D)40
E)41
Rationale: 5=3+2
9=5+4
15=9+6
23=15+8
33=23+10
ANSWER:B
Answer: B
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)35 Km/hr
B)48 Km/hr
C)57 Km/hr
D)72 Km/hr
E)83 Km/hr
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Km/hr multiply by 18/5)
Speed = 72 Km/hr
ANSWER:D
Answer: D
Question: A electricity company charges $3 for the first 500 units consumption plus $0.05 for each additional unit. What would this company charge for a consumption of 800 units ?
Options:
A)$10
B)$12
C)$15
D)$16
E)$18
Rationale: first 500 units harges = $3
rest of the units = 800 - (500) = 300
charge for the rest of the units = 300 *05 = 15
total charge = 3 + 15 = 18
Answer is E
Answer: E
Question: If b can complete the work in n days and if a and b can work together then they will complete in y days. what will be time to complete the work a alone?
Options:
A)(n-y)/yn
B)1/yn
C)yn/(n-y)
D)2^(yn/(n-y))
E)cannot be determined
Rationale: option C is answer.
one day work of b =1/n.
a+b=1/y(one day work)
a=(1/y)-b
=(1/y)-1/n
=(n-y)/yn(one day work of a)
No of days =yn/(n-y)
Answer: C
Question: A trader marks his product 40% above its cost. He sells the product on credit and allows 10% trade discount. In order to ensure prompt payment, he further gives 10% discount on the reduced price. If he makes a profit of Rs. 67 from the transaction, then the cost price of the product is
Options:
A)Rs. 300
B)Rs. 400
C)Rs. 325
D)Rs. 500
E)Rs. 600
Rationale: M.P = C.P *1.4
Profit = S.P - C.P = C.P ( 1.4 ) ( 0.9 ) ( 0.9 ) – C.P = 67
C.P ( 1.134 – 1 ) = 67,
C.P = 500
ANSWER:D
Answer: D
Question: If 638521 is to be divisible by 5, what is the least whole number that should be added to?
Options:
A)8
B)7
C)5
D)4
E)3
Rationale: A number is divisible by 5 if the last digit is either 0 or 5.
Here, 638521=1(last digit is neither 0 or 5).
the next multiple of 5 i.e to make the last digit 0 or 5 add 4
4 must be added to 638521 to make it divisible by 5
D
Answer: D
Question: A, B and C can do a piece of work in 6,8 and 12 days respectively. In how many days would all of them complete the same job working together?
Options:
A)2 3/4 days.
B)2 2/3 days.
C)2 3/2 days.
D)3 1/2 days.
E)3 3/4 days.
Rationale: Explanation:
In this type of questions we first get the finishing of work in 1 day for A,B,C then we will add them to get the result, as:
Part finished by A in 1 day= 1/6
Part finished by B in 1 day = 1/8
Part finished by C in 1 day =1/12
Part finished by (A+B+C) in 1 day = 9/24
= 9/24 Remaining work =1-9/20=11/20. Number days to finish the work by A+B+C =2 2/3 days.
Option B
Answer: B
Question: The food in a camp lasts for 10 men for 20 days. If 30 more men join, how many days will the food last?
Options:
A)8 days
B)4 days
C)5 days
D)10 days
E)17 days
Rationale: one man can consume the same food in 10*20 = 200 days.
30 more men join, the total number of men = 40
The number of days the food will last = 200/40 = 5 days.
Answer:C
Answer: C
Question: A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 456. What is the sum of the last 8 of the even integers?
Options:
A)580
B)584
C)588
D)592
E)596
Rationale: The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 456
The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) =
456 + 8(16) = 456 + 128 = 584
The answer is B.
Answer: B
Question: The perimeter of one square is 48 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)13√6
B)13√2
C)13√0
D)13√2
E)13√1
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2 Answer:B
Answer: B
Question: In a recent election, Ms. Robinson received 8000 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 40 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?
Options:
A) 0.06N+3200
B) 0.1N+7200
C) 0.24N+8000
D) 0.1N+8000
E) 0.06N+8000
Rationale: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 40% votes so, 0.4*0.6*N plus 8,000 votes from independents: total=0.4*0.6*N+8,000=0.24*N+8,000.
Answer: C.
Answer: C
Question: David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
Options:
A)Rs. 5000
B)Rs. 6500
C)Rs. 8000
D)Cannot be determined
E)None of these
Rationale: Let x, y and z be the amount invested in schemes A, B and C respectively. Then,
(x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200
10x + 12y + 15z = 320000
Now, z = 240% of y = 12/5 y
And, z = 150% of x = 3/2 x
x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y
16y + 12y + 36y = 320000
y = 5000
Sum invested in scheme B = Rs. 5000
ANSWER:A
Answer: A
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)11719
B)11710
C)11712
D)11750
E)11751
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer:D
Answer: D
Question: There are 16 balls in a jar: 8 red, 6 blue and 2 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?
Options:
A)1/12
B)1/4
C)7/8
D)2/3
E)3/4
Rationale: Blue + Red =14
Total number of balls is 8+6+2=16
So the answer is 14/16=7/8
Answer C
Answer: C
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 40%?
Options:
A)228
B)384
C)267
D)288
E)276
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 40% = 40% of 640 = Rs.256
SP = CP - Loss = 640 - 256 = Rs.384
Answer: B
Answer: B
Question: If x, y, and z are positive integers, and 4x = 5y = 8z, then the least possible value of x + y + z is
Options:
A)15
B)23
C)37
D)42
E)60
Rationale: Take LCM of 4,5 and 8 = 40
Now 4x = 40 => x =10
5y = 40 => y = 8
8z = 40 => z =5
10+8+5 = 23.
Option B.
Answer: B
Question: Twelve years ago, P was half of Q's age. If the ratio of their present ages is 3:4 what will be the total of their present ages?
Options:
A)33
B)37
C)29
D)31
E)42
Rationale: E
Let present age of P and Q be 3x3x and 4x4x respectively.
Twelve years ago, P was half of Q's age
â‡’(3xâˆ’12)=1/2(4xâˆ’12)
â‡’6xâˆ’24=4xâˆ’12
â‡’2x=12
â‡’x=6
Total of their present ages
=3x+4x=7x=7Ã—6=42
Answer: E
Question: 1. The simple interest on a sum of money is Rs. 50. What is the sum?
I. The interest rate is 10% p.a.
II. The sum earned simple interest in 10 years
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are necessary to answer
E)None of these
Rationale: Explanation:
Given : S.I. = Rs. 50.
I gives, R = 10% p.a.
II gives, T = 10 years.
Sum = (100 x S.I)/(t x r ) = Rs.(100 x 50)/(10 x 10) = Rs.50
ANSWER IS D
Answer: D
Question: (6)6.5 × (36)4.5 ÷ (216)4.5 = (6)?
Options:
A)1
B)2
C)4
D)6
E)8
Rationale: Explanation :
(6)6.5 × (36)4.5 ÷ (216)4.5
= (6)6.5 × [(6)2]4.5 ÷ [(6)3]4.5
= (6)6.5 × (6)9 ÷ (6)13.5
= (6)(6.5 + 9 - 13.5)
= (6)2
Answer : Option B
Answer: B
Question: A train 200 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Options:
A)5 sec
B)9 sec
C)12 sec
D)15 sec
E)18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 200 m at 50/3 m / sec
= 200 *3/ 50 sec = 12sec
Answer : C
Answer: C
Question: What inequality represents the condition 1<x<7?
Options:
A)|x|<3
B)|x+5|<4
C)|x-1|<9
D)|-4+x|<3
E)|3+x|<5
Rationale: 1<x<7 represents segment with
length: 7-1 = 6
center: (7+1)/2 = 4
For any |x-a|<b a is a center and b is a half of length. So, |x-4|<6/2 represents our inequality (answer D)
Answer: D
Question: Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?
Options:
A)502
B)512
C)523
D)521
E)500
Rationale: Let n be the total number of children.
More children, less notebooks(Indirect proportion)
If the number children = n, number of books each child will get = n/8
If the number children = n/2, number of books each child will get = 16
Hence we can write as
children n:n/2}::16:n/8
⇒n×n/8=n/2×16
⇒n8=16/2=8
⇒n=8×8=64
Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512
Answer is B.
Answer: B
Question: Vijay sells a cupboard at 16% below cost price. Had he got Rs.1200 more, he would have made a profit of 16%. What is the cost price of the cupboard?
Options:
A)3750
B)3600
C)7400
D)7500
E)None of these
Rationale: Explanation:
Cost price = 1200/(0.16 + 0.16) = 1200/0.32
= Rs.3750
ANSWER A
Answer: A
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Options:
A)75
B)28
C)279
D)271
E)27
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics
= (C + M)/2 = 150/2 = 75.
Answer:A
Answer: A
Question: A sum of money doubles itself in 7 years. In how many years it becomes four fold?
Options:
A)35 years
B)28 years
C)14 years
D)21 years
E)None of these
Rationale: Double in seven years.
So 4 times will be in = 7 × (4 − 1) = 21 years.
Answer:D.
Answer: D
Question: A car drove from Town A to Town B without stopping. The car traveled the first 50 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 110 miles if the car’s average speed for the entire trip was 40 miles per hour?
Options:
A)28
B)48
C)50
D)55
E)70
Rationale: KAPLANOFFICIAL SOLUTION:
To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.
For the first 50 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 50/25, because distance divided by rate equals time.
For the last 110 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 110 miles is 110/R.
If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(50/25 + 110/R) = 40. We can now solve for R and reach our answer.
160/(50/25 + 110/R) = 40
R = 55
55 is choice (D) and that’s our correct answer.
Answer: D
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 2:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Options:
A)10.18 p.m
B)10.29 p.m
C)10.30 p.m
D)10.38 p.m
E)9.30 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
2.30 + 7 h = 9.30 p.m.
Answer:E
Answer: E
Question: For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/8, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
Options:
A)5/27
B)2/9
C)1/2
D)4/9
E)2/3
Rationale: P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period)
P(of burning out in 1st 6 mnth)= 1/8
--->P( of not burning out in 1st 6 mnth)=1-1/8=7/8
---->P(of not burning out in a six mnth period)=1/2 *7/8=4/9
--->P(of burning out in a six mnth period)=1-4/9=4/7
now
P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth)
=7/8 *4/7 =1/2
Ans C
Answer: C
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 20 hour to row to a place and come back, how far is the place?
Options:
A)24km
B)30km
C)96km
D)12km
E)15km
Rationale: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 20
2x+3x = 480
x = 96 km
Answer is C
Answer: C
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)99
C)88
D)77
E)52
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Answer: A
Question: Sachin was twice as old as Ajay 10 years back. How old is Ajay today if Sachin will be 40 years old 10 years hence
Options:
A)76 years
B)88 years
C)97 years
D)20 years
E)55 years
Rationale: Sachin's age today = 30 years.
Sachin's age 10 years back = 20 years.
Ajay's age 10 years back = 10 years.
Ajay's age today =20 years
Answer: D
Answer: D
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)Rs. 1090
B)Rs. 1160
C)Rs. 1190
D)Rs. 1202
E)Rs. 1256
Rationale: S.P. = 85% of Rs. 1400 = Rs.85/100x 1400	= Rs. 1190
ANSWER :C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)100
B)110
C)120
D)130
E)150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer: Option E
Answer: E
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 10 minutes earlier. How far is the office from his house?
Options:
A)4 1/5 Km
B)4 1/7 Km
C)3 3/5 Km
D)3 1/7 Km
E)3 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 18/6
= 24/2 * 18/60
= 9 * 2/5
= 18/5 = 3 3/5 Km
C)
Answer: C
Question: Two brothers take the same route to school on their bicycles, one gets to school in 25 minutes and the second one gets to school in 36 minutes. The ratio of their speeds is
Options:
A)4 : 5
B)1 : 2
C)6 : 7
D)5 : 6
E)None
Rationale: Solution
Let us name the brothers
as A and B.	= (A'S speed) : (B's speed)
=âˆšb : âˆša
= âˆš25 : âˆš36
= 5 : 6
Answer D
Answer: D
Question: A number whose fifth part increased by 5 is equal to its fourth part diminished by 5, is
Options:
A)160
B)180
C)200
D)220
E)None of these
Rationale: x/5 + 5 = x/4 - 5
=> x/5 - x/4 = 10
x/20 = 10
=> x = 200
Answer: C.
Answer: C
Question: In how many different ways can the letters of the word 'RUMOUR' be arranged?
Options:
A)180
B)90
C)30
D)720
E)60
Rationale: The word 'RUMOUR' contains 6 letters, namely 2R, 2U, 1M and 1U.
Required number of ways =6!/(2!)(2!)(1!)(1!)=180.
Answer is A
Answer: A
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Options:
A)1840 ways
B)1440 ways
C)1490 ways
D)1447 ways
E)1240 ways
Rationale: In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer: B
Answer: B
Question: A train is 460 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)76 seconds
B)18 seconds
C)40 seconds
D)48 seconds
E)45 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 460+140 = 600 meter
Time = Distance/speed
= 600 * (2/25)
= 48 seconds
Answer: D
Answer: D
Question: Find the distance covered by a man walking for 30min at a speed of 5km/hr?
Options:
A)1km
B)3km
C)4km
D)2.5 km
E)6km
Rationale: Distance = 5*30/60 =2.5 km
Answer is D
Answer: D
Question: 90% of the population of a village is 45000. The total population of the village is?
Options:
A)26799
B)24000
C)50000
D)29973
E)12312
Rationale: X * (90/100) = 45000
X = 500 * 100
X = 50000
Answer: C
Answer: C
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:8
B)3:4
C)3:0
D)3:2
E)3:5
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer: B
Answer: B
Question: Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 56, 94
Options:
A)2
B)6
C)15
D)31
E)94
Rationale: 1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
31(result) + (5*5) = 56.
56(result) + (6*6) = 92.
Now we are getting 92 not 94.. So 94 is the wrong number of the given.
answer : E
Answer: E
Question: If f(x2 – 1) = x4 – 7x2 + k1 and f(x3 – 2) = x6 – 9x3 + k2 then the value of (k2 – k1) is _____
Options:
A)6
B)7
C)8
D)9
E)None of the above
Rationale: Explanatory Answer
Given Data
f(x2 – 1) = x4 – 7x2 + k1
f(x3 – 2) = x6 – 9x3 + k2
Approach and Solution
When x2 = 1, f(x2 – 1) = f(1 - 1) = f(0) =(1)2 - 7(1) + k1
f(0) = - 6 + k1 ..........(1)
Essentially, we have replaced all x2 with 1.
When x3 = 2,f(x3 – 2) = f(2 - 2) = f(0) =(2)2 - 9(2) + k2
f(0) = - 14 + k2 ..........(2)
Essentially, we have replaced all x3 with 2.
Equating f(0) in equations (1) and (2)
(-6 + k1) = (-14 + k2)
or k2 - k1 = 8
The correct answer is Choice C.
Answer: C
Question: There are 9 books on a shelf that consist of 2 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?
Options:
A)85
B)91
C)97
D)103
E)110
Rationale: The total number of ways to select 4 books is 9C4 = 126
The number of ways which do not include any paperbacks is 7C4 = 35
The number of combinations with at least one paperback is 126-35 = 91
The answer is B.
Answer: B
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed three times, what is the probability that the coin turns up tails on at least one of the tosses?
Options:
A)7/8
B)5/8
C)3/8
D)3/4
E)7/16
Rationale: P(3 heads)= 1/2*1/2*1/2=1/8.
P(at least one tail)=1-1/8=7/8.
The answer is A.
Answer: A
Question: Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?
Options:
A)11
B)14
C)15
D)17
E)19
Rationale: C
15
This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on.
Answer: C
Question: If y > 0, (10y)/20 + (3y)/10 is what percent of y?
Options:
A)40%
B)50%
C)60%
D)70%
E)80%
Rationale: can be reduced to y/2+3y/10 =4y/5=80%
E
Answer: E
Question: The average weight of 16 pupils in a class is 50.25 kg and that of the remaining 8 pupils is 45.15 kg. Find the average weights of all the pupils 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: The speed of a boat in still water is 60kmph and the speed of the current is 10kmph. Find the speed downstream and upstream?
Options:
A)40, 68 kmph
B)70, 50 kmph
C)90, 60 kmph
D)40, 60 kmph
E)20, 60 kmph
Rationale: Speed downstream = 60 + 10 = 70 kmph
Speed upstream = 60 - 10 = 50 kmph
Answer: B
Answer: B
Question: The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
Options:
A)71 years
B)72 years
C)74 years
D)77 years
E)75 years
Rationale: Explanation:
Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
Answer IS A
Answer: A
Question: From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.
Options:
A)4/13
B)1/52
C)1/4
D)1/3
E)None of above
Rationale: Explanation:
Total number of cases = 52
Total face cards = 16 [favourable cases]
So probability = 16/52 = 4/13
Answer: Option A
Answer: A