divelab/Sys2Bench huggingface dataset:
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 22 years. Find the average age of the women?
Options:
A)87
B)98
C)30
D)29
E)37
Rationale: 20 + 22 + 8 * 2
= 58/2
= 29
Answer:D
Answer: D
Question: A Katiland's train rails across an open track at 250 kilometers per hour. A regular passenger train travels at 68% of the Katiland's train speed. If the two trains start moving from the same station at the same time, how much time longer will it take the passenger train than the Katiland's to travel 850 kilometers?
Options:
A)1 hour and 24 minutes.
B)1 hour and 36 minutes.
C)2 hours and 24 minutes.
D)2 hours and 36 minutes.
E)5 hours.
Rationale: Difference in time = time taken by passenger train- time taken by Katiland's train
850/(250*68) *100 - 850/250
850 (100/ 250*68 - 1/250)
850*32/ (250*68)
1.6 hrs or 1 hr and 36 mins
B is the answer
Answer: B
Question: How many three digit no's are between 100-500,where sum of two digit is 3rd?
Options:
A)24
B)54
C)60
D)84
E)94
Rationale: TOTAL PERMUTATIONS POSSIBLE = 18+16+14+12 = 60
ANSWER:C
Answer: C
Question: The list price of an article is Rs.67. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)3.86%
B)4.86%
C)5.86%
D)6.86%
E)7.86%
Rationale: 67*(90/100)*((100-x)/100) = 56.16
x = 6.86%
ANSWER:D
Answer: D
Question: Which of the following numbers has a zero in its units digit?
I. (4!)×(4!)×(3!)×(11)×(17)×(31)
II. (2!)×(3!)×(3!)×(5)×(17)×(31)
III. (2!)^5×(3!)^5×(4!)^5
Options:
A)I only
B)II only
C)III only
D)I, II and III
E)II and III
Rationale: At a glance solution
0 in the units place will come only when you have at least a multiple of 2 and 5
Check clearly none of the given option is both a multiple of 2 and 5 except option (II)
Hence (B) is the correct answer.
Answer: B
Question: The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 900 gm and 700 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?
Options:
A)3.84
B)1.75
C)3.28
D)2.72
E)None of these
Rationale: Here's how I did it. My notes from reading the problem were:
1L A = 900 gm
1L B = 700 gm
We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Each part is 4/5 of a liter.
So if we have 3 parts A, we have 900*3*(4/5) = 2160
If we have 2 parts B, we have 700*2*(4/5) = 1120
2160 + 1120 = 3280
Solving for units gives us 3.28
So the answer is C
Answer: C
Question: How many factors of 990 are odd numbers greater than 1?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: prime factors of 330 are 2^1,3^2,5^1 and 11^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,11) = (2+1)(1+1)(1+1) =12
since we need odd divisors other than 1 =>12-1 = 11 odd divisors
A is the answer
Answer: A
Question: The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 294 sq. cm, what is the width of the rectangle?
Options:
A)10 cm
B)12 cm
C)14 cm
D)16 cm
E)18 cm
Rationale: 2L+2W = 5W
L = 3W/2
W*L = 294
3W^2/2 = 294
W^2 = 196
W = 14
The answer is C.
Answer: C
Question: If 15 men, working 9 hours a day, can reap a field in 16 days, in how many
days will 18 men reap the field, working 8 hours a day?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Since the number of days is to be found out , we compare each item with the number of days.
More men , less days (Indirect)
Less working hours More days (Indirect)
Men 18 : 15} ..
Working Hours 8 : 9 } .. 16 : x
18 x 8 x X = 15 x 9 x 16 or x=15
Required Number of days = 15
ANSWER:C
Answer: C
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 800 widgets?
Options:
A)1 hour and 20 minutes
B)1 hour and 24 minutes
C)1 hour and 30 minutes
D)1 hour and 36 minutes
E)1 hour and 40 minutes
Rationale: (350+250)t=800
600t=800
t=4/3
t=1 hour and 20 minutes
Answer: A
Answer: A
Question: Roy is now 6 years older than Julia and half of that amount older than Kelly. If in 2 years, Roy will be twice as old as Julia, then in 2 years what would be Roy’s age multiplied by Kelly’s age?
Options:
A)84
B)96
C)100
D)108
E)120
Rationale: R = J+6 = K+3
R+2 = 2(J+2)
(J+6)+2 = 2J+4
J = 4
R = 10
K = 7
In 2 years (R+2)(K+2) = 12*9 = 108
The answer is D.
Answer: D
Question: The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4800 sq cm. What is the ratio of the width and the area of the rectangle?
Options:
A)1:72
B)1:76
C)1:80
D)1:84
E)1:88
Rationale: Let the length and the width be 4x and 3x respectively.
Area = (4x)(3x) = 4800
12x^2 = 4800
x^2 = 400
x = 20
The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1 : 80
The answer is C.
Answer: C
Question: 5/25= 10/50. which method did you use to determine whether this proportion is true or false?
Options:
A)true
B)neutral
C)false
D)not sure
E)none
Rationale: 5/25= 10/50. cross multiplication: 5 * 50= 250, 10 *25 = 250,
we see that 250 are not equal to 250 so there is proportion. corrcet answer: (A)
Answer: A
Question: A sum of Rs.150 Has two types of coins Rs.1 and Rs.2. If total number of coins is 100 then number of Rs.2 coins is
Options:
A)50
B)44
C)65
D)40
E)None of the above
Rationale: x=1 rupee coin
y=2 rupee coin
x+2y=150
x+y=100
ANSWER:A
Answer: A
Question: The sum and the product of two numbers are 12 and 20 respectively, the difference of the number is?
Options:
A)1
B)6
C)7
D)8
E)2
Rationale: Explanation:
x + y = 12
xy = 20
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 144 - 80 => (x - y) = 8
Answer: D
Answer: D
Question: Find the odd man out
1, 2, 5, 14, 41, 125
Options:
A)2
B)14
C)124
D)41
E)125
Rationale: 1*3-1 =2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3 -1 = 122
ANSWER:E
Answer: E
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)s. 650
B)s. 690
C)s. 698
D)s. 708
E)s. 718
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (825 - 117) = Rs. 708.
Answer: Option D
Answer: D
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.6 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
Options:
A)1:2
B)2:3
C)2:4
D)2:1
E)2:9
Rationale: Let the ratio be k : 1. Then,
k * 16.6 + 1 * 15.4 = (k + 1) * 15.8
= (16.6 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 1/2
Required ratio = 1/1 : 1 = 1:2.
Answer:A
Answer: A
Question: If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 5?
Options:
A)1/5
B)1/3
C)1/2
D)2/3
E)2/5
Rationale: For n(n+1) to be a multiple of 5, either n or n+1 has to be a multiple of 5.
Thus n must be of the form 5k or 5k-1.
The probability is 2/5.
The answer is E.
Answer: E
Question: The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?
Options:
A)129
B)250
C)228
D)119
E)112
Rationale: Circumference = No.of revolutions * Distance covered
Distance to be covered in 1 min. = (66 X1000)/60 m = 1100 m.
Circumference of the wheel = 2 x (22/7) x 0.70 m = 4.4 m.
Number of revolutions per min. =(1100/4.4) = 250.
Answer: B
Answer: B
Question: Evaluate 28% of 450 + 45% of 280
Options:
A)232
B)242
C)252
D)262
E)282
Rationale: Explanation:
= (28/100) * 450 + (45/100) * 280
= 126 + 126 = 252
Answer: Option C
Answer: C
Question: A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 25% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?
Options:
A)a) $5.60
B)b) $7.20
C)c) $8.80
D)d) $9.60
E)e) $15.20
Rationale: We will get Lowest price with maximum discount
so the discount on 16 will be 40% - giving 9.6
then another discount of 25% on 9.6 to give 7.2
so b - $7.2 B
Answer: B
Question: How many seconds will a 420 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 30 km/hr?
Options:
A)25
B)63
C)40
D)45
E)60
Rationale: Explanation :
Speed of train relatively to man = ( 30 - 6)km/hr
= 24 km /hr
= (24x 5 / 18)m/sec
= 6.66 m/sec
Time taken to pass the man = (420 / 6.66)sec = 63 sec.
Answer : B
Answer: B
Question: Which of the following is equal to the average (arithmetic mean) of (x+2)^2 and (x-4)^2?
Options:
A)x^2
B)x^2+2
C)x^2-2x+10
D)x^2+2x+10
E)x^2+4x+5
Rationale: Avg = [(x+2)^2 + (x-4)^2] / 2
Expanding and simplifying, (x^2 + 4x + 4 + x^2 - 8x + 16 ) / 2 = x^2 - 2x +10
Answer C.
Answer: C
Question: 2x + y = 16
|y| <= 16
For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
Options:
A)12
B)13
C)16
D)17
E)19
Rationale: Hi - The questions says |y| <=16 so the values of y will range from 0 to 16. So the values of y will be 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. So 17 (d) is the answer. remember sign doesn't matter for y as y will always be positive.D
Answer: D
Question: A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
Options:
A)63,000
B)2,000,000
C)2,030,000
D)2,040,000
E)2,300,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-3/100(X)
If sales in 2006,X= 2.1 million find X-3/100(X)
(2.1 x 10^6)-3/100(2.1 x 10^6)
2100000-63000=2,037,000-----> 2,040,000(approx)
ANSWER:D
Answer: D
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is
Options:
A)Rs. 3800
B)Rs. 3900
C)Rs. 4000
D)Rs. 4200
E)Rs. 4400
Rationale: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5 x.
2
15x + 2y = 4000
15x + 2 x 5 x = 4000
2
20x = 4000
x = 200.
So, y = 5 x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
B
Answer: B
Question: Four unbiased coin are tossed. What is the probability of getting atmost
one head?
Options:
A)15/2
B)15/4
C)15/16
D)3/15
E)1/16
Rationale: Here n(S)= 2^4
Let E=event of getting atmost one head =
n(E)= 16
P(E)=n(E)/n(S)=15/16
Answer option C)
Answer: C
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
Options:
A)5
B)4
C)6
D)78
E)9
Rationale: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0 => x = 6.
Answer: C
Answer: C
Question: Find the number of ways in which 8 different flowers can be strung to form a garland so that for particular flowers are never separated.
Options:
A)576
B)567
C)676
D)356
E)456
Rationale: Considering four particular flowers as one flower, we have five flower, which can strung to form a garland in 4! ways. But for particular flowers can be arranged in 4! ways. Required number of ways =4!x4! =576. Answer :A
Answer: A
Question: In the coordinate plane a slope of the line K is 3 times the y-intercept of the line K. What is the x-intercept of the line K?
Options:
A)-4
B)4
C)-1/4
D)-1/3
E)2
Rationale: As Y=3mx+m, from 0=3mx+m we get x=-1/3. Hence, the correct answer choice is D.
Answer: D
Question: In a sequence of 41 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 281, what is the smallest term in the sequence?
Options:
A)1
B)-2
C)0
D)8
E)6
Rationale: Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term.
An = 281 + (41 - 1)*(-7)
An = 281 - 280 =1
A
Answer: A
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1: 96
B)1: 92
C)1: 93
D)1: 91
E)1: 97
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
Answer: A
Question: In State X, all vehicle license plates have 4 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
Options:
A)23,400
B)60,840
C)456,976,000
D)608,400
E)676,000
Rationale: The choices give us the answer without any calculations--
3 one digits places can take 10*10*10 ways..
4 letters places can be filled up in 26*26*26*26 ways
ans= 26*26*26*26*10*10*10=456,976,000
ans C
Answer: C
Question: It takes Joey the postman 1 hours to run a 5 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 8 mile/hour, what is the speed with which Joey returns?
Options:
A)11
B)12
C)13
D)14
E)20
Rationale: let his speed for one half of the journey be 5 miles an hour
let the other half be x miles an hour
now,
avg speed =8 mile an hour
2*5*x/5+x=8
10x=8x+40=>2x=40=>x=20
E
Answer: E
Question: Three years ago the average age of a family of seven members was 22 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
Options:
A)A)1
B)B)2
C)C)3
D)D)4
E)E)5
Rationale: 7 * 25 = 175
8 * 22 = 176
--------------
1
Answer: A
Answer: A
Question: Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 120 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from
Options:
A)30 to 70
B)50 to 80
C)110 to 130
D)130 to 150
E)150 to 170
Rationale: if there are 120 students majoring in electrical then there must be 80 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 50.
if there are 150 students majoring in mechanical there must be 50 students who are not majoring mechanical at all, since the number of the student who are not majoring electrical but majoring mechanical will be at least 50, hence the number of students both majoring mechanical and electrical will be at least 130
so there must be at least 130 students who major in both
see the answers option the only possible answer is D !
Answer: D
Question: In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 1, then the 3rd term is which of the following?
Options:
A)−1.5
B)−1
C)1.
D)0.5
E)2
Rationale: First = 1
Second = 2*1-1 = 1.
Second = 2*1-1 = 1.
Answer: option C
Answer: C
Question: If 13 men do a work in 80 days, in how many days will 20 men do it?
Options:
A)18 days
B)38 days
C)42 days
D)48 days
E)52 days
Rationale: 13 * 80 = 20 * x
x = 52 days
ANSWER:E
Answer: E
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
Options:
A)²²C₁₀
B)²²C₁₀ + 1
C)²²C₉ + ¹⁰C₁
D)²²C₁₀ - 1
E)None of these
Rationale: The total number of ways of forming the group of ten representatives is ²²C₁₀.
The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way
The required number of ways = ²²C₁₀ - 1
ANSWER:D
Answer: D
Question: A store sells nine different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?
Options:
A)32
B)33
C)34
D)35
E)36
Rationale: 9C2=36.
The answer is E.
Answer: E
Question: Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number G is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+G is odd?
Options:
A) 1/2
B) 2/3
C) 3/4
D) 4/7
E) 5/8
Rationale: All primes except 2 are odd, thus N must be odd. For N + G = odd + G to be odd, G must be even.
There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.
Therefore the probability that N + G is odd is 4/7.
Answer: D.
Answer: D
Question: If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
Options:
A)50 km
B)56 km
C)60 km
D)40 km
E)80 km
Rationale: Let the actual distance travelled be x km.
x/10 = (x+20)/15
15x = 10x + 200
5x = 200
x = 40 km.
answer :D
Answer: D
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 10010000 and 100100000 ?
Options:
A) 10
B) 11
C) 1001
D) 1011
E) 10001
Rationale: Binary Divison can provide a quick answer if you are comfortable with it.
as option E is the biggest binary number we try with it first :
100010000/ 1001 =10000
1000100000/ 1001 =100000
so answer is option is C
Answer: C
Question: According to a recent student poll, 5/6 out of 30 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
Options:
A)1/14
B)4/49
C)2/7
D)28/29
E)13/14
Rationale: 25 students are interested, 5 are not interested
Prob = 1 - 5C2/30C2 = 1 - (5*4/(30*29))=1 - 20/580
= 1- 1/29 = 28/29
Answer : D
Answer: D
Question: Look at this series: 53, 53, 39, 39, 25, 25, ... What number should come next?
Options:
A)A)12
B)B)11
C)C)27
D)D)53
E)E)86
Rationale: In this series, each number is repeated, then 14 is subtracted to arrive at the next number.
Answer: B
Answer: B
Question: B and C work together can complete work in 8 days A and B together can complete same work in 12 days and A& C together complete in 16 days in total how many days A,B and C complete the same work together?
Options:
A)3 9/13
B)7 5/13
C)7 5/12
D)3 5/12
E)4 5/12
Rationale: Explanation:
(A+B+C)’s 2 day work = (1/8+1/12+1/16 ) = 13/48
on day work =13/96
so they complete work in 96 /13 = 7 5/13 days
Answer: Option B
Answer: B
Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
Options:
A)6/18
B)3/13
C)2/14
D)9/18
E)7/21
Rationale: Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/52 = 3/13.
Answer B
Answer: B
Question: Two-third of a positive number and 16/216 of its reciprocal are equal. Find the positive number.
Options:
A)9/25
B)14/4
C)4 /12
D)144/25
E)144/29
Rationale: Explanation:
Let the positive number be x.
Then, 2/3 x = 16/216 * 1/x
x2 = 16/216 * 3/2
= 16/144
x = √16/144 =4 /12.
ANSWER:C
Answer: C
Question: if a@b = a * b^(1/2) then 5@9 = ?
self made
Options:
A)12
B)16
C)13
D)15
E)14
Rationale: a@b = a * b^(1/2)
5@9 = 5*9^(1/2) = 5*3 = 15
Correct Option: D
Answer: D
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
Options:
A)35
B)24
C)27
D)27 7/9
E)67
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: Option D
Answer: D
Question: Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water?
Options:
A)29 journeys
B)30
C)20
D)50
E)55
Rationale: Explanation :
Here, Large, Medium and Small ships are denoted by the symbol L, M and S.
Now, according to the question,
4L = 7S. ------(i)
3M = 2L + S. ------(ii)
Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :-
7: 6 : 4.
Let, the number of journeys required be x. Since, quantity of water remains the same, so :-
=((15×7+7×6+ 14×4)36) = x (12×7+14×6+21×4).
=>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x
=>x=7308/252
=>x=29.
Answer : A
Answer: A
Question: 30 square stone slabs of equal size were needed to cover a floor area of 50.7 sq.m. Find the length of each stone slab?
Options:
A)130cm
B)767cm
C)88cm
D)666cm
E)776cm
Rationale: Area of each slab
=50.7/30m2=1.69m2
Length of each slab √1.69=1.3m=130cm
Answer: A
Question: Six students wrote science exam. Their average marks are 70. Five Students got 65, 75, 55, 72 and 69 marks respectively. Therefore what is the marks of the sixth student?
Options:
A)84
B)68
C)85
D)75
E)42
Rationale: EXPLANATION
Total marks of 5 students = (65+75+55+72+69) = 336
Required marks = [ (70 x 6) – 336 ]
= (420 – 336)
= 84
Answer A
Answer: A
Question: Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?
Options:
A)12
B)14
C)18
D)20
E)22
Rationale: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -8/1 = -8
ab = 4/1 = 4
Hence a/b + b/a = [(-8)2 - 2(4)]/4 = 56/4 = 14.
B)
Answer: B
Question: Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: Explanation:
Total weight increased is 1.5 * 10 = 15.
So weight of new person is 45+15 = 60
Option C
Answer: C
Question: If the probability of rain on any given day in Chicago during the summer is 25%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7 inclusive?
Options:
A)1/16
B)3/32
C)5/32
D)3/64
E)7/64
Rationale: One possible case is: rainy-rainy-rainy-not rainy.
The probability of this case is 1/4*1/4*1/4*3/4 = 3/256
The number of possible cases is 4C3 = 4.
P(exactly 3 rainy days) = 4*3/256 = 3/64
The answer is D.
Answer: D
Question: The value of each of 5 numbers is at least 8. The average (arithmetic mean) of these 5 numbers is 24. If the average of two of the numbers is 18, what is the largest possible value that any of these 5 numbers can have?
Options:
A)28
B)50
C)68
D)76
E)84
Rationale: Average => (a1+a2+a3+a4+a5)/5 =24
Thus => a1+a2+a3+a4+a5 = 120
now least value is 8, so let a1 = 8
average of 2 numbers is 18
thus , let (a2+a3) /2 =18
a2+a3 = 36
This tells that sum of last 2 numbers should be :
120 -8-36 =76
Then by elimination , eliminate 84 and 76
highest possible value of a5 should be 68 from the answer choice
Answer : C
Answer: C
Question: 1, 6, 13, 22, 33, ?
Options:
A)35
B)46
C)48
D)49
E)38
Rationale: The pattern is + 5, + 7, + 9, + 11,....
Answer : B.
Answer: B
Question: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...
For every positive integer n that is greater than 1, the function f(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The f(n) could have any of the following units digits except…?
Options:
A)1
B)2
C)4
D)6
E)9
Rationale: For every positive integer n that is greater than 1, the function f(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The f(n) could have any of the following units digits except…?
Used brute force on this one to calculate. Not sure if there is a quicker way.
1+3=4 C is out
1+3+....15= 81 A is out
1+3+5+7=16 D is out
1+3+5=9 E i out
Answer: B
Answer: B