mathewhe/aqua_rat huggingface dataset:
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 287 Sec
(B) 190 Sec
(C) 187 Sec
(D) 286 Sec
(E) 276 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T =190 Sec
Answer: B
Answer: (B) 190 Sec
Question: In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
(A) 7
(B) 6
(C) 8
(D) 4
(E) 3
Rationale: A
7
Seven students are not taking a language. Add 7 + 10 + 4 to get 21. Then subtract 21 from the total students: 28 - 21 = 7.
Answer: (A) 7
Question: In what time will a railway train 80 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 4 sec
(B) 7 sec
(C) 2 sec
(D) 6 sec
(E) 8 sec
Rationale: T = 80/36 * 18/5
= 8 sec
Answer:E
Answer: (E) 8 sec
Question: In a role-play game, the attacker rolls 4 (6 sided dice) in a sword fight. If the dice add up to a prime number, score that number of strikes at opponent. If a non-prime number shows on any of the 4 die, score 1 extra strike for each non-prime number die. For a turn, the attacker scores 12, which roll did the player get?
I. 4 3 3 1
II. 3 3 3 3
III. 2 3 3 2
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: There are only 3 possibilities to choose from, so
I. is possible (one non-prime) 4 + 3 + 3 + 1 = 11 + 1 = 12
II. is possible (no non-prime) 3 + 3 + 3 + 3 = 12
III. is possible (2 non-prime) 2 + 3 + 3 + 2 = 10 + 2 = 12
Answer: E
Answer: (E) I, II and III
Question: 70% of x is greater than 1/3rd of x by 110.what is x?
(A) 100
(B) 200
(C) 300
(D) 350
(E) 400
Rationale: 7x/10-x/3=110
11x/30=110
x=300
ANSWER:C
Answer: (C) 300
Question: Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time S, in hours, that machine B must operate?
(A) 4
(B) 4 2/3
(C) 5 1/3
(D) 6
(E) 6 1/4
Rationale: Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time S , in hours, that machine B must operate?
a) 4
b) 4 and 2/3
c) 5 and 1/3
d) 6
e) 6 and 1/4
To minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.
Answer: A.
Answer: (A) 4
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is
(A) 1/38
(B) 1/36
(C) 1/35
(D) 1/32
(E) 1/31
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer:B
Answer: (B) 1/36
Question: Find the sum of all 2 digit numbers divisible by 3.
(A) 1535
(B) 1425
(C) 1325
(D) 1225
(E) 1665
Rationale: All 2 digit numbers divisible by 3 are :
12, 51, 18, 21, ..., 99.
This is an A.P. with a = 12 and d = 3.
Let it contain n terms. Then,
12 + (n - 1) x 3 = 99 or n = 30.
Therefore, Required sum = 30/2 x (12+99) = 1665.
Answer is E.
Answer: (E) 1665
Question: 5, 10, 13, 26, 29, 58, 61, (....)
(A) 122
(B) 125
(C) 128
(D) 64
(E) 130
Rationale: Numbers are alternatively multiplied by 2 and increased by 3
5 × 2 = 10
10 + 3 = 13
13 × 2 = 26
26 + 3 = 29
29 × 2 = 58
58 + 3 = 61
61 × 2 = 122
Answer is A.
Answer: (A) 122
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 250
(B) 277
(C) 255
(D) 278
(E) 281
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Answer: (A) 250
Question: Diana is painting statues. She has 3/6 of a gallon of paint remaining. Each statue requires 1/6 gallon of paint. How many statues can she paint?
(A) 3
(B) 20
(C) 28
(D) 14
(E) 19
Rationale: number of statues=all the paint÷amount used per statue
=3/6 ÷ 1/6
=3/6*6/1
=3/1
=3
Answer is A.
Answer: (A) 3
Question: A train covers a distance of 12 km in 10 minutes. If it takes 7 seconds to pass a telegraph post, then the length of the train is
(A) 100m
(B) 120m
(C) 140m
(D) 160m
(E) 170cm
Rationale: Explanation:
Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.
Length of the train = (Speed x Time) = (20 x 7) m = 140 m
Answer: Option C
Answer: (C) 140m
Question: A woman spends 12% of her income in house rent, 25% of the rest on his children’s education, 20% of the rest miscellaneous causes and 10% in medical expenses. If she now posses Rs. 3659 then her income is?
(A) A)Rs.36999
(B) B)Rs.40099
(C) C)Rs.45009
(D) D)Rs.69299
(E) E)Rs.99899
Rationale: X * (88/100) * (75/100) * (80/100) * (80/100)= 3659
X * 0.88 * 0.75 * 0.8 * 0.1 = 3659
X = 3659/0.0528
X = 69299
ANSWER:D
Answer: (D) D)Rs.69299
Question: Find the circumference and area of radius 7 cm.
(A) 151 cm²
(B) 152 cm²
(C) 154 cm²
(D) 155 cm²
(E) 157 cm²
Rationale: Circumference of circle = 2πr
= 2 × 22/7 × 7
= 44 cm
Area of circle = πr²
= 22/7 × 7 × 7 cm²
= 154 cm² ANSWER : C
Answer: (C) 154 cm²
Question: When (6767 +67) is divided by 68, the remainder is?
(A) 58
(B) 59
(C) 62
(D) 66
(E) 67
Rationale: => (67^67 + 1) is divisible by (67 + 1)
=> (67^67 + 1) is divisible by 68
=> (67^67+1) ÷ 68 gives a remainder of 0
=> [(67^67+1) + 66] ÷ 68 gives a remainder of 66
=> (67^67 + 67) ÷ 68 gives a remainder of 66
Option D
Answer: (D) 66
Question: A survey was sent to 95 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
(A) 2%
(B) 5%
(C) 7%
(D) 28%
(E) 63%
Rationale: case 1: (7/95)=x/100
x=7%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-7)%=7%
Answer is C
Answer: (C) 7%
Question: Calculate how many men are needed to finish a specific task in 25 days if it will take 30 men to complete the same task in 50 days?
(A) 90
(B) 79
(C) 60
(D) 65
(E) 70
Rationale: men required to finish the work in 25 days = 30*50/25 = 60
Answer is C
Answer: (C) 60
Question: In how many ways 4 boys and 5 girls can be seated in a row so that they are alternate.
(A) 144
(B) 288
(C) 12
(D) 256
(E) 2880
Rationale: Solution: Let the Arrangement be,
G B G B G B G B G
4 boys can be seated in 4! Ways.
Girl can be seated in 3! Ways.
Required number of ways,
= 4!*5! = 2880.
Answer: Option E
Answer: (E) 2880
Question: Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
(A) 288
(B) 320
(C) 2,880
(D) 3,200
(E) 28,800
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 96 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. Creating a proportion we have:
100/96 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 96
x = 30 * 96 = 2,880
Correct answer is C.
Answer: (C) 2,880
Question: When a natural number N is successively divided by 3,4,5,6 the remainders are 7,8,9,10. What will be the sum of the remainders if the order of the division is reversed?
(A) 11
(B) 78
(C) 44
(D) 19
(E) 72
Rationale: 3 4 5 6
7 8 9 10
leave the top right- most number 8
start with bottom right-most number 5
10*5+9=59
59*4+8=244
244*3+7=739
this is the number required
Now, do the successive division in the reverse order
The sum of the remainders is 19
Hence, the correct option is D
Answer: (D) 19
Question: What least number must be subtracted from 12702 to get number exactly 99 ?
(A) 49
(B) 30
(C) 29
(D) 31
(E) 32
Rationale: Explanation:
Divide the given number by 99 and find the remainder. If you subtract the remainder from the given number then it is exactly divisible by 99.
99) 12702 (128
99
280
198
822
792
30
Required number is 30.
ANSWER IS B
Answer: (B) 30
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
(A) 4/12
(B) 4/15
(C) 4/10
(D) 4/13
(E) 4/11
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer:D
Answer: (D) 4/13
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 15 mangoes. Find the gain percent?
(A) 27%
(B) 25%
(C) 11%
(D) 85%
(E) 24%
Rationale: SP = CP + g
150 SP = 150 CP + 15 SP
135 SP = 150 CP
135 --- 15 CP
100 --- ? => 11%
Answer:C
Answer: (C) 11%
Question: A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(A) 2:0
(B) 2:2
(C) 2:3
(D) 2:7
(E) 2:4
Rationale: Let the principal be P and rate of interest be R%.
Required ratio = [(P * R * 6)/100] / [(P * R * 9)/100] = 6PR/9PR = 6/9 = 2:3
Answer: C
Answer: (C) 2:3
Question: The pressure someone experiences as he or she dives deeper and deeper in the ocean increases linearly. On the surface, the pressure is close to 15 pounds per square inch. 33 feet below the surface, the pressure is 30 pounds. If 25000 pounds per sq inch can crush your bones, what depth is extremely dangerous for humans?
(A) 55522 feet
(B) 45522 feet
(C) 35522 feet
(D) 25522 feet
(E) None
Rationale: Solution:
First, model the pressure ( p ) in terms of depth ( d ) with a linear equation.
We will find the equation p = md + b
Use (0, 15) and (33, 30) to find m
m = 30 - 15/33 - 0
m = 15/33
= 0.45
p = 0.45d + b
Use (0, 15) to find b
15 = 0.45 × 0 + b
15 = b
p = 0.45d + 15
25000 = 0.45d + 15
25000 - 15 = 0.45d + 15 - 15
24985 = 0.45d
d = 24985/0.45
= 55522 feet
Answer A
Answer: (A) 55522 feet
Question: Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1245
(B) 1345
(C) 1455
(D) 1577
(E) 1671
Rationale: Let the smaller number be x. Then larger number = (x + 1395).
x + 1395 = 6x + 15
5x = 1380
x = 276
Large number = 276+1395 = 1671
E
Answer: (E) 1671
Question: A began business with 12500 and is joined afterwards by B with 75000. When did B join, if the profits at the end of the year are divided equally?
(A) 8 months
(B) 9 months
(C) 10 months
(D) 7 months
(E) None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12500 : (12 – x) × 75000
or 12 : 6(12 – x)
Since profit is equally divided so
12 = 6(12 – x) or x = 10. Thus B joined after 10 months.
Answer C
Answer: (C) 10 months
Question: Mohit sold an article for $24000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 16000
(B) 20000
(C) 15000
(D) 18000
(E) 17000
Rationale: Let the CP be $x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = $1.08x = 20000 - 10/100(20000) = 20000 - 2000 = $21600
=> 1.08x = 21600
=> x = 20000
B
Answer: (B) 20000
Question: If a is a positive integer, and if the units digit of a^2 is 1 and the units digit of (a+1)^2 is 0, what is the units digit of (a+2)^2?
(A) 1.
(B) 3.
(C) 5.
(D) 7.
(E) 9.
Rationale: If the units digit of a^2 is 1, then the units digit of a is either 1 or 9.
If the units digit of (a+1)^2 is 0, then the units digit of a+1 is 0.
To satisfy both conditions, the units digit of a must be 9.
Then a+2 has the units digit of 1, thus the units digit of (a+2)^2 will be 1.
The answer is A.
Answer: (A) 1.
Question: A and B start walking towards each other at 7am at speed of 12kmph and 13kmph. They were initially 25km apart. At what time do they meet?
(A) 8pm
(B) 6am
(C) 7am
(D) 10am
(E) 8am
Rationale: Time of meeting = distance / relative speed = 25/13+12 = 25/25 = 1 hr after 7pm = 8am
Answer is E
Answer: (E) 8am
Question: The population of a city increases at the rate of 4% p.a. but there is an additional annual increase of 1% in the population due to some job seekers. The percentage increase in the population after 2 years is?
(A) 10
(B) 11
(C) 10.25
(D) 10.15
(E) 10.45
Rationale: 100
5 ---- I
5
0.25 --- II
-----------
10.25%
ANSWER:C
Answer: (C) 10.25
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles ?
(A) 2413 sq.m
(B) 1234 sq.m
(C) 4312 sq.m
(D) 2143 sq.m
(E) 3243 sq.m
Rationale: Explanation:
Let the radii of the smaller and the larger circles be 's' m and 'l' m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏ - ∏
= ∏{1762/∏∏ - 1322/∏∏}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
ANSWER IS C
Answer: (C) 4312 sq.m
Question: If a man can cover 8 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 108
(B) 180
(C) 107
(D) 168
(E) 122
Rationale: 8 m/s = 8 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 8 * 18/5 * 15/4 km = 108 km.
Answer: A
Answer: (A) 108
Question: A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?
(A) 1280
(B) 1250
(C) 1320
(D) 1340
(E) 1350
Rationale: Speed = 5 km/hr
Time = 15 minutes = 1/4 hour
Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km=5×(1/4)×1000 metre=1250 metre
Answer is B
Answer: (B) 1250
Question: Two pipes A and B can fill a tank in 15 min and 24 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
(A) 14 min 19 sec
(B) 14 min 42 sec
(C) 14 min 20 sec
(D) 16 min 48 sec
(E) 14 min 10 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/24
1/24 : 8/15 :: 1 ; x
x = 8/15 * 1 * 24 = 12 4/5 min = 12 min 48 sec.
The tank will be full in (4 min. + 12 min. 48 sec) = 16 min 48 sec.Answer: D
Answer: (D) 16 min 48 sec
Question: Rihanna brought home 150 pens but while packing them, she misplaced some of them. When her brother asked how many she had misplaced, she told him:
If you count in pairs, one will remain
If you count in a group of three, two will remain
If you count in a group of four, three will remain
If you count in a group of five, four will remain
If you count in a group of six, five will remain
If you count in a group of seven, nothing will remain.
How many pens do you think has she misplaced ?
(A) 121
(B) 119
(C) 79
(D) 101
(E) 135
Rationale: B
She has misplaced 119 pens in total.
Answer: (B) 119
Question: In how many ways 10 examination papers be arranged so that the best and the worst papers never come together?
(A) 4*6!
(B) 5*8!
(C) 7*5!
(D) 7*8!
(E) 8*9!
Rationale: Required number of ways = (10-2) *(10-1)! = 8*9!
Answer is E
Answer: (E) 8*9!
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
(A) 110.43
(B) 120.65
(C) 124.75
(D) 134.56
(E) 165.9
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: (C) 124.75
Question: A starts business with Rs. 35,000 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B’s contribution in the capital?
(A) 22378
(B) 279889
(C) 2788
(D) 9000
(E) 2882
Rationale: Explanation:
Ratio in which profit is to be divided = 2 : 3
Assume that B's contribution to the capital = b
⇒ 3500 × 12 : b × 7 = 2 : 3
⇒ 3500 × 12/7 b = 2/3
⇒ b = (3500 × 12 × 3)/(2 × 7) = 500 × 6 × 3 = 9000
Answer: D
Answer: (D) 9000
Question: Amar, Bhavan and Chetan divide an amount of Rs. 5600 among themselves in the ratio 3 : 6 : 5. If an amount of Rs. 400 is deducted from each of their shares, what will be the new ratio of their shares of the amount?
(A) 2 : 5 : 6
(B) 2 : 5 : 5
(C) 2 : 5 : 4
(D) 2 : 5 : 9
(E) 2 : 5 : 1
Rationale: Let the shares of Amar, Bhavan and Chetan be Rs. 3x, Rs. 6x and Rs. 5x respectively.
3x + 6x + 5x = 5600 => 14x = 5600 => x = 400.
Required ratio = 3x - 400 : 6x - 400 : 5x - 400
= 3x - x : 6x - x : 5x - x
= 2x : 5x : 4x => 2 : 5 : 4
Answer: C
Answer: (C) 2 : 5 : 4
Question: By selling an article at Rs.400, a profit of 60% is made. Find its cost price?
(A) 228
(B) 267
(C) 287
(D) 250
(E) 811
Rationale: SP = 400
CP = (SP)*[100/(100+P)]
= 400 * [100/(100+60)]
= 400 * [100/160] = Rs.250
Answer: D
Answer: (D) 250
Question: If 4^k + 4^k = (4^9)^(4^9) - 4^k, then k = ?
(A)  11/3
(B)  4^11 - 1
(C)  242
(D)  3^10
(E)  3^11 - 1
Rationale: 4^k + 4^k = (4^9)^4^9 -4^k
4*(4^k) = 4^ (16 * 4^9 ) = 4^(4^2 * 4^9) = 4(4^11)
4^k+1 = 4^(4^11)
So k+1 = 4^11
So k = 4^11 -1
Answer is B
Answer: (B)  4^11 - 1
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 20, 35, 45
(D) 33,42,43
(E) None of these
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
ANSWER:B
Answer: (B) 16, 28, 36
Question: What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?
(A) 264
(B) 259
(C) 269
(D) 270
(E) 282
Rationale: LCM(8,11,24)=24x11=264
So the least divisible number is 264, and the number we are looking for is 259.
Answer is B
Answer: (B) 259
Question: If the cost price of 19 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
(A) 18.75% loss
(B) 18.75% profit
(C) 33.33 % loss
(D) 30.33% loss
(E) None of these
Rationale: Explanation :
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 19 articles = Rs. 19.
Selling price of 16 articles = Rs. 19
Therefore, Selling price of 19 articles is :-
=>19/16Ã—19
=>22.56.
Therefore, Profit = Selling price - Cost price.
=>22.56âˆ’19=3.56.
Hence, the percentage of profit = profit x 100/C.P.
=>3.56/19Ã—100.
=>18.75% Profit.
Answer : B
Answer: (B) 18.75% profit
Question: When 242 is divided by a certain divisor the remainder obtained is 4. When 698 is divided by the same divisor the remainder obtained is 8. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 7. What is the value of the divisor?
(A) 5
(B) 17
(C) 13
(D) 23
(E) None of these
Rationale: let that divisor be x
since remainder is 4 or 8 it means divisor is greater than 8.
now 242-4=238 =kx (k is an integer and 234 is divisble by x)
similarly 698-8=690 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (238+690)+4+8
=x(k+l) + 12
when we divide this number by x then remainder will be equal to remainder of (12 divided by x) = 7 hence x = 12-7 = 5
hence A
Answer: (A) 5
Question: Two boys starts from the same place walking at the rate of 5.3 kmph and 5.6 kmph respectively in the same direction. What time will they take to be 10.5 km apart?
(A) 32
(B) 36
(C) 39
(D) 38
(E) 35
Rationale: Explanation:
Relative speed = 5.6 - 5.3 = 0.3 kmph (because they walk in the same direction)
distance = 10.5 km
time = distance / speed=10.5/0.3=35 hr
Answer :E
Answer: (E) 35
Question: In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained 35 as quotient.What is the correct quotient ?
(A) 13
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Number =(12*35)=270.
correct quotient =420/21=20.
Answer is D
Answer: (D) 20
Question: 01-Jan-2007 was Monday. What day of the week lies on 01-Jan-2008?
(A) Wednesday
(B) Sunday
(C) Friday
(D) Tuesday
(E) saturday
Rationale: Given that January 1, 2007 was Monday.
Odd days in 2007 = 1 (we have taken the complete year 2007 because we need to find out the odd days from 01-Jan-2007 to 31-Dec-2007, that is the whole year 2007)
Hence January 1, 2008 = (Monday + 1 Odd day) = Tuesday
Answer: Option D
Answer: (D) Tuesday
Question: In a class of students, 2/3 of the number of girls is equal to 1/4 of the total number of students. What is the ratio of boys to girls in the class?
(A) 1/3
(B) 2/3
(C) 4/3
(D) 5/3
(E) 7/3
Rationale: (2/3)G=(1/4)(B+G)
8G=3B+3G
5G=3B
B/G=5/3.
The answer is D.
Answer: (D) 5/3
Question: The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that y > 0 and y > x?
(A) 1/8
(B) 1/6
(C) 3/8
(D) 1/2
(E) 3/4
Rationale: The line y=x divides the circle into two equal areas.
All the points above the line y=x satisfy the condition that y > x.
All the points above the x-axis satisfy the condition that y > 0.
The intersection of these two areas is 3/8 of the circle.
The answer is C.
Answer: (C) 3/8
Question: The side of a square is increased by 20% then how much % does its area increases?
(A) 52.65
(B) 56.25
(C) 44
(D) 42.75
(E) 52.75
Rationale: a = 100 a2 = 10000
a = 120 a2 = 14400
----------------
10000 --------- 4400
100 -------? => 44 %
ANSWER: C
Answer: (C) 44
Question: A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
(A) 6
(B) 5
(C) 5.5
(D) 7
(E) 8
Rationale: B's 10 day's work = ( 1 x 10 ) = 2 .
15 3
Remaining work = ( 1 - 2 ) = 1 .
3 3
Now, 1 work is done by A in 1 day.
18
Therefore 1 work is done by A in ( 18 x 1 ) = 6 days.
Answer: (A) 6
Question: The price of 2 sarees and 4 shirts is 16000. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall one have to pay?
(A) 2,400
(B) 4,800
(C) 1,200
(D) Cannot be determined
(E) None of these
Rationale: Let the price of one saree and one shirt be x and y respectively.
Then, 2x + 4y = 1600
or, x + 2y = 800 ... (i)
Also, x + 6y = 1600 ... (ii)
Solving equations (i) and (ii), we get
4y = 800 or,y = 200
∴ cost of 12 shirts = 12 × 200 = 2400
Answer A
Answer: (A) 2,400
Question: Sara bought both German chocolate and Swiss chocolate for some cakes she was baking. The Swiss chocolate cost $2.5 per pound, and German chocolate cost $1.5 per pound. if the total the she spent on chocolate was $15 and both types of chocolate were purchased in whole number of pounds, how many total pounds of chocolate she purchased?
(A) 9
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: If there were all the expensive ones 2.5....
There would be 15/2.5 or 6 of them but since 1.5$ ones are also there, answer has to be >6....
If all were 1.5$ ones, there will be 15/1.5 or 10...
So ONLY 8 is left
Ans B..
Answer: (B) 8
Question: In an electric circuit, two resistors with resistances 8 ohms and 9 ohms are connected in parallel. In this case, if R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of two resistors. What is R value ?
(A) 17
(B) 45/78
(C) 72/17
(D) 17/72
(E) 72
Rationale: The wording is a bit confusing, though basically we are told that 1/R = 1/8 + 1/9, from which it follows that R=72/17.
Answer: C.
Answer: (C) 72/17
Question: The sum of first n odd numbers (i.e., 1 + 3 + 5 + 7 + ...+ 2n – 1) is divisible by 11111 then the value of n is
(A) 12345
(B) 11111
(C) can't be determined
(D) None of these
(E) 22222
Rationale: Solution
Go through option Sn = 1 + 3 + 5 + 7 +...+ 22221
S11111 = (11111)2
Hence it is divisible by 11111.
Thus Answer B
Answer: (B) 11111