divelab/Sys2Bench huggingface dataset:
Question: How many days per calendar year is the month a factor of the day
Options:
A)0
B)1
C)45
D)90
E)101
Rationale: Solution: 45
All 31 days in January, because 1 is a factor of all integers
14 of the 28 days in February (because every other day is divisible by 2)
10 of the 31 days in March (the multiples of 3 between 3 and 30)
7 days in April (the multiples of 4 between 4 and 28)
6 days in May (the multiples of 5 between 5 and 30)
5 days in June (the multiples of 6 between 6 and 30)
4 days in July (the multiples of 7 between 7 and 28)
3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)
3 days in September (9th, 18th, 27th)
3 days in October (10th, 20th,30th)
2 days in November (11th, 22nd)
2 days in December (12th, 24th)
And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!
C
Answer: C
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 14 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
Options:
A)40
B)56
C)60
D)Data inadequate
E)None of these
Rationale: E+H+G+M/4âˆ’E+S+M+H/4=14
â‡’ G - S = 56
Answer B
Answer: B
Question: A train 150 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options:
A)20 sec
B)32 sec
C)36 sec
D)38 sec
E)40 sec
Rationale: Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(150×2/15) sec=20 sec
ANSWER :A
Answer: A
Question: If 12 men do a work in 80 days, in how many days will 16 men do it?
Options:
A)60
B)30
C)50
D)40
E)20
Rationale: 12 * 80 = 16 * x
x = 60 days
ANSWER A
Answer: A
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. Find out the teacher's age in years?
Options:
A)51 years
B)49 years
C)53 years
D)50 years
E)52 years
Rationale: Explanation:
average age of 36 students in a group is 14
Sum of the ages of 36 students = 36 × 14
When teacher's age is included to it, the average increases by one
=> average = 15
Sum of the ages of 36 students and the teacher = 37 × 15
Hence teachers age
= 37 × 15 - 36 × 14
= 37 × 15 - 14(37 - 1)
= 37 × 15 - 37 × 14 + 14
= 37(15 - 14) + 14
= 37 + 14
= 51
Answer: Option A
Answer: A
Question: If x and y are positive integers and y ≠ 1, then xy(y −1) is
Options:
A)Always even
B)Always odd
C)Odd only when x is odd
D)Even only when y is even
E)Odd only when xy is odd
Rationale: Expression is xy(y-1). We can ignore x and only work with y.
If y = even -> entire expression is even since anything multiplied by even is even
If y = odd, y-1 -> even -> entire expression is even since anything multiplied by even is even
Hence, entire expression will always be even.
Answer (A).
Answer: A
Question: n is an integer chosen at random from the set
{1, 5 , 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 15 ?
Options:
A)0.1
B)0.2
C)0.15
D)0.3
E)0.4
Rationale: Set N: there is 4 ways to chose a number
Set P: there is 5 ways to chose a number
so total outcome is 4*5 = 20 which is represent 20 pairs of number
now we have 3 pairs can give us 15 which are (1,14),(5,10) and (9,6) .
3/20 = 0.15
Answer C
Answer: C
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 18 gallons of ethanol, how many gallons of fuel A were added?
Options:
A)160
B)150
C)100
D)80
E)350
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 18 gallons then 0.12A+0.16(200-A)=18 --> A=350.
Answer: E.
Answer: E
Question: If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?
Options:
A)33
B)38
C)60
D)88
E)22
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirct Proportion)
\inline \fn_jvn \therefore 15:36 ::25:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{15}=60
Hence, 15 men can do it in 60 hours.
Answer: C
Answer: C
Question: Find the remainder when 3^27 is divided by 5?
Options:
A)3
B)2
C)4
D)1
E)5
Rationale: Solution : 3^27= ((3^4)^6) * (3^3) = (81^6) * 27 then unit digit of (81^6) is 1 so on multiplying with 27,
unit digit in the result will be 7. now, 7 when divided by 5 gives 2 as remainder.
Answer B
Answer: B
Question: If 9a - b = 10b + 80 = -12b - 2a, what is the value of 2a + 22b?
Options:
A)-4
B)-2
C)- 80
D)2
E)4
Rationale: This implies 9a - b = 10b + 80, 9a -b = -12b -2a, 10b + 80 = -12b -2a
Manipulating the second equation gives us 10b + 80 = -12b - 2a ==> 2a + 22b = - 80
Answer is C
Answer: C
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)456
B)234
C)285
D)342
E)213
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C
Answer: C
Question: A trader sells two brands of petrol; one is Extra Premium and other one is speed. He mixes 12 litres Extra Premium with 3 litres of speed and by selling this mixture at the price of Extra Premium he gets the profit of 9.09. If the price of Extra Premium Rs. 48 per litre, then the price of Speed is:
Options:
A)Rs. 38 per litre
B)Rs. 42 per litre
C)Rs. 28 per litre
D)Rs. 28 per litre
E)None of These
Rationale: Solution: Selling price mix EP,
= (CP + 9.09% of CP)
48 = 12/11 of CP
CP = 44
No, using Alligation method,
MCQ Aptitude Profit and Loss11
4:1 Thus,
X = 44
Thus, the price of speed brand is Rs. 28/litre.
Answer: Option C
Answer: C
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)3 kmph
B)1.5 kmph
C)13 kmph
D)6.5 kmph
E)7.5 kmph
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
ANSWER:B
Answer: B
Question: a man have 8 t-shirt and some pant.he can dress in 72 ways.then tell me the no. of pant that man have.
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: let he have x pant.
by fundamental principle total no. of ways in which he can dress=8x
8x=72
x=9pants
answer B
Answer: B
Question: If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 6 € (4 € 5) =
Options:
A)480
B)120
C)160
D)240
E)360
Rationale: working inside out,
(4 € 5) = 2*4*5 = 40
6 € 40 = 2*6*40 = 480
Hence, answer is A
Answer: A
Question: The line r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2) and is parallel to the line s ≡ mx + 2y − 13 = 0. Calculate the values of m and n.
Options:
A)-6,-1
B)-3,-2
C)3,2
D)6,1
E)7,2
Rationale: r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2)
3. 3 +nN . 2 - 7 = 0 n = -1
3/m = - 1/2
m=6
ANSWER : A -6,-1
Answer: A
Question: Present ages of Abi and Suji are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Suji's present age in years?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: present ages = 5x:4x
Three hence =5x+3:4x+3
5x+3:4x+3=11:9
weget x=6
suji age is =4x=4*6=24
ANSWER:E
Answer: E
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)7 kmph
B)4 kmph
C)8 kmph
D)3 kmph
E)9 kmph
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer:B
Answer: B
Question: 1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams
Options:
A)48 paise
B)77 paise
C)96 paise
D)66 paise
E)55 paise
Rationale: Explanation:
Let 200 gm potato cost X paise
According to question,
Cost of 1/4 Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise
=> 1 Kg = 1000 gm
=> 1/4 Kg = 1000/4 gm = 250 gm
By direct proportion, more quantity, more cost
200 grams : 250 grams = X : 60
=> 200*60 = 250 X
=> 12000 = 250 X
=> X = 48
=> Thus, the cost of 200 grams is 48 paise.
ANSWER: A
Answer: A
Question: In how many ways can you line up 7 apples in a row if one of them cannot be in the middle or at the either end?
Options:
A)1,790
B)52
C)2,880
D)98
E)2,560
Rationale: Since the apple cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: C.
Answer: C
Question: A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest is 12% per annum,how much cash should he pay ?
Options:
A)Rs. 9025.20
B)Rs. 9200
C)Rs. 9600
D)Rs. 9560
E)None of these
Rationale: Solution
Required money = P.W. of Rs.10028 due 9 months hence
= Rs. [ 10028x 100/100+( 12 x9/12)] = Rs. 9200
Answer B
Answer: B
Question: The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?
Options:
A)440
B)512
C)620
D)700
E)750
Rationale: Solved it the prime factorization way
440= 2*2*2*5*11 Sum=22
512= 2^6 Sum=2*6=12
620=2*2*5*31 Sum=40>35
Hence correct.
Ans is C
Answer: C
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
Options:
A)2.15 p.m
B)1.15 p.m
C)4.15 p.m
D)3.15 p.m
E)12.15 p.m
Rationale: Suppose they meet x hours after 10 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Ans: A
Answer: A
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?
Options:
A)9! * ⁷P₆
B)6! * ⁷P₆
C)9! * ⁷P₆
D)6! * ⁷9₆
E)7! * ⁷P₆
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
Answer:B
Answer: B
Question: Solve below question 2x + 1 = -15
Options:
A)-8
B)-9
C)9
D)8
E)-7
Rationale: 2x + 1 = -15
x = -8
A
Answer: A
Question: If Sam shares his books in the ratio of 1/8 : 1/9 : 1/10 : 1/11 between his four friends A, B, C and D, then find the total number of books Sam should have?
Options:
A)1611
B)1692
C)1591
D)1691
E)16911
Rationale: Here, A : B : C : D = 1/8 : 1/9 : 1/10 : 1/11
1) L.C.M of 8 : 9 : 10 : 11 is 3960
2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/8) x 3960 = 495
B = (1/9) x 3960 = 440
C = (1/10) x 3960 = 396
D = (1/11) x 3960 = 360
3) Total number of toys = (495 x + 440 x + 396 x + 360 x) = 1691 x
Minimum number of pens (x) = 1
Therefore, total number of items = 1691 items.
Correct option :E
Answer: E
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)2387
B)1640
C)2781
D)2778
E)1781
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640
Answer: B
Answer: B
Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is?
Options:
A)23
B)25
C)27
D)31
E)35
Rationale: Let the numbers be x and y.
Then, xy = 120 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
x + y = 529 = 23.
Option A
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
Options:
A)Insufficient data
B)3 : 1
C)1 : 3
D)3 : 2
E)2 : 3
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
=> (27x + 17 y)/(x + y) = 23
=> (27x + 17 y) = 23(x + y)
=> 4x = 6y
=> x/y = 6/4 = 3/2
ANSWER:D
Answer: D
Question: Sentence B can only be a concluding sentence; we find in the answer choice–b, a sequence of the sentences logically leading to the concluding sentence
Options:
A)17
B)88
C)171
D)19
E)111
Rationale: Answer:B
Answer: B
Question: 35% of the people read newspaper X, 55% read newspaper Y and 15% read both the papers.What percentage of the people read neither newspaper ?
Options:
A)20%
B)10%
C)15%
D)30%
E)25%
Rationale: n(A)=35,n(B)=55,n(AnB)=15.
n(AuB)=n (A)+n (B)-n(AnB)=35+55-15=75.
Hence, percentage passed =(100-75)%=25%.
Answer is E
Answer: E
Question: 5100−(102÷20.4)=?
Options:
A)5200
B)5150
C)5250
D)6150
E)5095
Rationale: Explanation:
=5100−(102/204×10)
=5100−5=5095
Option E
Answer: E
Question: Two trains 130 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9
B)10.7
C)10.3
D)10.44
E)10.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 130 + 160 = 290 m.
Required time = 290 * 9/250 = 261/25 = 10.44 sec.
'Answer: D
Answer: D
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Options:
A)671.5
B)600
C)672.5
D)673
E)773.5
Rationale: Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds;
Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours;
So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: B.
Answer: B
Question: In a sequence of 11 numbers, each term, except for the first one, is 11^11 less than the previous term. If the greatest term in the sequence is 11^12, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
Options:
A)−12^11
B)0
C)11^11
D)11·12^11
E)12^12
Rationale: there are total 11 terms. andgreatestterm is 11^12. Each term is 11^11 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 11^11 less than previous one')
Therefore, 11^12 is the first term of the AP and -11^11 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 11^12 + 10*(-11^11)
=> Last term = 11^12 - 10*11^11
=> Last term = 11^11 (11-10) = 11^11
Which is the smallest term.
Hence Ans C it is.
Answer: C
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 10. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 13. How many cooks does the restaurant have?
Options:
A)4
B)6
C)9
D)12
E)15
Rationale: Originally there were 3k cooks and 10k waiters.
13k = 10k+12
k=4
There are 12 cooks.
The answer is D.
Answer: D
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,U,R,S,and T so that letter P is to the left of letter R?
Options:
A)60
B)30
C)90
D)120
E)75
Rationale: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
A
Answer: A
Question: If the product 4864*9 P 2 is divisible by 12, the value of p?
Options:
A)1
B)5
C)6
D)7
E)9
Rationale: Explanation:
clearly 4864 is divisible by 4
So 9 P 2 must be divisible by 3.So(9+P+2) must be divisible by 3.
so P=1.
Answer: A) 1
Answer: A
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 144 of the workers of that company are men, how many of the workers are women?
Options:
A)80
B)95
C)105
D)120
E)126
Rationale: Set up equation:
x = total number of workers
144 = 0,4 * 2/3 * x + 0,8 * 1/3 * x
144 = 16/30 x
x = 270
270 - 144 = 126
Answer E
Answer: E
Question: The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 156.4, what is the average of the other half?
Options:
A)12.8
B)24.2
C)49.1
D)72.1
E)96.8
Rationale: The average of this half is 156.4/4 = 39.1
This is 5 below the overall average, thus the average of the other half of the numbers must be 5 above the overall age, that is 44.1+5 = 49.1
The answer is C.
Answer: C
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87, and 98
Options:
A)80
B)85
C)92
D)97
E)100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median quiz score was 92. (Four quiz scores were higher than 92 and four were lower.)
C
Answer: C
Question: 12 men can complete any work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only the women were to complete the remaining work in 4 days, then how many women would be required?
Options:
A)60
B)74
C)68
D)75
E)70
Rationale: 1 Man, 1 Day work=1/(12*36)
1 Woman, 1 Day work=1/(18*60)
So 8 men and 20 women's 20 days work= 20[ 8/(12*36) + 20/(18*60) ] =20/27
Remaining work= 7/27
If remaining work is to be completed by 'x' women in 4 days, then 4*x/(18*60)= 7/27
=> x=(7*18*60)/(27*4)=70
ANSWER:B
Answer: B
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)7 sec.
B)6 sec
C)3 sec.
D)1 sec.
E)8 sec.
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Answer: B
Question: An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
Options:
A)23.000 degrees / second
B)43.000 degrees / second
C)52.000 degrees / second
D)18.000 degrees / second
E)29.000 degrees / second
Rationale: 3000 revolutions / minute
= 3000*360 degrees / 60 seconds
= 18,000 degrees / second
correct answer D
Answer: D
Question: A car traveled the first quarter of a certain distance at five times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
Options:
A)1/14
B)1/15
C)1/16
D)1/17
E)1/18
Rationale: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be five times, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 2 km/h for the remaining quarters.
He'll take 1 hour to do the first quarter and then 15 hours for the second ,third and fourth quarter. On total he will take 16 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/16. Answer C.
Answer: C
Question: Jerry received a 10% raise each month for two consecutive months. What was his starting salary if after the two raises his salary is $1452?
Options:
A)$1,200
B)$1,300
C)$1,331
D)$1,380
E)$1,403
Rationale: S * 1.1 * 1.1 = 1452 so,
S = 1200
Answer: A
Answer: A
Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
A)32
B)28
C)40
D)27
E)21
Rationale: S = (200 + 300)/45 = 500/45 * 18/5 = 40
Answer: C
Answer: C
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
Options:
A)11
B)10
C)19
D)187
E)12
Rationale: Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days. Answer: B
Answer: B
Question: A baseball player just signed a new contract in which he will earn a 12% raise in base pay over last year. Last year he earned no performance bonus, but this year he will have the opportunity to earn up to $50,000 in extra pay through performance. If he earns the full performance bonus, his salary will effectively have been raised by 12.5% from the last year. Assuming he earns the full performance bonus, what will his new salary be?
Options:
A)5,150,000
B)10,550,000
C)11,250,000
D)11,450,000
E)12,250,000
Rationale: let x = the old salary
the new base pay + 50,000 = the new pay
(1+.12)*x + 50,000 = (1+.125)*x
1.12x + 50,000 = 1.125x
50,000 = .005x
10,000,000 = x
thus the new pay = (1+.125)*10,000,000 = 11,250,000
C
Answer: C
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)6520
D)6629
E)6609
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: A
Question: The average of 6 observations is 12. A new observation is included and the new average is decreased by 1. The seventh observation is?
Options:
A)1
B)3
C)5
D)6
E)7
Rationale: Let seventh observation = X.
Then, according to the question we have
=> (72 + X) / 7 = 11
=> X = 5.
Hence, the seventh observation is 5.
ANSWER:C
Answer: C
Question: Company A has 13 employees, 8 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 3 union members work each shift, then how many different combinations of employees might work any given shift?
Options:
A)56
B)231
C)336
D)350
E)406
Rationale: Looks easy: -- 8C3*5C1 + 8C5 -- 336 (C).
Answer: C
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
Options:
A)20
B)30
C)40
D)50
E)None of these
Rationale: Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
(a + b + c) = 400 = 20
Answer:A
Answer: A