mathewhe/aqua_rat huggingface dataset:
Question: 72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand?
(A) Rs. 3.23
(B) Rs. 5.11
(C) Rs. 5.51
(D) Rs. 7.22
(E) None
Rationale: Explanation :
The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7.
To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.
It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase .
Let us now roughly multiply the decimal values of the options also by 72,
e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36.
So, option (1) will yield (216 + 14) = 230 (approximately),
option(2) will yield (360 + 7) = 367 (approximately),
option(3) will yield (360 + 36) = 396 (approximately),
and option(4) will yield (504 + 14) = 528 (approximately).
Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96.
Answer : C
Answer: (C) Rs. 5.51
Question: what is the nearest no. to 2304 which is divisible by 21?
(A) 2289
(B) 2310
(C) 2333
(D) 2456
(E) 2309
Rationale: remainder when 2304 is divided by 21=15
so,no. should added to make 15 to 21=6
no.=2304+6=2310
answer B
Answer: (B) 2310
Question: A manufacturer of a certain type of screw rejects any screw whose length is less than 2.47 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?
(A) |k + 0.03| > 2.5
(B) |k — 0.03| <= 2.5
(C) |k — 2.5| > 0.03
(D) |k — 2.5| >= 0.06
(E) |k — 2.5| <= 0.03
Rationale: So, let's go through this step by step:
Any screw that is less than: 2.47 or greater than 2.53 will be rejected.
If k represents the length of a screw
In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:
2.47 ≤ K ≤ 2.53
You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.
Let's look at (E):
|k — 2.5| <= 0.03
For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53
For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47
2.47 ≤ k ≤ 2.53
(E)
Answer: (E) |k — 2.5| <= 0.03
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
(A) 22
(B) 77
(C) 40
(D) 26
(E) 18
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
Answer: C
Answer: (C) 40
Question: The least perfect square, which is divisible by each of 21, 36 and 66 is
(A) 213414
(B) 213424
(C) 213434
(D) 213444
(E) None of these
Rationale: Explanation:
L.C.M. of 21, 36, 66 = 2772
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444
Option D
Answer: (D) 213444
Question: What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area?
(A) 11 + √5
(B) 11 + √6
(C) 11 + 4√7
(D) 11 + √65
(E) 11 + 3√17
Rationale: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65
The perimeter is 11 + √65
The answer is D.
Answer: (D) 11 + √65
Question: A certain collage has total of 700 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
(A) 100
(B) 80
(C) 75
(D) 155
(E) 50
Rationale: Answer D
700 = 525 + 20 + x => x = 155
= 3/4 * 700 in 4 subjects + 20 min for 5th subject + x = 700
Answer: (D) 155
Question: If 20% of a = b, then b% of 20 is the same as:
(A) 4% of a
(B) 5% of a
(C) 6% of a
(D) 3% of a
(E) 2% of a
Rationale: Here, 20% of a=b i.e.,(20/100)a=b
then, b% 20 i.e.,(b/100)x20---I
then sub b=(20/100)a in I
we get,
=(20/100)a x (1/100) * 20
=(20/100)a x (20/100)
=(400/10000)a
=(4/100)a
= 4% of a
ANSWER :A
Answer: (A) 4% of a
Question: If (1+y)x=xwhich of the following must be true?
(A) x=-1 or y=0
(B) x=0 or y=-1
(C) x=1 or y=1
(D) x=-1 or y=-1
(E) y=0 or x=0
Rationale: We have (1+y)x=x
If x=0, y=y. True
If y=0, (1+x)*0=0 True
So, E will be the answer.
Answer: (E) y=0 or x=0
Question: If −2≤e≤0 and n > 19, which of the following CANNOT be the value of en?
(A) -48
(B) -38
(C) -20
(D) 0
(E) 19
Rationale: value of en not equal to -19=E -19....Rest all are achievable
Answer: (E) 19
Question: A 8% stock yielding 10% is quoted at :
(A) 80
(B) 110
(C) 112
(D) 120
(E) 160
Rationale: Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 8, money invested = Rs.(100/10X8) = Rs. 80.
âˆ´ Market value of Rs. 100 stock =Rs. 80
Answer A
Answer: (A) 80
Question: A women paid $1650 a year in interest on a loan with an annual rate of 11%. How w\much more money could she have borrowed for the same amount of interest if she had been able to get a loan amount with an annual rate of 10%?
(A) $165
(B) $1500
(C) $1815
(D) $ 15000
(E) $16500
Rationale: Let P = Principal amount
R1 = Interest Rate for case 1
R2 = Interest Rate for case 2
Time = T = 1year
Now Interest = (P * R1* T)/ 100
We have 1650 = (P*11*1)/100 => we get P = 15000$
now Case 2 : P = 15000 R2= 10% T= 1year
Interest Amount is $1650( Interest Amount Remains same)
Now on $15000 with 10% Interest Amount is $1500.
We get, Difference in Interest Amount's is $ 150
Solve for
150 = (P * 10 * 1)/100
P = $ 1500 . So the women can borrow $1500 more.
Answer: B
Answer: (B) $1500
Question: Train A left station T at 3:30 p.m. and traveled on straight tracks at a constant speed of 60 miles per hour. Train B left station T on adjacent straight tracks in the same direction that train A traveled on. Train B left station T 40 minutes after train A, and traveled at a constant speed of 75 miles per hour. Train B overtook train A on these straight tracks. At what time did train B overtake train A?
(A) 4:10
(B) 5:40
(C) 6:10
(D) 6:50
(E) 7:30
Rationale: Train A left 40 mins before Train B at a speed of 60 mph
So distance traveled by Train A in 40 mins= 40 miles
Let's say the total distance at the point of overtaking is x
So, the time taken for covering the remaining distance x-40 by Train A=x-40/60
Time taken for covering the distance x at 75 mph by Train B=x/75
Both Time should be equal which gives us,
x-40/60=x/75
x=160 mins=2 hr 40 mins
Time when train B overtake train A = 3:30+40 mins+ 2 hr 40 mins= 6:50
Correct Answer is D.
Answer: (D) 6:50
Question: An error 2% in excess is made while measuring the side of asquare. The % of error in the calculated area of the square is?
(A) 4.00%
(B) 4.04%
(C) 4.26%
(D) 4.56%
(E) 4.67%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: (B) 4.04%
Question: Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 38 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
(A) 2:5
(B) 5:16
(C) 3:5
(D) 4:7
(E) 14:5
Rationale: Answer = B) 5:16
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:32= 5:16
B
Answer: (B) 5:16
Question: What is the unit digit in (4137)754?
(A) 1
(B) 3
(C) 7
(D) 9
(E) 6
Rationale: Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
Option D
Answer: (D) 9
Question: If x and y are integers and x + y = 6, which of the following must be true?
(A) x and y are consecutive integers.
(B) If x < 0, then y > 0.
(C) If x > 0, then y < 0.
(D) Both x and y are even.
(E) Both x and y are less than 5.
Rationale: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option B is right could you explain
B
Answer: (B) If x < 0, then y > 0.
Question: The greatest possible length which can be used to measure exactly the length 6m, 3m 85cm, 12 m 95 cm is
(A) 2
(B) 7
(C) 5
(D) 8
(E) 9
Rationale: Explanation:
Required Length = H.C.F of 600 cm, 385 cm and 1295 c
= 5 cm.
Answer: C) 5 cm
Answer: (C) 5
Question: A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
(A) 1 ½ days
(B) 2 ½ days
(C) 3 ½ days
(D) 4 ½ days
(E) 5 ½ days
Rationale: A
1 ½ days
3/20 * 2 + (2 + x)/5 = 1
x = 1 ½ days
Answer: (A) 1 ½ days
Question: The probability of having a girl is identical to the probability of having a boy. In a family with four children, what is the probability that all the children are of the same gender?
(A) 1/8.
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/2
Rationale: There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2= 1/16
case 2 .all girls.
1/2*1/2*1/2*1/2=1/16
We will add the cases to get 1/8
Answer: (A) 1/8.
Question: The sum of two consecutive number is 67. Which is the larger number?
(A) 34
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=67
2x+1=67
2x=66
x=33
Therefore larger number is x+1=34
ANSWER:A
Answer: (A) 34
Question: A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
(A) 270 m
(B) 210 m
(C) 340 m
(D) 130 m
(E) 140 m
Rationale: Explanation:
Speed= 72 kmph = 72×10/36 = 20 m/s
Distance covered = 250+ x where x is the length of the train
Time = 26 s
(250+x)/26 = 20
250+x = 26×20 = 520 m
x = 520-250 = 270 m
Answer: Option A
Answer: (A) 270 m
Question: Simplify (3^y + 3^y + 3^y) (3^y + 3^y + 3^y)
(A)  4^4y * 3^3y
(B)  9^y+1
(C)  16^y + 9^y
(D)  12^y
(E)  4^y * 12^y
Rationale: B
(3^y + 3^y + 3^y) (3^y + 3^y + 3^y)
(3*3^y)(3*3^y)
9*9^y=9^(y+1)..
Answer: (B)  9^y+1
Question: A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.
(A) 40m3
(B) 42m3
(C) 44m3
(D) 46m3
(E) None of these
Rationale: Explanation:
Volume=πr2hVolume=(22/7∗1∗1∗14)m3=44m3
Option C
Answer: (C) 44m3
Question: D and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 144:25 and BC=13 cm, then find the length of DE.
(A) 12
(B) 13
(C) 14
(D) 11
(E) 15
Rationale: ABC and ADE are similar triangles.
So (side of ABC/side of ADE)^2=25/169
side of ABC/side of ADE = 5/13
So the length of DE = 5
Answer - C
Answer: (C) 14
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
(A) 20/67
(B) 20/63
(C) 20/68
(D) 20/28
(E) 20/27
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer:B
Answer: (B) 20/63
Question: Which of the following inequalities is always true for any non-negative real number 'x' and 'y'?
(A) √(x+y) <= √x + √y
(B) √(x-y) <= √x - √y
(C) √(x+y) = √x + √y
(D) √(x-y) >= √x - √y
(E) √(x+y) >= √x + √y
Rationale: Using the principle of subadditivity which we know applies with square roots, we know that evaluating the function for the sum of two elements will always produce something less than or equal to the sum of the function's values at each element. Therefore, the answer is A.
Answer: (A) √(x+y) <= √x + √y
Question: The number 83 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13
Rationale: 7^2+5^2+3^2=49+25+9 = 83
7+5+3 =15
Hence answer is C
Answer: (C) 15
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?
(A) 37
(B) 29
(C) 11
(D) 15
(E) 12
Rationale: Explanation:
i) Let the ages of the five members at present be a, b, c, d & e years.
And the age of the new member be f years.
ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)
iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years
So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)
==> a + b + c + d + e = 5x + 15
==> a + b + c + d = 5x + 15 - e ------ (3)
iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,
The new average is: (5x + 15 - e + f)/5
Equating this to the average age of x years, 3 yrs, ago as in (2) above,
(5x + 15 - e + f)/5 = x
==> (5x + 15 - e + f) = 5x
Solving e - f = 15 years.
Thus the difference of ages between replaced and new member = 15 years.
Answer: D
Answer: (D) 15
Question: Suppose you flip a fair coin 8 times. What is the probability that, in 8 flips, you get at least one head?
(A) 55/256
(B) 255/256
(C) 155/256
(D) 5/256
(E) 201/256
Rationale: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads
probability of flipping either a head or a tail = 1/2
probability of flipping 3 tails in a row (1/2)^5
probability of flipping at least 1 head = 1 - (1/2)^8 = 255/256
Answer : B
Answer: (B) 255/256
Question: If athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream
(A) 1kmph
(B) 2 kmph
(C) 1.5 kmph
(D) 12 kmph
(E) 15 kmph
Rationale: Speed upstream = 16/4 = 4 kmph
Speed down stream = 24/4 = 6 kmph
Speed of stream = ½ (6-4) = 1 kmph
ANSWER:A
Answer: (A) 1kmph
Question: The breath of a rectangular landscape is 6 times its length. There is a playground in it whose area is 4200 square mtr & which is 1/7 th of the total landscape. What is the breath of the landscape?
(A) 520
(B) 420
(C) 320
(D) 550
(E) 450
Rationale: Sol. 6x * x =7* 4200
x = 70
Length = 6* 70 = 420 B
Answer: (B) 420
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 12 years at the same rate?
(A) 2P
(B) 3P
(C) 4P
(D) 5P
(E) 7P
Rationale: P ---- 2P ---- 8 years
3 P ---- 12 years
ANSWER:B
Answer: (B) 3P
Question: A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?
(A) 50
(B) 8
(C) 60
(D) 42
(E) 32
Rationale: in the first case the lady takes up 32 red colour
then he takes up 24 y (cause he should take up pair)
then he takes up 1y+1blue
then 2blue(cause to make sure he has a pair of each color in hand)
32+24+2+2=60
ANSWER:C
Answer: (C) 60
Question: What is the greatest positive integer n such that 3^n is a factor of 36^300?
(A) 100
(B) 200
(C) 300
(D) 600
(E) 900
Rationale: 36 = 3^2 * 2^2.
36^300 = 3^600 * 2^600
The answer is D.
Answer: (D) 600
Question: If x and y are different prime numbers, each greater than 6, which of the following must be true? I. x+y is an even integer II. xy is an odd integer III. (x/y) is not an integer
(A) II only
(B) II,III only
(C) I,II and III
(D) III only
(E) I only
Rationale: Given: x and y are different prime numbers, both greater than 6
Statement I: x+y is an even integer
Since x and y are prime numbers greater than 6, they will be odd
Therefore sum will be even.
Correct
Statement II: xy is an odd integer
Since x and y are prime numbers greater than 6, they will be odd
Therefore multiplication will be odd.
Correct
Statement III: (x/y) is not an integer
Since x and y are prime integers, therefore they will not have any common factor apart from 1
Hence (x/y) will not be an integer
Correct
Hence all three statements I, II and III are correct
Answer : C
Answer: (C) I,II and III
Question: A sum of Rs. 2795 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?
(A) 1642
(B) 1640
(C) 1720
(D) 2795
(E) 6386
Rationale: (x*8*3)/100 = ((2795 - x)*3*5)/100
24x/100 = 41925/100 - 15x/100
39x = 41925 => x = 1075
Second sum = 2795 – 1075
=1720
Answer:C
Answer: (C) 1720
Question: A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.0 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(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 he has sold X. Therefore in 2007 he should have sold 97/100×X.
97/100×2100=2037
-->2,037,000 sold in 2007. When rounded to the nearest 10,000 :
2,030,000
C
Answer: (C) 2,030,000
Question: 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.4 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
(A) Four
(B) Six
(C) Nine
(D) Ten
(E) Twelve
Rationale: Mean = 8.1
Standard Deviation = 0.4
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.4 = 8.7
and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.4 = 7.5
all values are within the range hence, 12 values fall within 1.5 SD from Mean
Answer: Option E
Answer: (E) Twelve
Question: If x/y = 5/z, then 25z^2 =
(A) x²y²
(B) 25y²/ x²
(C) 625x²y²
(D) y²/ x²
(E) 625y²/ x²
Rationale: This question is most easily solved by isolating y in the equation and substituting into the expression 25z²:
x/y = 5/z
x = 5y/z
5y = xz
z = 5y/x.
If we substitute 5y/x into the expression for z, we get:
25(5y/x)² = 25(25y²/ x²) = 625y²/ x².
The correct answer is choice (E)
Answer: (E) 625y²/ x²
Question: Find the greatest four digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24.
(A) 9974
(B) 9125
(C) 9565
(D) 9997
(E) None of these
Rationale: Since the difference between the divisors and the respective remainders is not constant, back substitution is the convenient method. None of the given numbers is satisfying the condition.
ANSWER:E
Answer: (E) None of these
Question: If 50! × 50!/50^n is an integer, what is the largest possible value of n?
(A) 36
(B) 24
(C) 8
(D) 4
(E) 2
Rationale: 50! × 50!/50^n is an integer.
Or 50! × 50!/(5^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 50! = [50/5] + [50/25] = 12
Since there are 2 20!'s, power of 12 in the numerator = 2*12 = 24
Hence the largest value of b for which 50! × 50!/50^n is integer = 24
Correct Option : B
Answer: (B) 24
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
(A) 56.8 m2
(B) 82.9 m2
(C) 52.8 m2
(D) 17.9 m2
(E) 72.9 m2
Rationale: 42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer:C
Answer: (C) 52.8 m2
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3:7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) Rs. 15.50
(B) Rs. 16.90
(C) Rs. 13.50
(D) Rs. 16.50
(E) Rs. 16.40
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:D
Answer: (D) Rs. 16.50
Question: A car averages 75 mph for the first 4 hours of a trip and averages 60 mph for each additional hour. The average speed for the entire trip was 70 mph. How many hours long is the trip?
(A) 6
(B) 78
(C) 8
(D) 9
(E) 10
Rationale: Let the time for which car averages 60 mph = t
70*(t+4)= 75*4 + 60 t
=>10 t= 20
=> t = 2
Total duration of the trip = 4+2=6
Answer A
Answer: (A) 6
Question: Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
(A) 7
(B) 8
(C) 6
(D) 5
(E) 4
Rationale: Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total routes = 8
Answer: B
Answer: (B) 8
Question: In covering a distance of 42 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
(A) 5 kmph
(B) 6 kmph
(C) 6.25 kmph
(D) 7 kmph
(E) 7.8 kmph
Rationale: Let Abhay's speed be x km/hr.
Then,	42/X	-	42/2X	= 3
6x = 42
x = 7 km/hr. Answer: Option D
Answer: (D) 7 kmph
Question: On a map, 1 inch represents 28 miles. How many C inches would be necessary to represent a distance of 383.6 miles?
(A) 5.2
(B) 7.4
(C) 13.7
(D) 21.2
(E) 28.7
Rationale: C inches necessary to represent a distance of 383.6 miles = 383.6/28
= 13.7
Answer C
Answer: (C) 13.7
Question: Each side of a certain parallelogram has length 8. If the area of the parallelogram is 16. Which of the following is the measure of one of its angles?
(A) 14.5
(B) 45
(C) 60
(D) 90
(E) 120
Rationale: Ans is 30deg
area of a parallelogram = b*h
b*h=16
h=16/8=2
sin theta =opp/hyp = 2/8 = 1/4
theta = sin inv of 1/4 = 14.5 deg
A
Answer: (A) 14.5
Question: Half a number plus 5 is 11.What is the number?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Solution
Let x be the number. Always replace "is" with an equal sign
(1/2)x + 5 = 11
(1/2)x + 5 - 5 = 11 - 5
(1/2)x = 6
2 × (1/2)x = 6 × 2
x = 12
Answer C
Answer: (C) 12
Question: How many seconds will a 900 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 287
(B) 288
(C) 500
(D) 400
(E) 121
Rationale: Let length of tunnel is x meter
Distance = 900+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
900+x = (65/3) * 60
900+x = 20 * 65 = 1300
x = 1300 - 900 = 400 meters
Answer: D
Answer: (D) 400
Question: If 15 students in a class average 70% on an exam and 10 students average 95% on the same exam, what is the average in percent for all 25 students?
(A) 77%
(B) 78%
(C) 79%
(D) 80%
(E) 81%
Rationale: (15*70 + 10*95) / 25 = 80%
The answer is D.
Answer: (D) 80%
Question: The ages of 2 persons differ by 32 years. If 12 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.
(A) 30
(B) 48.5
(C) 50.4
(D) 62.6
(E) 47.9
Rationale: age of the younger person = x
age of the elder person = x+32
6(x-12) = x+32-12
x= 18.4
age of elder person = 18.4+32=50.4
Answer is C
Answer: (C) 50.4