mathewhe/aqua_rat huggingface dataset:
Question: How many integers are between 5 and 74/5, inclusive?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 10
Rationale: 74/5 = 14.xx
We are not concerned about the exact value of 74/5 as we just need the integers.
The different integers between 5 and 74/5 would be 5, 6, 7, 8, 9, 10, 11, 12,13,14.
Total number of integers = 10
Option E
Answer: (E) 10
Question: A diner is having lunch at a salad bar. There are three types of lettuce to choose from, as well as four types of tomatoes, and five types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: 3*4*5 = 60
The answer is E.
Answer: (E) 60
Question: There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(56)-A(55)?
(A) 2^22+1
(B) 2^23
(C) 2^23+1
(D) 2^55
(E) 2^23+1
Rationale: A1= 3
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A56-A55= 2^55
D is the answer
Answer: (D) 2^55
Question: What is 3/7 of 7/8 of 1/3?
(A) 1/4
(B) 3/8
(C) 9/16
(D) 1/8
(E) 16/9
Rationale: 3/7 * 7/8 * 1/3= 1/8
Answer: D
Answer: (D) 1/8
Question: The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 34 on the fourth day, his average earning for the whole week is ?
(A) Rs . 15.95
(B) Rs 16
(C) Rs. 18
(D) Rs. 25.71
(E) None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -34
= Rs. 126
âˆ´ Average earning = 126 / 7
= Rs. 18
Correct Option: C
Answer: (C) Rs. 18
Question: UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 4:6. If 40% of the Toyota bought and 60% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
(A) 66%
(B) 64%
(C) 68%
(D) 52%
(E) 72%
Rationale: let total no of Vehicles bought be 100, Toyota 40 and Honda 60, so total number of SUV's bought for Toyota and Honda respectively 40* 40/100=16 and 60* 60/100=36
so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52%
ANSWER:D
Answer: (D) 52%
Question: If R is between (4) and (-4), which of the following can be greatest?
(A) (7/(R+1))
(B) R^2
(C) R^3
(D) R^4
(E) 100^7
Rationale: 7/(R+1) - can be as large as possible.
for eg. if R = -1.000001 => 7/(R+1) = 7000000
Ans A
Answer: (A) (7/(R+1))
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 110 mph. On the way home, I flew 88 mph. What was my average speed for the trip?
(A) 198 mph
(B) 110 mph
(C) 88 mph
(D) 100 mph
(E) 99 mph
Rationale: (110 mph +88 mph)/2= 99 mph
Correct answer is: E
Answer: (E) 99 mph
Question: Bradley owns b video game cartridges. If Bradley’s total is one-fourth the total owned by James and three times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) (16/3)b
(B) (17/4)b
(C) (13/4)b
(D) (19/12)b
(E) (16/3)b
Rationale: b = Bradley’s total
4b = James’s total
(1/3)b = Charlie’s total
Add each total
b + 4b+ (1/3)b = 5b + (1/3)b = = (16/3)b
Answer : E
Answer: (E) (16/3)b
Question: In a school class of 30 youngsters , the average weight of male is 20 kg and the average weight of the female is 25 kg . The fraction of male out of the total youngsters of the class is
(A) data insufficient
(B) 1/2
(C) 3/5
(D) 6/5
(E) 7/5
Rationale: the number of male = B and number of female = G.
=>B + G = 30
total weight of male = W1 and total weight of female = W2
average weight of male = total weight of male/number of male
total weight of male/number of male= 20
W1/B = 20
W1 = 20B
average weight of female = total weight of female/number of female
25 = W2/G
W2 = 25G
Data is not sufficient to solve the equation
ANSWER A
Answer: (A) data insufficient
Question: A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?
(A) 150 m
(B) 350 m
(C) 420 m
(D) 600 m
(E) 700 m
Rationale: Explanation:
Length of the train = distance covered in crossing the post = speed × time = speed × 18
Speed of the train = 300/18 m/s = 50/3 m/s
Time taken to cross the platform = 39 s
(300+x)/(50/3) = 39 s where x is the length of the platform
300+x = (39 × 50) / 3 = 650 meter
x = 650-300 = 350 meter
Answer: Option B
Answer: (B) 350 m
Question: If (2x + 1) times (3x + 1) is an odd integer, then x must be:
(A) an odd integer
(B) an even integer
(C) a prime number
(D) a composite number
(E) a negative integer
Rationale: Solution:
(2x + 1) times (3x + 1) means (2x + 1)(3x + 1)
(2x + 1)(3x + 1) = 6x^2+5x+1
For 6x^2+5x+1 to be odd, 5x+1 must be odd since 6x^2 is always even.
So 5x must be even, hence x must be even.
Therefore x is an even integer.
Answer: B
Answer: (B) an even integer
Question: The probability of pulling a black ball out of a glass jar is 1/C. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
(A) 1/(XY)
(B) C/Y
(C) Y/X
(D) 1/(X+Y)
(E) 1/(X-Y)
Rationale: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y
P of pulling a black ball out of a glass jar is 1/C
Lets say P of breaking the jar = n
That means 1/C*n=1/Y
n= C/Y
B is the answer
Answer: (B) C/Y
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 2 women and 10 children take to complete the work?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 10
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(2 women + 10 children)'s 1 day work
= (2/70 + 10/140) = 1/10
2 women and 10 children will complete the work in 10 days.
E
Answer: (E) 10
Question: A work can be finished in 16 days by 5 women. The same work can be finished in 8 days by sixteen men. The ratio between the capacity of a man and a woman is
(A) 1:3
(B) 4:3
(C) 2:3
(D) 2:1
(E) 5:8
Rationale: Work done by 5 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×5)
Work done by 16 men in 1 day = 1/8
Work done by 1 man in 1 day = 1/(8×16)
Ratio of the capacity of a man and woman =1/(8×16) : 1/(16×5) = 1/8 : 1/5
= 1/8 :1/5 = 5:8
Option E
Answer: (E) 5:8
Question: Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 38400, how much amount per month would he have spent on clothes and transport?
(A) 4038
(B) 8076
(C) 3200
(D) 4845.6
(E) None of these
Rationale: ∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
∵ Amount, spent on clothes and transport
= 38400⁄12 = 3200
Answer C
Answer: (C) 3200
Question: The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 130 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 170, 10 kmph
(B) 35, 27 kmph
(C) 50, 60 kmph
(D) 115, 15 kmph
(E) 45, 65 kmph
Rationale: Speed of the boat in still water = (100+130)/2 = 115 kmph. Speed of the stream = (100-130)/2 = 15 kmph
ANSWER:D
Answer: (D) 115, 15 kmph
Question: A leak in the bottom of a tank can empty the tank in 6hrs. An pipe fills water at the rate of 4ltrs/ minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs. The capacity of the tank is?
(A) 2345
(B) 2350
(C) 2457
(D) 4657
(E) 5760
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
E
Answer: (E) 5760
Question: Last year, sales at Company Dopler were 2% greater in February than in January, 4% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 10% greater in June than in May. In which month were sales closest to Jan?
(A) Mar
(B) April
(C) Feb
(D) May
(E) June
Rationale: Jan = $100
2% greater in February than in January ---> Feb = $102
4% less in March than in Feb ---> Mar = $97.92
20% greater in April than in March ---> Apr = $117.50
10% less in May than in April ---> May $105.75
10% greater in June than in May --->Jun = $116.33
Answer : C
Answer: (C) Feb
Question: Tom wants to buy items costing $25.35, $100.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour.
(A) 8 hours
(B) 48 hours
(C) 36 hours
(D) 18 hours
(E) 28 hours
Rationale: $6.50 x .10 = $.65 is 10% of his hourly income
$6.50 - .65 = $5.85 hourly amount available to spend
$25.35 + $100.69 + $85.96 = $212 total needed
$212 ÷ $5.85 = 36.2... rounds to 36 hours
correct answer C
Answer: (C) 36 hours
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, how many birds A has killed?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Let the total number of shots=x
Shots fired by A=5x/8
Shots fired by B=3x/8
Killing shots by A=5x/8×1/3=5x/24
Missing shots by B=3x/8×1/2=3x/16
B has missed 27 times⇒3x/16=27
⇒x=27×16/3=144
Hence, killing shots by A=5x/24=(5×144)/24=5×12/2=30
i.e., A has killed 30 birds
Answer is C.
Answer: (C) 30
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 20% profit?
(A) 2000
(B) 2778
(C) 2299
(D) 1920
(E) 2771
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 120 % of Rs. 1600 = 120/100 * 1600 = Rs. 1920.
Answer:D
Answer: (D) 1920
Question: A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
(A) 76 days
(B) 48 days
(C) 98 days
(D) 31 days
(E) 22 days
Rationale: B = 1/16 – 1/24 = 1/48 => 48 days
Answer: B
Answer: (B) 48 days
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
(A) 741
(B) 756
(C) 787
(D) 988
(E) 576
Rationale: We may have (3 men and 2 women) = (7C3 x 6C2) = 525
or (4 men and 1 woman) = (7C4 x 6C1) = 210
or (5 men only) = (7C5) = 21
Required ways = 756
ans - B
Answer: (B) 756
Question: If 20% of a number = 300, then 120% of that number will be?
(A) 20
(B) 120
(C) 360
(D) 1800
(E) 1820
Rationale: Let the number x. Then,
20% of x = 300
x = (300 * 100)/20 = 1500
120% of x = (120/100 * 1500) = 1800.
ANSWER:D
Answer: (D) 1800
Question: 1 ÷ [1 + 1 ÷ {1 + 1 ÷ (1 ÷ 1)}] = ?
(A) 5/3
(B) 4/3
(C) 2/3
(D) 1/3
(E) 1/5
Rationale: Explanation:
1 ÷ [1 + 1 ÷ {1 + 1 ÷ (1 ÷ 1)}]
= 1 ÷ [1 + 1 ÷ {1 + 1 ÷ 1}]
= 1 ÷ [1 + 1 ÷ {1 + 1}]
= 1 ÷ [1 + 1 ÷ 2]
= 1 ÷ [1 + (1/2)] = 1 ÷ 3/2 = 1 × 3/2 = 1 × 2/3 = 2/3
Answer: Option C
Answer: (C) 2/3
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 2 years?
(A) 10%
(B) 2%
(C) 4%
(D) 5%
(E) 3%
Rationale: 150 = (750*2*R)/100
R = 10%
Answer: A
Answer: (A) 10%
Question: The sum of two numbers is 16, and twice their difference is 4. What are the two numbers?
(A) 6,7
(B) 6,8
(C) 5,11
(D) 7,9
(E) 10,6
Rationale: Let the two numbers be x and y.
Equation (i): x + y = 16
Equation (ii): 2(x - y) = 4
Solve system of equations:
x=16-y
2(16-y-y)=4
16-2y=2 --- y=7
x+7=16 --- x=9
The two numbers are 7 and 9, so answer D is correct.
Answer: (D) 7,9
Question: Pat's watch gains an extra 10 seconds every 2 hours. Kim's watch loses 5 seconds every 3 hours. If both watches are set to correct time at 8 o'clock in the morning and run without interruption, after 60 hours, what will be the difference in time between Pat's watch and Kim's watch?
(A)  2 min 40 sec
(B)  3 min 40 sec
(C)  4 min 40 sec
(D)  5 min 40 sec
(E)  6 min 40 sec
Rationale: In 60 hours Pat's watch will gain an extra 60/2*10 = 300 seconds.
In 60 hours Kim's watch will lose 60/3*5 = 100 seconds.
Hence the difference will be 300 + 100 = 400 seconds.
Answer: E.
Answer: (E)  6 min 40 sec
Question: P and Q started a business investing Rs 10000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
(A) 2:7
(B) 2:6
(C) 17:6
(D) 2:3
(E) 7:8
Rationale: Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 10000:15000
= 10:15
= 2:3
Option D
Answer: (D) 2:3
Question: How many 3-digit even numbers are possible such that if one of the digits is 3, the next/succeeding digit to it should be 7?
(A) 495
(B) 305
(C) 365
(D) 405
(E) 5
Rationale: 370, 572, 374, 376, and 378, so total 5. Hence Option E.
Answer: (E) 5
Question: The unit digit in the product 7858*1086*4582*9783 is?
(A) 0
(B) 1
(C) 8
(D) 3
(E) 4
Rationale: Unit digit in the given product = unit digit in 8*6*2*3 = 8
Answer is C
Answer: (C) 8
Question: A contest will contain n questions each of which is to be answered either true or false. Anyone who answers all n questions correctly will be a winner what is the least value of n for which the probability is less then 1/1000 then a person who randomly guesses the answer to each q's will be a winner?
(A) 5
(B) 10
(C) 50
(D) 100
(E) 1000
Rationale: The probability that a person will randomly guess all nn questions correctly is 1/2n1, so we want the value of nmin for which 1/2n<1<11000 --> 2n>1000 as nn is an integer nmin==10 (2^10=1024>1000).
Answer: B.
Answer: (B) 10
Question: Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: D
4
9 x + x = 13 + 27
10 x = 40 => x = 4
Answer: (D) 4
Question: An article is bought for Rs.600 and sold for Rs.350, find the loss percent?
(A) 16 1/8%
(B) 41 1/3%
(C) 19 2/3%
(D) 41 2/3%
(E) 16 8/3%
Rationale: 600 ---- 250
100 ---- ? => 41 2/3%
Answer: D
Answer: (D) 41 2/3%
Question: A train 140 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 15 sec
(B) 16 sec
(C) 18 sec
(D) 11 sec
(E) 8 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 140 * 2/35 = 8 sec
ANSWER: E
Answer: (E) 8 sec
Question: If n is the smallest integer such that 72 times n is the square of an integer, what is the value of n?
(A)  2
(B)  3
(C)  6
(D)  12
(E)  24
Rationale: 72 can written as = 2 * 2 * 2 * 3 * 3 --> 2^3 * 3^2---(1)
so for 72 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.
here 2 already has even power -> So n has to be 3 to make the power of 2 in (1) even
Option A is correct
Answer: (A)  2
Question: Find the smallest +ve mathematical number which is spelled in an alphabetical order ?
(A) Fifty
(B) Twenty
(C) Forty
(D) Thirty
(E) Ten
Rationale: C
Forty
Answer: (C) Forty
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:
(A) 20:15:33
(B) 20:25:33
(C) 20:15:12
(D) 20:15:09
(E) 20:15:11
Rationale: Explanation:
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 train passes a station platform in 42 seconds and a man standing on the platform in 22 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 299
(B) 277
(C) 240
(D) 300
(E) 112
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 22) m = 330 m.
Let the length of the platform be x meters.
Then, x + 330 / 42 = 15
x + 330 = 630
x = 300 m.
Answer:D
Answer: (D) 300
Question: The Product of two number is 20. The sum of square of the two number is 81. Find the sum of the numbers
(A) 21
(B) 19
(C) 9
(D) 11.
(E) 8
Rationale: Solution
Let the numbers be x, y
= x2+y2= 81
=2(x+y)=40
=> (x+y)2=81+40=121,
=> x+y=sqrt(121)=11.
Answer D
Answer: (D) 11.
Question: A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 3 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
(A) $1220
(B) $1330
(C) $1550
(D) $1770
(E) $1880
Rationale: The total surface area is 2(3*4 +4*5 + 3*5) = 94 square feet
The total cost is 94*$20 = $1880
The answer is E.
Answer: (E) $1880
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1998. She ended on her
(A) a) thumb
(B) b) the index finger
(C) c) the middle finger
(D) d) the ring finger
(E) e) the little finger
Rationale: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1998 has to be the middle finger
Answer is (C)
Answer: (C) c) the middle finger
Question: A light has a rating of 60 watts, it is replaced with a new light that has 12% higher wattage. How many watts does the new light have?
(A) 105
(B) 67
(C) 80
(D) 60
(E) 100
Rationale: Final number = Initial number + 12%(original number) = 60 + 12%(60) = 60 + 7 = 67
Answer B
Answer: (B) 67
Question: A reduction of 10% in the price of a pen enabled a trader to purchase
9 more for Rs. 540. What is the reduced price of the pen?
(A) 8
(B) 6
(C) 5
(D) 4
(E) 9
Rationale: Due to 10% tot cost req to purchase the same no of pens will dec by rs 54
and tot add 9 pen eql this amt
=>54/9=6
ANSWER B
Answer: (B) 6
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
(A) 4
(B) 5
(C) 6
(D) 1
(E) 9
Rationale: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%.Answer: B
Answer: (B) 5
Question: In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent Q of his family’s total income?
(A)  15%
(B)  17%
(C)  24%
(D)  30%
(E)  33%
Rationale: Lets suppose the Total Family income in Feb = 100x
Wilson's earning in Feb = 40% of 100x = 40x
Earnings of remaining family in Feb = 100x - 40x = 60x
Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x
Earnings of remaining family in March = Earnings of remaining family in Feb = 60x
Thus Wilson's earning as % of Total family income in March Q= 30x/ (30+60)x = 30x/90x = 33.33%
Thus Answer is E
Answer: (E)  33%
Question: Initially 150. Reduced by 20%. How it is to be reduced to become 108?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: 150*20/100=30
so now we have 150-30=120 in hand
to make it 108, reduce 12
12=120*x/100,
x% is to be reduced
x=10%
ANSWER:A
Answer: (A) 10%
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 95 units raises the average to 55 units per day, what is the value of n?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The average daily production was raised by 5 units for n days, which has a weighting of 5n.
5n = 95-55 = 40
n = 8
The answer is C.
Answer: (C) 8
Question: The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?
(A) 9, 10
(B) 10, 11
(C) 11, 12
(D) 12, 13
(E) None of these
Rationale: Let the two consecutive positive integers be x and x + 1
x2 + (x + 1)2 - x(x + 1) = 91
x2 + x - 90 = 0
(x + 10)(x - 9) = 0 => x = -10 or 9.
As x is positive x = 9
Hence the two consecutive positive integers are 9 and 10.
ANSWER:A
Answer: (A) 9, 10
Question: 5 identical snow plows can clear an iced parking lot in 6 hours. How long would it take 6 such snow plows to clear the same parking lot?
(A) 1 hour, 15 minutes
(B) 2 hours, 30 minutes
(C) 3 hours
(D) 7 hours, 30 minutes
(E) 5 hourss
Rationale: 6/5 as many plows will take 5/6 as many hours --> 6*5/6=5 hours.
Answer: E.
Answer: (E) 5 hourss
Question: The average of five consecutive odd numbers A, B, C, D and E is 13. What percent of B is C ?
(A) 98.2
(B) 102.8
(C) 108.2
(D) 118.2
(E) 122.8
Rationale: Explanation :
In such a case the middle number (C) is the average
∴ C = 13 and B = 11
Required percentage = 13/11 x 100 = 118.2
Answer : Option D
Answer: (D) 118.2
Question: Cost of 16 mirror and 8 comb is Rs.336 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
(A) 10
(B) 18
(C) 20
(D) 21
(E) 22
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 336 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 144
=> m = 18
B
Answer: (B) 18
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds R in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
(A) 25%
(B) 35%
(C) 45%
(D) 70%
(E) 80%
Rationale: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out R: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Answer: (B) 35%
Question: A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there?
(A) 1260
(B) 2100
(C) 3600
(D) 3200
(E) 5200
Rationale: Let the total number of trucks = 3x
total number of sedans = 7x
total number of motorcycles = 2x
total number of sedans = 11200
=> 7x = 11200
=> x = 1600
total number of motorcycles =2x = 2*1600
=3200
Answer D
Answer: (D) 3200
Question: Three hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.30 worth of fuel per hour. At this rate, how many hours are required to consume the 300 gallons of fuel?
(A) 600
(B) 650
(C) 700
(D) 750
(E) 800
Rationale: The fuel is consumed at this rate: $0.30/$0.80 = 3/8 gallons per hour.
The time it takes to consume 300 gallons is: 300 / (3/8) = 800 hours.
The answer is E.
Answer: (E) 800
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2475?
(A) s.800
(B) s.810
(C) s.825
(D) s.900
(E) s.920
Rationale: 2475 * 1/3 = 825
Option C
Answer: (C) s.825
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
A. 5 kmph
(A) 5
(B) 8
(C) 9
(D) 3
(E) 2
Rationale: US = 25
DS = 35
M = (35 - 25)/2
= 5
Answer:A
Answer: (A) 5
Question: The decimal 0.1 is how many times greater than the decimal (0.01)^3?
(A) 10
(B) 10^2
(C) 10^5
(D) 10^8
(E) 10^10
Rationale: 0.1 = 10^-1
(0.01)^3 = (10^-2)^3 = 10^-6
10^5 * 10^-6 = 10^-1
The answer is C.
Answer: (C) 10^5
Question: 60% of a number is added to 160, the result is the same number. Find the number?
(A) 300
(B) 400
(C) 266
(D) 99
(E) 121
Rationale: :
(60/100) * X + 160 = X
2X = 800
X = 400
Answer: B
Answer: (B) 400