divelab/Sys2Bench huggingface dataset:
Question: The function f is defined for each positive three-digit integer n by f(n)=2x3y5zf(n)=2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
Options:
A)8
B)9
C)18
D)20
E)80
Rationale: Soln:-
m=xyz
v=pqr
m-v = 100(x-p) + 10(y-q) + (z-r)............................(1)
f(m)= 2^x*3^y*5^z
f(v)= 2^p*3^q*5^r
Given that,
f(m) = 9 f(v)
=> 2^x*3^y*5^z = 9* 2^p*3^q*5^r
=> 2^x*3^y*5^z = 3^2*2^p*3^q*5^r
=> 2^x*3^y*5^z = 2^p*3^(q+2)*5^r
=> 2^[x-p]*3^[y-q-2]*5^[z-r] = 1
=> 2^[x-p]*3^[y-q-2]*5^[z-r] = 2^0*3^0*5^0
(x-p)=0
(z-r)=0
(y-q)=2
Substituting the above values in equation (1).
m-v = 100(x-p) + 10(y-q) + (z-r)
=> 0 + 10*2 + 0
=>20
ANSWER:D
Answer: D
Question: How many different possible arrangements Z can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
Options:
A)360
B)720
C)900
D)1800
E)5040
Rationale: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans Z= 7!/ (2!2!) -6!/2! = 900
HENCE C.
Answer: C
Question: How many ways can 3 friends be arranged around a circular dinner table?
Options:
A)A)16
B)B)2
C)C)96
D)D)120
E)E)720
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (3 - 1)! = 2! = 2.
Answer: B.
Answer: B
Question: A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.35 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.40 In what ratio should he mix the water and milk?
Options:
A)1:20
B)1:10
C)1:8
D)1:4
E)6:11
Rationale: water = w (liter)
Milk = m (liter)
==> Cost = Price x Quantity = 0.35m
==> Revenue = Price x Quantity = 0.40(m + w)
==> Profit =0.40(m+w) - 0.35m = 0.2*(0.35m)[20% of cost]
==> 0.40m + 0.40w - 0.35m = 0.07m
==> 0.02m = 0.40w
==> m/w = 0.40/0.02 = 20
--OR--
w/m = 1/20
A is correct.
Answer: A
Question: If x and y are positive integers, and x^3*y^4 = 16,000 which of the following is the value of xy?
Options:
A)10
B)12
C)15
D)16
E)20
Rationale: 16,000 = 10^3*2^4
xy = 10*2 = 20
The answer is E.
Answer: E
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
Options:
A)150,287
B)150,219
C)150,200
D)150,298
E)150,217
Rationale: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer:C
Answer: C
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
Options:
A)1:8
B)1:6
C)1:9
D)1:3
E)1:4
Rationale: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1:9
Answer: C
Answer: C
Question: The greatest possible length which can be used to measure exactly the length 8m ,2m 15cm, 8m 90 cm is?
Options:
A)25cm
B)101cm
C)56cm
D)42cm
E)5cm
Rationale: Required length = H.C.F of 800cm, 215cm, 890cm = 5cm
Answer is E
Answer: E
Question: The probability that B can shoot a target two out of two times is 0.45. What is the probability that the target will be missed by B immediately after such two shots?
Options:
A)0.25
B)0.5
C)0.55
D)0.4
E)0.8
Rationale: Suppose there are total 'x' shots.
B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.
therefore, 2/x = 0.25 (given)
the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.
thus, the probabilty of missing just after 2 shots is (x-2)/x.
(x-2)/x = 1 - 2/x
= 1 - 0.45
= 0.55
Answer : C
Answer: C
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 3 days, then the fraction of the work that is left is
Options:
A)8/17
B)7/15
C)3/15
D)8/15
E)13/20
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 15 ) ( 20 ) (-)
Rate - ( 20 ) ( 15 ) ( 35 )
Work -(300) (300) (300)
therefore A+B requires (300/35) days to complete entire work
For 1st 4 days they work 35 * 3 = 105
Remaining work is 300 - 105 = 195
Remaining fraction of work is = 195/300 = 13/20
Answer E
Answer: E
Question: A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/4 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?
Options:
A)x + 2000 = 1/3*(x - 3000)
B)1/3*(x - 3000) = x
C)x + 3000 = 1/3*x
D)x - 7000 = 1/3*x
E)x - 3000 = 1/4*x
Rationale: Plane's original altitude = x
Plane's new altitude after ascending 2000 ft = x+2000
Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000
So, after two changes plane is at 1/4 its original altitude => x-3000 = x/4
Answer (E)
Answer: E
Question: The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers
Options:
A)9
B)10
C)16
D)17
E)20
Rationale: The only possible sum for 4 different squares of an integer with total sum number is 95 are :
49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17)
or
81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15)
hence the answer is (D)
Answer: D
Question: If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new number is :
Options:
A)30
B)40
C)70
D)90
E)80
Rationale: Solution
A.M of 75 numbers = 35.
sum of 75 numbers = (75 × 35) = 2625.
total increase = (75 × 5) = 375 .
increased sum = (2625 + 375) = 3000.
increased average = 3000/75 =40 Answer B
Answer: B
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)270
B)227
C)268
D)198
E)176
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer:A
Answer: A
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts Q needed to confirm that each of the 5 keys matches each of the 5 locks?
Options:
A)5,15
B)4,15
C)5,10
D)4,10
E)5,20
Rationale: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of Q=4 + 3 + 2 + 1 = 10 attempts.D
Answer: D
Question: In a class if 1 is absent the rest of them can be divided into 6 equal groups and if two are absent can be divided into 7 equal groups. Find the minimum number of students in the class
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: Multiple of 6 and 7 with difference 1 are 36 and 35
So the number of students in the class is 37
ANSWER:C
Answer: C
Question: In one hour a boat goes 18 km long the stream and 14 km against the stream.The speed of the boat in still water is?
Options:
A)17
B)18
C)16
D)15
E)11
Rationale: Speed in still water A = ½ ( 18+14) km/hr A= 16 kmph
Answer: C
Answer: C
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
Options:
A)33.5
B)33.4
C)33.3
D)33.1
E)33.7
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer: C
Answer: C
Question: If a·b·c·d=270, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?
Options:
A)7
B)10
C)11
D)13
E)15
Rationale: prime factorize : 270 = 2*3*5*9
Hence a = 2 and d = 9 .
Hence answer is 9 - 2 = 7
Answer A
Answer: A
Question: Seven unbiased coin are tossed. What is the probability of getting almost
one head?
Options:
A)1/2
B)1/4
C)127/128
D)127/5
E)127/6
Rationale: Here n(S)= 2^7
Let E=event of getting atmost one head =
n(E)= 127
P(E)=n(E)/n(S)=127/128
Answer option C)
Answer: C
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)11 1/7
B)11 1/4
C)11 8/4
D)11 9/4
E)11 3/4
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer:B
Answer: B
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)444 km
B)400 km
C)450 km
D)500 km
E)550 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
ANSWER A
Answer: A
Question: If q and r are even integers, which of the following is an odd integer?
Options:
A)qr + 2
B)q(r − 1)
C)q(q + 5)
D)3q + 4r
E)(q + 3)(r − 1)
Rationale: If q and r are even integers, then:
A. qr + 2: even + even = even
B. q(r − 1): even(odd) = even
C. q(q + 5): even(odd) = even
D. 3q + 4r: even + even = even
E. (q + 3)(r − 1): (odd)(odd) = odd.
Answer is E.
Answer: E
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
Options:
A)2
B)4
C)5
D)67
E)9
Rationale: 1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
Answer: B
Answer: B
Question: A tap can fill a tank in 4 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)2 hr
B)2 hr 30 min
C)2 hr 50 min
D)2 hr 20 min
E)1 hr 30 min
Rationale: A tap can fill a tank in 4 hours
The tap can fill half the tank in 2 hours
Remaining part = 1/2
After half the tank is filled, three more similar taps are opened.
Hence, total number of taps becomes 4.
Part filled by one tap in 1 hour = 1/4
Part filled by four taps in 1 hour = 4×1/4=1
i.e., 4 taps can fill remaining half in 30 minutes
Total time taken = 2 hour + 30 minute = 2 hour 30 minutes
Answer is B
Answer: B
Question: Jony walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:40. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 40 meters. What is Jony's speed in meters per minute?
Options:
A)88
B)100
C)198
D)216
E)252
Rationale: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×40(per block dist)
Speed = 4000mts/40min =100m/min
B is the answer
Answer: B
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 19,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
Options:
A)1 million
B)1.25 million
C)10 million
D)12.6 million
E)125 million
Rationale: If you type that into the calculator, it results in 12.7 mil
[D], 12.6 mil, is the correct answer... see 2 posts above for quick approx method
Answer: D
Question: A train covers a certain distance at a speed of 300kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
Options:
A)600km/hr
B)700km/hr
C)800km/hr
D)900km/hr
E)1000km/hr
Rationale: Explanation:
Distance = 300×4 = 1200km
Required speed = (1200/2) = 600km/hr
Answer: Option A
Answer: A
Question: The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number?
Options:
A)A)9
B)B)10
C)C)12
D)D)7
E)E)13
Rationale: The total of twelve numbers = 12X7 = 84
The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74
So, the middle number is (84 - 74 ) = 10
B
Answer: B
Question: If 37 /2% of a number is 900,then 62 1/2% of the number is ?
Options:
A)1200
B)1350
C)1500
D)540
E)None
Rationale: Answer
Let 371/2% of A = 900
⇒ {(75/2) x A} x 100 = 900
∴ A = (900 x 2 x 100) / 75 = 2400
So, 621/2% of A = (125/2) x (1/100) x 2400 =1500
Correct Option: C
Answer: C
Question: P is the brother of Q and R. S is R's mother. T is P's father. Which of the following statements cannot be definitely true ?
Options:
A)Q is K's son
B)Q is L's son
C)Q is S's son
D)Q is T's son
E)I is T's son
Rationale: Explanation:
P, Q, R are children of same parents. So. S who is R's mother and T, who is R's father will be mother and father of all three.
However, it is not mentioned whether Q is male or female So, D cannot be definitely true.
Answer: D) Q is T's son
Answer: D
Question: If Bella's income is Rs 27000, calculate her savings given that her income and expenditure are in the ratio 6:5.?
Options:
A)Rs.4300
B)Rs.4500
C)Rs.7500
D)Rs.2500
E)Rs.5500
Rationale: Let the income and the expenditure of the person be Rs.6x and Rs.5x respectively.
Income, 6x = 27000 => x = 4500
Savings = Income - expenditure = 6x - 5x = x
So, savings = Rs.4500
Answer: B
Answer: B
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has
Options:
A)66
B)63
C)62
D)64
E)61
Rationale: Required average
= Old average + New average
= 60 + 6 = 66
answer :A
Answer: A
Question: How many four-digit odd numbers do not use any digit more than once?
Options:
A)1728
B)2160
C)2240
D)2268
E)2520
Rationale: Let a 4-digit number be represented by ABCD
Here A can have any value between 1 to 9 - so total 9
B can have any value between 0 to 9, but not A - so total 9
C can have any value between 0 to 9, but not A or B - so total 8
D can have any value between 0 to 9, but not A, B or C - so total 7
No. of ALL possible 4-digit nos (without repeating any digit) = 9*9*8*7 = 4536
Half of these would be odd.
Therefor, no. of ODD possible 4-digit nos (without repeating any digit) = 4536 / 2 = 2268
Answer should be D.
Answer: D
Question: A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?
Options:
A)400
B)1550
C)1575
D)1600
E)1625
Rationale: Area Covered by Road Along the Length = 5*200 = 1000 Square Meter
Area Covered by Road Along the Width = 5*120 = 600 Square Meter
Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25
Total Area of the Roads = 1000+600-25 = 1575
Answer: option C
Answer: C
Question: Patrick has a locker with a 3 number combination. The lock contains numbers from 1 thru 30. No number may be used more than once. Patrick is superstitious and never uses numbers that end with an odd number. He also only uses 2 digit numbers. How many possible 3 digit combinations could he use?
Options:
A)110
B)440
C)550
D)880
E)990
Rationale: Permutation calc is: n P r = n! / (n-r)! 11 P 3 = 11!/(11-3)! = 11x10x9x(8x7x6x5x4x3x2x1)/8!=11x10x9=990 Correct answer is E (990)
Answer: E
Question: In a certain group of 9 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
Options:
A)40
B)50
C)74
D)80
E)100
Rationale: Case 1
1french 2either German or Spanish: 4C1 * 5C2 = 40
Case 2
2french 1either German or Spanish: 4C2 * 5C1 = 30
Case 3
3french 4C3 = 4
Answer is C = 74
Answer: C
Question: 2+9=20
3+4=19
4+3=25
5+2=34
6+1=??
Solve it?
Options:
A)37
B)26
C)43
D)42
E)19
Rationale: x+y=x[y+(x-1)]=x^2+xy-x
2+9=2[9+(2-1)]=4+18-2=20
3+4=3[4+(3-1)]=9+12-2=19
4+3=4[3+(4-1)]=16+12-3=25
5+2=5[2+(5-1)]=25+10-4=34
6+1=6[1+(6-1)]=36+6-5=37
Answer :A
Answer: A
Question: Of the 80 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
Options:
A) 15
B) 17
C) 20
D) 25
E) 30
Rationale: I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
40 will be in team A
60 will be in team B
The larger diff is
70 want team A so diff is 80-40=40. At least 30 people will NOT get their wish, so for 50 researchers the same number is 20.
Answer choice C
Answer: C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)2.89 km
B)2.88 km
C)3.99 km
D)3.78 km
E)3.98 km
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: B
Question: 80% of a number is added to 20, the result is the same number. Find the number?
Options:
A)300
B)288
C)270
D)100
E)281
Rationale: (80/100) * X + 20 = X
4x+ 100 = 5 x
x=100
Answer :: D
Answer: D
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many D women are currently in the room?
Options:
A)12
B)14
C)15
D)24
E)36
Rationale: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
Answer: D
Question: If a and b are digits, and the number a99,99b/88 = an integer, what are the values of a and b?
Options:
A)a = b = 7
B)a = b = 6
C)a = b = 3
D)a = b = 1
E)a = b = 2
Rationale: a99,99b, divisible by 88.
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
99b/8 => 992/8 = 124 => b = 2
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a9999-2 => a999-7 => a99-2 => a9-7 => a2 => 22/11 = 2.
So a = 2.
Answer: E
Answer: E
Question: Two cubes of tire sides ratio 2 : 3. Find its cube volumes ratio?
Options:
A)2:27
B)3:27
C)1:27
D)8:27
E)5:27
Rationale: a(power3) : b(power3) = 2(power3) : 3(power3)
= 8 : 27
Answer is D.
Answer: D
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Options:
A)250
B)882
C)772
D)512
E)211
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Answer: A
Question: An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 50 cm, find the sum of the perimeters of all the triangles.
Options:
A)180 cm
B)220 cm
C)240 cm
D)270 cm
E)300 cm
Rationale: We have 50 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 25 and continues.
So we have 50,25,12.5,...
We have ratio = 1/2, and it is GP type.
Sum of infinite triangle is a/1-r = 50/1-(1/2) = 100
Equilateral triangle perimeter is 3a = 3*100 = 300.
So option E.
Answer: E
Question: How many numbers between 11 and 90 are divisible by 7 ?
Options:
A)23
B)11
C)22
D)32
E)15
Rationale: The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, Tn = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Required number of terms = 11
ANSWER B 11
Answer: B
Question: How many integer values Y are there for x such that 1 < 3x + 5 < 17?
Options:
A)Two
B)Three
C)Four
D)Five
E)Six
Rationale: 1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values Y -1,0 , 1 , 2 , 3
Answer D
Answer: D
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)60%
B)23%
C)30%
D)56%
E)73%
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer: C
Answer: C
Question: The average of five numbers id 27. If one number is excluded, the average becomes 22. What is the excluded number?
Options:
A)30
B)40
C)32.5
D)35
E)47
Rationale: Explanation:
Sum of 5 numbers = 5 × 27
Sum of 4 numbers after excluding one number = 4 × 22
Excluded number
= 5 × 27 - 4 × 22
= 135 - 88 = 47
Answer: Option E
Answer: E
Question: Which of the following points falls outside of the region defined by 2y≤6x−8?
Options:
A)(5, 1)
B)(3, -8)
C)(1, 0)
D)(2, 0)
E)(0, -14)
Rationale: Equation given is 2y<=6x-8
Simplifying this; y<=3x-4
Plug in the values provided in the options,
A. 1<=11
B. -8<=3
C. 0<=-1
D.0<=0
E. -14<=-12
Option C is the answer.
Answer: C
Question: A farmer has enough food to feed her 1000 cows for 50 days. After 10 days some of the cows run away and the food was now enough for the same period of 50 days as before. How many cows ran away?
Options:
A)300
B)200
C)500
D)400
E)250
Rationale: 1000 ---- 50
1000 ---- 40
x ---- 50
x*50 = 1000*40
x = 800
1000
-------
200
Answer = B
Answer: B
Question: Find the L.C.M of 15, 18, 28 and 30.
Options:
A)1800
B)1260
C)1460
D)1600
E)960
Rationale: Explanation:
2 x 3 x 5 x 3 x 14 = 1260
Answer: Option B
Answer: B
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 36 years now, the son's age five years back was:
Options:
A)13
B)15
C)20
D)25
E)30
Rationale: Let the son's present age be x years. Then, (36 - x) = x
2x = 36.
x = 18.
Son's age 5 years back (18 - 5) = 13 years.
Answer: Option A
Answer: A
Question: A train 310 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)56
C)41
D)36
E)34
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 310 + 140 = 450 m
Required time = 450 * 2/25 = 36 sec
Answer: Option D
Answer: D
Question: A sum fetched a total simple interest of $4241.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Options:
A)$8829
B)$2840
C)$6578
D)$7782
E)$8930
Rationale: E
8930
Principal
= $100 x 4241.25/9 x 5
= $424125/45
= $8930.
Answer: E
Question: 9 3/4 + 8 2/17 - 9 1/15=?
Options:
A)7 719/1020
B)9 817/1020
C)9 719/1020
D)8 817/1020
E)None of them
Rationale: Given sum=9+3/4+8+2/17-(9+1/15)
=(9+8-9)+(3/4+2/17-1/15)
=8+(765+120-68/1020
=8 817/1020
Answer is D
Answer: D
Question: There are 10 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
Options:
A)10
B)30
C)45
D)60
E)90
Rationale: 10 players are there.
two players play one game with one another.
so 10C2=10*9/2
=45
SO OPTION C is correct
Answer: C