mathewhe/aqua_rat huggingface dataset:
Question: Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4,3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (4,3). What would be the exact root of the original quadratic equation ?
(A) (6, 1)
(B) (-3,-4)
(C) ( 4, 3)
(D) (-4, -3)
(E) None of these
Rationale: Explanation :
Equation of quadratic equation is
ax2 + bx + c = 0 .
x2 + bx + c = 0 . First roots = (4, 3)
Sum of the roots -b / a = -7 .
=> b = 7.
Product of the roots = c / a = 12.
=> c =12.
∴ Equation formed x2 – 7b + 12 = 0 ............ (i)
Another boy gets the wrong roots (2, 3).
∴ Sum of the roots = -b / a = -5.
=> b = 5.
Products of the roots = c / a = 6.
=> c = 6.
Equation formed x2 – 5b + 6 = 0 ............ (ii)
x2 + b′x + c1 = 0.
b′ = 2 + 3 .
∴ c = 6
Hence, x2 – 7x + 6 = 0.
=> x2 – 6x – x + 6 = 0.
=> x(x – 6) – 1(x – 6) = 0.
=> (x – 6)(x – 1) = 0.
∴ x = 6, 1.
Hence, the actual roots = (6, 1).
Answer : A
Answer: (A) (6, 1)
Question: The G.C.D. of 1.08, 0.36 and 0.4 is:
(A) 0.04
(B) 0.9
(C) 0.18
(D) 0.108
(E) 0.118
Rationale: Given numbers are 1.08, 0.36 and 0.40. H.C.F. of 108, 36 and 40 is 18,
H.C.F. of given numbers = 0.04.
Answer: Option A
Answer: (A) 0.04
Question: A parking space have 9 different slots. 9 cars has to arrange in 8 slots. But there are exactly 4 cars between 5 specified cars. In how many ways cars can be arranged?
(A) 1210
(B) 650
(C) 1500
(D) 1640
(E) 2880
Rationale: we arranged 4 specified cars in 4 slots = 4!
remaining 5 cars in 5 slots = 5!
number of ways = 4!*5! = 1440
correct option is E
Answer: (E) 2880
Question: Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?
(A) 26 × 3 × 10 × 4
(B) 26 × 25 × 24 × 10 × 9 × 8 × 7
(C) 26³ × 9 × 9 × 9 × 9
(D) 26 × 25 × 24 × 10 000
(E) 26³ × 10 000
Rationale: Solution:
3 repeated letters can be chosen as 26 * 26 * 26
4 repeated digits can be chosen as 10 * 10 * 10 * 10
Answer E
Answer: (E) 26³ × 10 000
Question: There are some fruits in box, 1/3rd eaten by children . Then 2/5th of the remaining by men , then 2/3rd of the remaining by women . At last 4 were remaining . How many fruits were in total ?
(A) 45
(B) 30
(C) 28
(D) 26
(E) 91
Rationale: Sol:
If x fruits were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 4
x×2/3 × 3/5 × 1/3 = 30
x = 30
Answer:B
Answer: (B) 30
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 3 students is 14 years and that of the other 11 students is 16 years. The age of the 15th student is
(A) 9 years
(B) 11 years
(C) 14 years
(D) 7 years
(E) 25 years
Rationale: Solution
Age of the 15th student	=[15x15-(14x3+16x11)]
= (225 - 218)
= 7 years.
Answer D
Answer: (D) 7 years
Question: A company, Chauncy Co., has an annual travel budget of $51,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
(A) Expenses will not go over the budget.
(B) $500
(C) $4,225
(D) $9,725
(E) $60,725
Rationale: annual travel budget of $51,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 51000-60725 = 9725
Answer: Option D
Answer: (D) $9,725
Question: On a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 140 points, how many points did Bill receive?
(A) 30
(B) 40
(C) 50
(D) 80
(E) 100
Rationale: consider john's points as x
so bill's points are x +20
So sue's points are 2x +40
total of all three students is 4x +60, but this total is given as 140
x = 20
so bill's points = 20 +20 = 40
correct answer option B
Answer: (B) 40
Question: A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls, making the ratio of white balls to yellow balls 6:5. How many tennis balls did the store originally order?
(A) 120
(B) 150
(C) 180
(D) 300
(E) 330
Rationale: (X+30)/(X)= 6/5
Cross multiply: 5X + 150 = 6X
X = 150
And since we originally ordered 2X balls the answer is 300.D
Answer: (D) 300
Question: Can you find a seven digit number which describes itself.
The first digit is the number of zeros in the number.
The second digit is the number of ones in the number, etc.
For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.
(A) 4211000
(B) 1211000
(C) 5211000
(D) 2211000
(E) 3211000
Rationale: E
3211000
Answer: (E) 3211000
Question: A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
(A) 400 m
(B) 450 m
(C) 560 m
(D) 600 m
(E) 700 m
Rationale: Explanation:
Let the length of the first train be x metres.
Then, the length of the second train is(x/2)metres.
Relative speed = (48 + 42) kmph =(90x5/18)m/sec = 25 m/sec.
[x + (x/2)]/25	= 12 or	3x/2	= 300 or x = 200.
Length of first train = 200 m.
Let the length of platform be y metres.
Speed of the first train =(48 x5/18)m/sec =	40	/3m/sec.
(200 + y) x	3/40=45
600 + 3y = 1800
y = 400 m.
ANSWER IS A
Answer: (A) 400 m
Question: The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, The average of
remaining numbers is?
(A) 35.5
(B) 37.5
(C) 39.5
(D) 34.5
(E) 38.5
Rationale: Total of 50 numbers = 50 * 38 = 1900
Average of 48 numbers = 1900-(45+55) / 48
= 1800 / 48 = 37.5
Answer is B.
Answer: (B) 37.5
Question: If n is a positive integer, which of the following expressions must be even?
(A) (n − 5)( n + 3)
(B) (n − 6)( n + 3)
(C) (n − 6)( n + 8)
(D) (n − 7)( n + 5)
(E) (n − 9)( n + 11)
Rationale: Whether n is even or odd, (n-6)(n+3) will have one odd factor and one even factor.
The product will be even.
The answer is B.
Answer: (B) (n − 6)( n + 3)
Question: Set A of 8 positive integers may have the same element and have 35. And set B of 8 positive integers must have different elements and have 35. When m and n are the greatest possible differences between 35 and other elements’ sums in set A and set B, respectively, m-n=?
(A) 20
(B) 26
(C) 23
(D) 25
(E) 21
Rationale: This is maximum-minimum. Hence, 35-(1+1+1+1+1+1+1)=28 and 35-(1+2+3+4+5+6+7)=7. So, 28-7=21. The correct answer is E.
Answer: (E) 21
Question: average weight of 20 boys and 15 girls in a class is 29 kg and 22 kg respectively.find the average weight of all the students in the class.
(A) 20 kg
(B) 26 kg
(C) 22 kg
(D) 24 kg
(E) 28 kg
Rationale: totl wght of boy's=20*29=580
simrlly girls=15*22
totl ave=(totlboywght+tolgirlwght)/tole no of boys and gils
26 kg
ANSWER:B
Answer: (B) 26 kg
Question: A car travels a distance of 160 miles in 2 hours and 40 minutes, what is the speed of the car in miles per hour?
(A) 54
(B) 60
(C) 84
(D) 116
(E) 120
Rationale: Given time = 2 hours 40 mins
40 mins can be written as 40/60 hours = 2/3 hrs
total time = 2 + (2/3) = 8/3 hrs
therefore, speed = 160 /(8/30) = 60
option B
Answer: (B) 60
Question: In a certain alphabet, 9 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
(A) 7
(B) 8
(C) 14
(D) 20
(E) 28
Rationale: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 9 +24 = 33;
Next, we find the total # of letters without line: 40 - 33 = 7;
Finally, we find the # of letters that contain a dot but do not contain a straight line: 7- 0 = 7.
A
Answer: (A) 7
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?
(A) 87
(B) 98
(C) 30
(D) 29
(E) 37
Rationale: 20 + 22 + 8 * 2
= 58/2
= 29
Answer:D
Answer: (D) 29
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?
(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) 1 hour and 36 minutes.
Question: How many three digit no's are between 100-500,where sum of two digit is 3rd?
(A) 24
(B) 54
(C) 60
(D) 84
(E) 94
Rationale: TOTAL PERMUTATIONS POSSIBLE = 18+16+14+12 = 60
ANSWER:C
Answer: (C) 60
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?
(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) 6.86%
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
(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) II only
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?
(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) 3.28
Question: How many factors of 990 are odd numbers greater than 1?
(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) 3
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?
(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) 14 cm
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?
(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) 15
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?
(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) 1 hour and 20 minutes
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?
(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) 108
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?
(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) 1:80
Question: 5/25= 10/50. which method did you use to determine whether this proportion is true or false?
(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) true
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
(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) 50
Question: The sum and the product of two numbers are 12 and 20 respectively, the difference of the number is?
(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) 8
Question: Find the odd man out
1, 2, 5, 14, 41, 125
(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) 125
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:
(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) s. 708
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:
(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) 1:2
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?
(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) 2/5
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 ?
(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) 250
Question: Evaluate 28% of 450 + 45% of 280
(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) 252
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?
(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) b) $7.20
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?
(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) 63
Question: Which of the following is equal to the average (arithmetic mean) of (x+2)^2 and (x-4)^2?
(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) x^2-2x+10
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?
(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) 17
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?
(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) 2,040,000
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
(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) Rs. 3900
Question: Four unbiased coin are tossed. What is the probability of getting atmost
one head?
(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) 15/16
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?
(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) 6
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.
(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) 576
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?
(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) -1/3
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?
(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) 1
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?
(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) 1: 96
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?
(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) 456,976,000
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?
(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) 20
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?
(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) A)1
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
(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) 130 to 150
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?
(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) 1.