mathewhe/aqua_rat huggingface dataset:
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 277 m
(B) 240 m
(C) 627 m
(D) 892 m
(E) 288 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x
= 240 m.
Answer: B
Answer: (B) 240 m
Question: If two positive numbers are in the ratio 1/9 : 1/5, then by what percent is the second number more than the first?
(A) 80%
(B) 90%
(C) 60%
(D) 50%
(E) 65%
Rationale: Given ratio = 1/9 : 1/5 = 5 : 10
Let first number be 5x and the second number be 9x.
The second number is more than first number by 4x.
Required percentage = 4x/5x * 100 = 80%.
Answer:A
Answer: (A) 80%
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full?
(A) 9:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 2:00 a.m.
Rationale: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m.
Answer: B.
Answer: (B) 7:00 a.m.
Question: C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used?
(A) months
(B) months
(C) months
(D) months
(E) months
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D
Answer: (D) months
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 1,600 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A) 5.55%
(B) 5.65%
(C) 5.75%
(D) 5.85%
(E) 5.95%
Rationale: The amount of sodium chloride is 0.05*10,000 = 500 gallons
500/8400 = 5/84 which is about 5.95%
The answer is E.
Answer: (E) 5.95%
Question: The product of two successive numbers is 4160. Which is the smaller of the two numbers?
(A) 78
(B) 64
(C) 88
(D) 67
(E) 37
Rationale: B
4160
From the given alternatives,
64 × 65 = 4160
∴ Smaller number = 64
Answer: (B) 64
Question: A basket has 6 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is
(A) 25/42
(B) 25/48
(C) 19/42
(D) 25/47
(E) 25/43
Rationale: Total fruits = 10Since there must be at least two apples,(6C3 * 4C1)/10C4 + 6C4/10C4 = 19/42.Answer:C
Answer: (C) 19/42
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
(A) 271 km
(B) 224 km
(C) 243 km
(D) 222 km
(E) 215 km
Rationale: B
224 km
Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Answer: (B) 224 km
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 16 8/3% loss
(C) 19 2/3% loss
(D) 13 2/3% loss
(E) 26 2/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: (A) 16 2/3% loss
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 288
(B) 286
(C) 298
(D) 2776
(E) 8811
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer:D
Answer: (D) 2776
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.096
(B) 0.125
(C) 0.128
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.6
Therefore, probability of no rain = 0.4
0.6*0.6*0.4 = 0.096
Hence A
Answer: (A) 0.096
Question: How many combinations of three letters taken from letters (a, b, b, c, c, d) are possible?
(A) 10
(B) 13
(C) 35
(D) 36
(E) 56
Rationale: So 4C3 for abcd - 4 choices
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 10
Ans :A
Answer: (A) 10
Question: If x#y is defined to equal x^3/y for all x and y, then (-1#2)#3 =
(A) 4/3
(B) 1/3
(C) 1/12
(D) -1/12
(E) 1/24
Rationale: (-1)^3 / 2 = 1/2
(1/2)^3 / 3 = 1/24
so E is my answer
Answer: (E) 1/24
Question: A part-time employee’s hourly wage was increased by 25%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
(A) 9%
(B) 15%
(C) 20%
(D) 50%
(E) 100%
Rationale: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 25% wage increase, the employee makes $1.25/hour
We want the employee's income to remain at $100/week.
So, we want ($1.25/hour)(new # of hours) = $100
Divide both sides by 1.25 to get:
new # of hours = 100/1.25
≈ 80 hours
So, the number of hours decreases from 100 hours to (approximately) 80 hours.
This represents a 20% decrease (approximately) .
Answer : C
Answer: (C) 20%
Question: Find the median of the data 25, 37, 47, 18, 19, 26, 36.
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47
Here, the number of observations is odd, i.e., 7.
Therefore, median = (n + 1/2)th observation.
= (7 + 1/2)th observation.
= (8/2)th observation
= 4th observation.
4th observation is 26.
Therefore, median of the data is 26. ANSWER :E
Answer: (E) 26
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother three years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 5 years
(D) 7 years
(E) 8 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 3) years = 41 years.
Required difference = (41 - 36) years = 5 years.
Answer: Option C
Answer: (C) 5 years
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction E of the cookies that were placed in the other tins were placed in the green tin?
(A) 15/2
(B) 9/4
(C) 5/9
(D) 7/5
(E) 9/7
Rationale: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction E= 5N/12 * 12/9N = 5/9 (C)
Answer: (C) 5/9
Question: If the cost price is 96% of the selling price, then what is the profit percent?
(A) 4.17%
(B) 5%
(C) 6.12%
(D) 3.25%
(E) 5.75%
Rationale: Let S.P. = $100
C.P. = $96
Profit = $4
Profit% = 4/96 * 100 = 25/6 = 4.17%
Answer is A
Answer: (A) 4.17%
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
(A) 2:9
(B) 3:1
(C) 3:4
(D) 3:9
(E) 3:6
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y
= 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y
= 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y
= 80
Ratio of speeds = 60:80 = 3:4
Answer:C
Answer: (C) 3:4
Question: A train running at the speed of 48 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 120 meter
(B) 299 meter
(C) 666 meter
(D) 155 meter
(E) 144 meter
Rationale: Speed = 48*(5/18) m/sec = 40/3 m/sec
Length of Train (Distance) = Speed * Time
(40/3) * 9
= 120 meter
Answer: A
Answer: (A) 120 meter
Question: John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
(A) 45
(B) 65
(C) 70
(D) 77
(E) 98
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.
D)
Answer: (D) 77
Question: If the tens digit of positive integer x is 3 and the tens digit of positive integer y is 3, how many possible values of the tens digit of 2(x+y) can there be?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 30 + p and 30 + q respectively.
2(30+p+30+q)= 120 + 2(p + q)
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 20 up to 56.
There can be 4 possibilities for the tens digit.
The answer is C.
Answer: (C) 4
Question: The editor of an anthology of short stories will select authors from a pool of 10 authors, of which 4 are female. If the anthology is to include the work of 6 authors of which at least 2 are female, in how many ways can the editor select the authors?
(A) 155
(B) 165
(C) 175
(D) 185
(E) 195
Rationale: 10C6 = 210
The number of ways to select 6 males is 6C6 = 1
The number of ways to select 5 males and 1 female is 6C5*4C1 = 24
210 - 1 - 24 = 185
The answer is D.
Answer: (D) 185
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.15000 at the end of the year, B's share is
(A) Rs.4000
(B) Rs.5400
(C) Rs.7500
(D) Rs.6600
(E) None
Rationale: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(15000 x 4 / 11)
= Rs.5400.
Answer B
Answer: (B) Rs.5400
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 228
(B) 280
(C) 287
(D) 115
(E) 191
Rationale: Explanation:
x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Answer: (B) 280
Question: 82
a7
+ 6b
____
190
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 2b ?
(A) 2
(B) 6
(C) 9
(D) 11
(E) 12
Rationale: Adding the digits in unit's place , 2+ 7 + b = 10 (Since a and b are positive single digits )
=> b = 1
Now adding the digits in ten's place , 8+a + 6 + 1= 19 (1 has been carried over from unit's place addition)
=> a= 4
a+2b = 4+2*1
=6
Answer B
Answer: (B) 6
Question: Two persons Raj and Ramu started working for a company in similar jobs on January 1, 1991. Raj's initial monthly salary was Rs 400, which increases by Rs 40 after every year. Ramu's initial monthly salary was Rs 500 which increases by Rs 20 after every six months. If these arrangements continue till December 31, 200. Find the total salary they received during that period.
(A) Rs 108000
(B) Rs 144000
(C) Rs 132000
(D) Rs 152400
(E) None of these
Rationale: Explanation :
Raj's salary as on 1 jan 1991 is Rs 400 per month.
His increment in his month salary is Rs 40 per annum
His total salary from 1 jan 1991 to 31st dec 2000
i.e. in ten years
=>12[2(400)+(10−1)40]×10/2.
=>Rs 69,600.
Ramu's salary as on Jan 1st 1991 is Rs 550 and his half yearly increment in his month salary is Rs 20.
His total salary from 1 jan 1991 to dec 31, 2000
=>6[2(500)+(20−1)20]×20/2.
=>Rs 82,000.
Total salary of Raj and Ramu in the ten year period:
=> Rs. 69600+ Rs. 82800.
=>Rs 1,52,400.
Answer : D
Answer: (D) Rs 152400
Question: A completes a work in 15 days and B complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be
(A) 8 days
(B) 9 days
(C) 10 days
(D) 12 days
(E) 13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 15 ×30/ 45 = 10 days.
Answer : C
Answer: (C) 10 days
Question: Which of the following numbers is between 1⁄2 and 1⁄4?
(A) .65
(B) .55
(C) .29
(D) .22
(E) .20
Rationale: Isn't it C?
1/2 = .50
1/4 = .25
The only answer between that is C, .29.
Answer: (C) .29
Question: if 2 pipes take an hour to fill a tank, then how long should 8 pipes take to fill the same tank?
(A) 20 min
(B) 10 min
(C) 15 min
(D) 25 min
(E) 30 min
Rationale: if 2 pipes take an hour to fill a tank, then
8 pipes will take 2*60/8 = 15 mins to dig a ditch of the same type.
ANSWER:C
Answer: (C) 15 min
Question: Find √? /19 = 4 ?
(A) 76
(B) 5776
(C) 304
(D) 1296
(E) None
Rationale: Answer
Let √N/19 = 4
Then √N = 19 x 4 = 76
∴ N = 76 x 76 = 5776.
Correct Option: B
Answer: (B) 5776
Question: Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?
(A) 6200
(B) 6300
(C) 6400
(D) 6500
(E) 6600
Rationale: Let the sum invested in Scheme A be x and that in Scheme B be (13900 - x).
Then, (x x 14 x 2)/100 + ((13900 - x) x 11 x 2)/100 = 3508
28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = (13900 - 7500) = 6400.
answer : C
Answer: (C) 6400
Question: How many numbers between 200 and 400 begin or end with 2?
(A) 20
(B) 60
(C) 100
(D) 110
(E) 120
Rationale: How many numbers between 200 and 400 begin or end with 2?
Just think that those numbers are:
i) The ones ending in 2: 202, 212, 222, ... , 392 --> 20 numbers
ii) The ones beginning in 3: 200, 201, 202, 203, ... , 293, ... , 299 --> 100 numbers
BUT 10 out of the first 20 numbers are repeated in the second set.
THEREFORE, the solution is 110 numbers.
Answer: D
Answer: (D) 110
Question: A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?
(A) 9:8
(B) 15:8
(C) 27/8
(D) 8:9
(E) 8:15
Rationale: let x be side of square
perimeter of square=4x=perimeter of triangle=3*side of triangle
so side of eq. triangle=(4/3)*x
diameter of circle circumscribing the square=sqrt(2)*x
area of circle circumscribing the square= pi*(sqrt(2)*x)^2/4=(pi/2)*x^2 ----(1)
to find radius of the circle inscribed in the triangle
area of triangle=r*s=sqrt(3)/4 * (4x/3)^2
now s=(4/3)*x+(4/3)*x+(4/3)*x/2=2x
so sqrt(3)/4 * (4x/3)^2=r*2x gives
r={2/3*(3^1/2)}*x
area of the circle inscribed in the triangle=pi*[{2/3*(3^1/2)}*x]^2
=pi*(4/27)*x^2 -------(2)
so reqd ratio= eqn(1)/eqn(2)
=[(pi/2)*x^2]/[pi*(4/27)*x^2]=27/8
so reqd ratio=27:8
ANSWER:C
Answer: (C) 27/8
Question: If 600y is a perfect square (the square of an integer) and y is a positive integer, then which of the following must also be an integer?
I y/6
II y/42
III y/30
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: 600∗y=2^3∗3^1∗5^2∗y
For an integer to be a perfect square means that all its prime factors must have even powers.
Min value of yy required fo that is 2^1∗3^1
Answer A
Answer: (A) I only
Question: If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ?
(A) 1
(B) m
(C) n
(D) 0
(E) 2
Rationale: mth term of an A.P.
Am = a + (m-1)d
nth term of an A.P.
An = a + (n+1)d
[here a= First term of an A.P
d= difference between two consecutive terms
Am= mth term of A.P.]
According to the question;
m*Am = n*An
m(a + (m-1)d)= n(a + (n-1)d)
m(a + md - d)= n(a + nd - d)
am + m^2d-md = an + n^2d - nd
a(m-n)+ (m^2-n^2)d -(m-n)d = 0
a(m-n)+ (m-n)(m+n)d -(m-n)d= 0
(m-n)[a + (m+n)d - d ]= 0
[a + (m+n)d - d ]= 0
[a + (m+n-1)d ]= 0
So Am+n = 0
so answer will be 0
ANSWER:D
Answer: (D) 0
Question: A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 24 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
(A) 15
(B) 12
(C) 8
(D) 6
(E) 5
Rationale: A+P+G= 24*2
A=3G
P=2.5G
3G+2G+G= 24*2
G= 24*2/6= 8
A= 8*2=16
Difference = 16-8=8
'C' is the answer
Answer: (C) 8
Question: Kim finds a 5-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
(A) 8/15
(B) 1/2
(C) 7/5
(D) 3/5
(E) 7/5
Rationale: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be
2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15
Which gives us 2/5 + 1/15 + 2/15 -----> 3/5
Answer is D
Answer: (D) 3/5
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 228
(B) 277
(C) 350
(D) 882
(E) 121
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer:C
Answer: (C) 350
Question: If log a/b + log b/a = log (a + b), then:
(A) a = b
(B) a - b = 1
(C) a + b = 1
(D) 15
(E) 22
Rationale: Explanation:
log a/b + log b/a = log (a + b)
log (a + b)=log(b/a*a/b)= log 1
So, a + b = 1.
answer C
Answer: (C) a + b = 1
Question: At Tea factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?
(A) 8/17
(B) 1/2
(C) 8/9
(D) 9/8
(E) 17/8
Rationale: At Tea factory,Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A.
Answer: (A) 8/17
Question: The mean of 50 observations was 36. It was found later that an observation 58 was wrongly taken as 43. The corrected new mean is?
(A) 36.7
(B) 36.1
(C) 36.5
(D) 36.9
(E) 36.3
Rationale: Correct sum
= (36 * 50 + 58 - 43)
= 1815.
Correct mean = 1815/50
= 36.3
Answer:E
Answer: (E) 36.3
Question: In a class, the average age of 40 boys is 18 years and the average of 30 girls is 15 years. what is the average age of the whole class?
(A) 12 Years
(B) 12.3 Years
(C) 12.6 Years
(D) 16.7 Years
(E) 15 Years
Rationale: Total age of 70 students
(40X 18+30 X 15) = 1170
Average = 1170/70 = 16.7 Years
D
Answer: (D) 16.7 Years
Question: In a theater, the first row has 14 seats and each row has 2 more seats than previous row. If the last row has 56 seats, what is the total number of seats in the theater?
(A) 770
(B) 780
(C) 790
(D) 800
(E) 810
Rationale: The number of seats in the theater is
14 + (14+2) + ...+ (14+42)=
22(14) + 2(1+2+...+21)=
22(14) + 2(21)(22)/2=
22(14+21) = 22(35) = 770
The answer is A.
Answer: (A) 770
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 30
(B) 33 1/3
(C) 35
(D) 25
(E) 20
Rationale: 100---150
150----50
100-----? ==>33 1/3
ANSWER B
Answer: (B) 33 1/3
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
(A) 51
(B) 61
(C) 66
(D) 71
(E) 76
Rationale: 66 bikes.
Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.
factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.
Hence 66.
ANSWER:C
Answer: (C) 66
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 4?
(A) y = -1/2*x + 3
(B) y = 1/2*x - 4
(C) y = 1/2*x + 3
(D) y = 2x + 3
(E) y = 2x − 3
Rationale: Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)
y-intercept of line L is same as y intercept of line y = 2x − 4
y - intercept of line L = -4
Required line = 1/2* x - 4
Answer B
Answer: (B) y = 1/2*x - 4
Question: The average of first ten prime numbers which are odd is?
(A) 15.9
(B) 15.0
(C) 15.2
(D) 15.8
(E) 15.1
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Answer: (D) 15.8
Question: For positive integers s and t, which of the following can be written as t^2?
(A) s^2+9
(B) s^2+2
(C) s^2+3
(D) s^2-1
(E) s^2-9
Rationale: Plug values: if s=4, then 4^2+9=25
The question asks which of the following CAN be written as t^2. If s=4, then s^2+9 CAN be written as 5^2.
Answer: A
Answer: (A) s^2+9
Question: If x is a number such that x^2 + 3x - 10 = 0 and x^2 + x - 20 = 0, then x =
(A) 2
(B) 4
(C) -4
(D) 5
(E) -5
Rationale: x^2 + 3x - 10 = (x+5)(x-2) = 0
Then x=-5 or x=2.
x^2 + x - 20 = (x-4)(x+5) = 0
Then x=4 or x=-5.
Thus x=-5.
The answer is E.
Answer: (E) -5
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
(A) 4 3/9 km
(B) 4 7/8 km
(C) 4 3/8 km
(D) 8 3/8 km
(E) 4 3/2 km
Rationale: Explanation:
RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8
= 4 3/8 km
Answer:C
Answer: (C) 4 3/8 km
Question: Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6.30 a.m. and travels at 50 kmph towards Baroda situated 100 km away. At 7.00 a.m. Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7.30 a.m. Mr Shah, the traffic controller at Baroda realizes that both the trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?
(A) 15 min
(B) 20 min
(C) 25 min
(D) 30 min
(E) 35 min
Rationale: Explanation :
Let A be ahmedabad and B for baroda.
At 7:30 train from A to B would have covered 50km while train from B to A would have covered 20 km since it travels for only half an hour.
Distance remaining between the trains = 100-(50+20) i.e. 30km and the relative speed =90kmph. Therefore, time =30/90 hours = 20mins.
Answer : B
Answer: (B) 20 min
Question: A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 60%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (60 - 15)/(15 - 0) = 3/1
1/x = 3/1
x = 1/3
Answer: B
Answer: (B) 1/3