mathewhe/aqua_rat huggingface dataset:
Question: If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers?
(A) 2x + 2n^2
(B) 3x + 4n^2
(C) 4x + 2n
(D) 4x + n^2
(E) 4x + 2n^2
Rationale: n(n+1)/2 = x
or n^2 + n = 2x (1)
If the series has first 2n numbers, sum of n odd numbers = n^2.
So sum of n even numbers= Sum of first 2n numbers - n^2
In this case we have 2n even numbers so 2n odd numbers will be there, hence a total of 4n first numbers.
Sum of first 4n numbers = 4n(4n+1)/2 -----------(2)
Sum of first 2n odd numbers is (2n)^2 = 4n^2 ---------------- (3)
So sum of 2n even numbers is (2)-(3)
or 4n^2+2n
or 2n^2 + 2 (n^2+n)
or 2n^2 + 2(2x)
or 2n^2 + 4x
ANSWER:E
Answer: (E) 4x + 2n^2
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 7
(B) 8.2
(C) 2
(D) 10.8
(E) 11.2
Rationale: Answer: Option D
Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec
Answer: (D) 10.8
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) 6 Â½ days
(B) 1 Â½ days
(C) 8 Â½ days
(D) 5 Â½ days
(E) 2 Â½ days
Rationale: Explanation:
3/20 * 2 + (2 + x)/5 = 1
x = 1 Â½ days
Answer:B
Answer: (B) 1 Â½ days
Question: If x ≠ 0 and x - (2- x^2)/x = y/x, then y =
(A) − 2 − 3x^2
(B) x^2 − 2
(C) 2x^2 − 2
(D) x − 2 − x^2
(E) x − 2 + x^2
Rationale: We're told that x ≠ 0 and x - (2- x^2)/x = y/x. We're asked for the value of y.
IF.... X = 3
3 - (2 - 3^2)/3 = y/3
9/3 - (-7/3) = y/3
Multiply everything by 3....
9 - (-7) = y
16 = y
So we're looking for an answer that equals 16 when x = 3...
Answer A) − 2 − 3x^2 This will be NEGATIVE, so no need to calculate it.
Answer B) x^2 − 2 = 7. NOT a match.
Answer C) 2x^2 − 2 = 16. This IS a match.
Answer D) x − 2 − x^2 This will be NEGATIVE, so no need to calculate it.
Answer E) x − 2 + x^2 = 10. NOT a match.
Final Answer:C
Answer: (C) 2x^2 − 2
Question: If takes 25.5 minutes to download a file using Modem A. Modem B work at 17% of the speed of Modem A. How long does it take to download a file using a Modem B?
(A) 130 minutes
(B) 140 minutes
(C) 150 minutes
(D) 160 minutes
(E) 170 minutes
Rationale: Let Speed of modem A be k
So Speed of modem B is 17/100*k
Time taken by modem A = 25.5 minutes
Let time taken by modem B = x
k*25.5 = 17/100*k*x
0.17*x = 25.5
x = 25.5/0.17
= 150 minutes
ANSWER:C
Answer: (C) 150 minutes
Question: If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage?
(A) 50%
(B) 100%
(C) 45%
(D) 55%
(E) 65%
Rationale: Let the C.P of each book be Re 1. Then,
S.P of 5 books= C.P of 10 books= Rs. 10
Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10
Gain = Rs ( 10 -5 ) = Rs 5.
Gain% = ( 5/5× 100 ) % = 100%
Answer : B
Answer: (B) 100%
Question: Two trains of equal length, running with the speeds of 50 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 5.55 sec
(B) 4.55 sec
(C) 5.95 sec
(D) 6.55 sec
(E) 9.55 sec
Rationale: RS = 50 -40 = 10 * 5/18 = 50/18
T = 50
D = 50 * 50/18 = 1250/9
RS = 50 + 40 = 90 * 5/18=25
T = 1250/9 * 1/25 = 5.55 sec
ANSWER:A
Answer: (A) 5.55 sec
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is:
(A) 22
(B) 28
(C) 32
(D) 48
(E) 92
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 => x = 22.
answer is A.
Answer: (A) 22
Question: if b is a positive integer greater than 8, which of the following must be divisible by 4?
(A)  b(b-1)(b+2)(b+3)
(B)  b(b-1)(b+3)(b+4)
(C)  b(b-3)(b+2)(b+4)
(D)  b(b-3)(b+2)(b+3)
(E)  b(b+1)(b+3)(b+4)
Rationale: D.
For any integer b, D is the only answer choice which will always be divisible by 4.
A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice isb* [(b-1)OR(b+3)] * [(b-2)OR(b+2)] * [(b-3)OR(b+1)]. (answer D)
Answer: (D)  b(b-3)(b+2)(b+3)
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
(A) 44%
(B) 46%
(C) 48%
(D) 50%
(E) 51%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120 x m = 6 x m.
100 5
New breadth = 120 y m = 6 y m.
100 5
New Area = 6 x x 6 y m2 = 36 xy m2.
5 5 25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11 xy x 1 x 100 % = 44%.
25 xy
A
Answer: (A) 44%
Question: 3,9,27,81,....
(A) 583
(B) 604
(C) 616
(D) 243
(E) 636
Rationale: 1*3=3
3*3=9
9*3=27
27*3=81
81*3=243
ANSWER:D
Answer: (D) 243
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
(A) 21
(B) 27
(C) 26
(D) 80
(E) 28
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80.Answer: D
Answer: (D) 80
Question: A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than six people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
(A) x/15
(B) x/30
(C) x/6
(D) x/5
(E) 5x/6
Rationale: If 6 people share the rent, each person would pay x/6.
If 5 people share the rent, each person will pay x/5.
The extra amount each person pays is x/5 - x/6 = 6x/30 - 5x/30 = x/30
The answer is B.
Answer: (B) x/30
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an even number
II. P is a multiple of 6
III. P is a multiple of 24
(A) I only
(B) II only
(C) III only
(D) None of the above
(E) All of the above
Rationale: The correct answer is E.
Answer: (E) All of the above
Question: The price of 5 kilograms of premium fertilizer is the same as the price of 8 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?
(A) y/30
(B) 5/6*y
(C) 6/5*y
(D) 5y
(E) 8y/3
Rationale: Usingpfor premium andrfor regular, I got two equations from the question stem:
5p = 8r and p = r+y
Substitute for p: 5(r+y) = 8r
Distribute: 5r + 5y = 8r
Subtract 5r from both sides: 5y = 3r
Plug back into the first equation: 5p = 8(5y/3)
Distribute: 5p = 40y/3
Divide both sides by 5: p = 8y/3
The answer is E.
Answer: (E) 8y/3
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Q are in s(99)?
(A) Q=350
(B) Q=353
(C) Q=354
(D) Q=356
(E) 357
Rationale: Focus on the points where the number of digits Q in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353.B
Answer: (B) Q=353
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 20:15:16
(B) 20:15:68
(C) 20:15:12
(D) 20:15:11
(E) 20:15:19
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: (C) 20:15:12
Question: A pizzeria in Castroville creates its own special blend of shredded cheese at a cost of $696.05 per kilogram. The blend includes Mozzarella, at $504.35 per kilogram, and Romano cheese, at $887.75 per kilogram. If the employees have already shredded 19 kilograms of Mozzarella cheese, how many kilograms of Romano cheese will they need to shred now?
(A) 19kg
(B) 13kg
(C) 10kg
(D) 23kg
(E) 15kg
Rationale: 504.35(19)+887.75x	=696.05(19 + x)
Solve the equation.
504.35(19) + 887.75x = 696.05(19 + x)
9,582.65 + 887.75x = 13,224.95 + 696.05x
9,582.65 + 191.7x = 13,224.95
191.7x = 3,642.3
x = 19	.
Answer is A.
Answer: (A) 19kg
Question: A sum of money becomes triple itself in 16 years. In how many years will it become 5 times at the same rate?
(A) 32
(B) 15
(C) 27
(D) 30
(E) 35
Rationale: Let sum be Rs.100. After 16 years it become 300. With in 16 years it increased Rs.200 i.e. after 8
years it is doubled. So after 32 years interest become Rs.400. Total Rs.500 i.e. 5 times more than the
sum. So 32 years is the answer.
ANSWER:A
Answer: (A) 32
Question: How many positive integers less than 50 are multiples of 6 but NOT multiples of 8?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: The LCM of 6 and 8 is 24.
If x <50 and x is divisible by 6 not by 8 --> x is NOT divisible by 24.
From 1--> 50, we have 2 numbers which is divisible by 24: 24, 48.
From 1-->50, we have (48-6)/6 +1 =8 numbers divisible by 6.
Therefore, our answer is 8-2 = 6 numbers.
B
Answer: (B) 6
Question: Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 10 cm and 6 cm?
(A) 189 cm2
(B) 150 cm2
(C) 240 cm2
(D) 177 cm2
(E) 187 cm2
Rationale: 1/2 * 30(10 + 6)
= 240 cm2
Answer: C
Answer: (C) 240 cm2
Question: A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
(A) 31
(B) 41
(C) 51
(D) 61
(E) 71
Rationale: LCM = 30
=> 30 + 1 = 3
ANSWER:A
Answer: (A) 31
Question: Which of the following is the sum of all the even numbers between 1 and 93, inclusive?
(A) 2550
(B) 2450
(C) 2600
(D) 2447
(E) 2652
Rationale: This question can be solved withbunching.
We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 2, 4, 6, 8.....98.
If you take the next smallest and next biggest numbers, you have...
8+92 = 100
This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...
44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.
Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-3 = 2447
Final Answer:
D
Answer: (D) 2447
Question: A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
(A) 72
(B) 84
(C) 96
(D) 108
(E) 120
Rationale: Each side of the cube has 6 x 6 = 36 cubelets.
Only the interior cubelets are painted one colour.
On each side, 4 x 4 = 16 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*16 = 96
The answer is C.
Answer: (C) 96
Question: A man engaged a servant on the condition that he would pay him Rs.710 and a uniform after a year service. He served only for 8 months and got Rs.460 and a uniform. Find the price of the uniform?
(A) Rs.40
(B) Rs.30
(C) Rs.25
(D) Rs.20
(E) Rs.45
Rationale: 8/12 = 2/3 * 710 = 473.33
460.00
---------------
13.33
1/3 uniform 13.33
1 --------------- ? => Rs.40
ANSWER:A
Answer: (A) Rs.40
Question: Set R has a mean of 11 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
(A) {15, 13}
(B) {11, 14}
(C) {10, 12}
(D) {14, 19}
(E) {14, 11}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 11,the values (10,12) are closer than others.
Hence Answer : C
Answer: (C) {10, 12}
Question: There are 9 orators A, B, C, D, E, F, G,H and I. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
(A) 9! / 3!
(B) 8! / 6!
(C) 5! x 3!
(D) 8! / (5! x 3!)
(E) 8! / (5! x 4!)
Rationale: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 6 people have to be arranged in 6 places.
Thus, 9C3 x 6! = 9! / 3!
ANSWER:A
Answer: (A) 9! / 3!
Question: A circular rim A having a diameter of 24 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 30 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.
(A) 5x/4
(B) 4x/3
(C) 6x/5
(D) 8x/7
(E) 9x/8
Rationale: t = S1/V1 = S2/V2
or, 24/x = 30/y
or, y = 30x/24 = 5x/4 (Answer A)
Answer: (A) 5x/4
Question: What is the value of 1×1!+2×2!+3!×3!+............n×n!;where n! means n factorial or n(n−1)(n−2)...1
(A) n(n−1)(n−1)!
(B) n(n−1)(n−1)!
(C) n(n−1)(n−1)!
(D) (n+1)!−1!
(E) None of these
Rationale: Explanation :
1×1!=(2−1)×1!=2×1!−1×1!=2!−1!2×2!=(3−1)×2!=3×2!−2!=3!−2!3×3!=(4−1)×3!=4×3!−3!=4!−3!......n×n!=(n+1−1)×n!=(n+1)(n!)−n!=(n+1)!−n!Summing up all these terms, we get (n+1)! - 1!
Answer : D
Answer: (D) (n+1)!−1!
Question: Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms?
(A) 30 km per hour
(B) 32 km per hour
(C) 49 km per hour
(D) 54 km per hour
(E) 65 km per hour
Rationale: Given that the diesel consumption is at the rate
1400×[1000x+x]1400×[1000x+x]
Cost of diesel = Rs 35 per litre
Payment to the driver = Rs 125 per hour.
Also given that the SUV is driven at the speed of xx km per hour.
Total cost (c)(c)
=1400×[1000x+x]×800×35+125×800x=1400×[1000x+x]×800×35+125×800x
=70000x+70x+100000x=70000x+70x+100000x
Now differentiating both sides in the above equation with respect to xx.
dcdx=−170,000x2+70=0dcdx=−170,000x2+70=0
⇒ x=49 km per hour.
C
Answer: (C) 49 km per hour
Question: The ratio of two numbers is 3:4 and their sum is 21. The greater of the two numbers is?
(A) 12
(B) 14
(C) 16
(D) 17
(E) 19
Rationale: 3:4
Total parts = 7
= 7 parts --> 21 (7 Ã— 3 = 21)
= 1 part ---->3 (1 Ã— 3 = 4)
= The greater of the two number is = 4
= 4 parts ----> 12 (4 Ã— 3 = 12)
A
Answer: (A) 12
Question: A plane flies 880 km with the wind and 720 km against the wind in the same length of time. If the speed of the wind is 20 km/h, what is the speed of the plane in still air?
(A) 140 km/h
(B) 160 km/h
(C) 180 km/h
(D) 200 km/h
(E) 220 km/h
Rationale: The speed of the plane in still air = x km/h
The speed of the wind is 20 km/h
Speed with the wind = (x + 20) km/h
Speed against the wind = (x â€“ 20) km/h
Time = Distance/ Speed
880 / (x+20) = 720 / (x-20)
880(x-20) = 720(x+20)
88x - 1760 = 72x + 1440
16x = 3200
x = 200
Therefore, the speed of the plane in still air is 200 km/h.
The answer is D.
Answer: (D) 200 km/h
Question: Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 24 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?
(A) 12 km/hr
(B) 16 km/hr
(C) 20 km/hr
(D) 24 km/hr
(E) 28 km/hr
Rationale: Let the speed of the slower train be x m/s
Then, the speed of the faster train is 2x m/s
The relative speed is 3x m/s
(100 + 100)/24 = 3x
x = 25/9 m/s
So, the speed of the faster train is 50/9 = 50/9 * 18/5 = 20 km/hr
The answer is C.
Answer: (C) 20 km/hr
Question: We can rent a cabin for x dollars per day for the first 5 days and then y dollars for each additional day. How much will it cost to rent a cabin for z days, where z>5?
(A) 5x + zy
(B) 5y+(z-5)x
(C) xz + 5y
(D) 5x - z + y
(E) 5x+(z-5)y
Rationale: The first 5 days cost 5x.
The next (z-5) days cost (z-5)y.
The total cost is 5x+(z-5)y.
The answer is E.
Answer: (E) 5x+(z-5)y
Question: If 4a – 2b – 2c = 32 and √3a-√(2b+2c)=4, what is the value of a + b + c?
(A) 3
(B) 9
(C) 10
(D) 12
(E) 14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
D
Answer: (D) 12
Question: By selling a book for 290, 20% profit was earned. What is the cost price of the book?
(A) A)215
(B) B)241
(C) C)230
(D) D)235
(E) E)240
Rationale: SP = 120% of CP; :. CP = 290 × 100/120 = 241
Option 'B'
Answer: (B) B)241
Question: One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt.Then find the price of the shirt.
(A) 126
(B) 217
(C) 127
(D) 120
(E) 182
Rationale: 12 months == Rs 200 + shirt --(1)
9 months == Rs 120 + shirt --(2)
After subtracting equation (2) from (1) we get,(shirt is cancelled)
3 months = Rs 80
12 months = (80 × 12)/3= 320
Hence from equation (1) we get 320 = 200 + shirt
Therefore shirt = 120 Rs/-
Answer: D
Answer: (D) 120
Question: Three friends Ram, Rahul and Raj divide $1000 amongs them in such a way that if $1, $2 and $8 are removed from the sums that Ram, Rahul and Raj received respectively, then the share of the sums that they got will be in the ratio of 6 : 7 : 10. How much did Raj receive?
(A) $434
(B) $458
(C) $438
(D) $448
(E) $478
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 1 : y - 2 : z -8 is 6a : 7a : 10a
When $1, $2 and $8 are removed, we are removing a total of $11 from $1000.
Therefore, 6a + 7a + 10a = 1000 - 11 = 989
i.e., 23a = 989
or a = 43
We know that z - 8 = 10a = 10 * 43 = 430
Therefore, z = 430 + 8 = $438
The correct choice is (c)
Answer: (C) $438
Question: What is the smallest possible common multiple of three integers, all larger than 22?
(A) 27.
(B) 54.
(C) 846.
(D) 19,656.
(E) 23
Rationale: The Least common positive multiple would be for the immediate least number(s) after 22 i.e 22.
Since nowhere is it stated that the three integers must be different, the integers could be 22,22 and 22... leading to least possible positive common multiple to be 22. Answer E.
Answer: (E) 23
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years R in which the population would be doubled assuming there is no emigration or immigration is
(A) 20
(B) R=25
(C) R=30
(D) R=35
(E) 40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000= 1000(1+(2/100))^n
n=35 Answer is D.
Answer: (D) R=35
Question: If Jan 1, 2006 was a Friday, What was the day of the week Jan 1, 2010?
(A) Friday
(B) Thursday
(C) Tuesday
(D) Saturday
(E) Wednesday
Rationale: Explanation :
Given that Jan 1 2006 was a Friday
Number of odd days in the period 2006-2009
= 3 normal years + 1 leap year
= 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)
Hence Jan 1 2010 = (Friday + 5 odd days) = Wednesday.. Answer : Option E
Answer: (E) Wednesday
Question: A 6-liter solution is 35% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?
(A) 1.5
(B) 1.8
(C) 2.1
(D) 2.4
(E) 2.7
Rationale: Let x be the amount of pure alcohol required.
0.35(6) + x = 0.5(x+6)
0.5x = 3 - 2.1
x = 1.8 liters
The answer is B.
Answer: (B) 1.8
Question: At what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years?
(A) 9%
(B) 11%
(C) 8%
(D) 10%
(E) 20%
Rationale: If rate=r, then 10000[1+(r/100)]^2 =12100 ,(100+r)^2 /100^2 =121
r^2 +200r -2100=0
(r-10)(r+210)=0
r=10
ANSWER:D
Answer: (D) 10%
Question: A thief is spotted by a policeman from a distance of 160 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
(A) 350m
(B) 240m
(C) 440m
(D) 640m
(E) None of them
Rationale: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover
(160m/1000) x 1/2 hr = 2/25hr.
In 2/25 hr/s, the thief covers a distance of 8 x 2/25 km = 16/25 km = 640 m
Answer is D.
Answer: (D) 640m
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
(A) 110
(B) 120
(C) 128
(D) 134
(E) 154
Rationale: First Purchased = 250 Wes= 128
C
Answer: (C) 128
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 22
(B) 77
(C) 30
(D) 99
(E) 12
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: (C) 30
Question: ((1^5m)/(5^5m))((1^18)/(4^18)) = 1/(2(10)^35)
What is m?
(A) 7
(B) 18
(C) 34
(D) 35
(E) 36
Rationale: ((1^5m)/(5^5m))((1^18)/(4^18)) = 1/(2(10)^35)
((1/5)^5m ) * ((1/2)^36) = 1/ (2 * (2*5)^35))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^5m= (1/5)^35
((1/5)^5m ) * ((1/2)^36) = 1/[(2^36)*(5^35)]
So, m=7
Answer A
Answer: (A) 7
Question: Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
(A)  124%
(B)  120%
(C)  96%
(D)  80%
(E)  84%
Rationale: Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 84 (40 percent more than Tim's income).
Thus, Mary's income (84) is 84% of Juan's income (100).
Answer: E.
Answer: (E)  84%
Question: What strength of 20 ml alcohol should be added to 10ml of 50% alcohol to get an average strength of 20% alcohol.
(A) 0.5 %
(B) 5 %
(C) 50 %
(D) 5.5 %
(E) 0.05 %
Rationale: 20*x + 10*0.5 = (20 + 10)*0.2 --> x = 0.05 = 5%.
Answer: B.
Answer: (B) 5 %
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
(A) 2800
(B) 2700
(C) 2900
(D) 2200
(E) 2300
Rationale: B
Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
= (45/100 x 6000) = 2700.
Answer: (B) 2700
Question: How much is 80% of 45 is greater than 4/5 of 25?
(A) 15
(B) 57
(C) 16
(D) 16
(E) 73
Rationale: (80/100) * 45 â€“ (4/5) * 25
36 - 20 = 16
Answer: C
Answer: (C) 16
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.695 in all. Find the share of B?
(A) 130
(B) 120
(C) 218
(D) 144
(E) 145
Rationale: A+B+C = 695
A = 3B
3B+B+B-25 = 695
5B = 720
B = 144
Answer: D
Answer: (D) 144