mathewhe/aqua_rat huggingface dataset:
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 75.
(A) 3
(B) 4
(C) 12
(D) 32
(E) 35
Rationale: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by 75, remainder will be -4 i.e. n will be 4 less than a multiple of 75. So you must add 35 to n to make it a multiple of75
E
Answer: (E) 35
Question: What percent of 120 are 90?
(A) 78%
(B) 85%
(C) 75%
(D) 72%
(E) 23%
Rationale: (?% /100) * 120 = 90
? = 75%
Answer:C
Answer: (C) 75%
Question: If p=125×243×16/405, how many digits are in p?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: p = 125 * 243 * 16 / 405
p= 5^3 * 3 * 9^2 * 4^2 / (5 * 9^2)
p= 5^2 * 3 * 4^2
p = 20^2 * 3 = 1200
answer D
Answer: (D) 4
Question: If x<0, y>0, and |x| < |y|, which of the following must be true?
(A) x > y
(B) y^2 > x^2
(C) x^3 > y^2
(D) –x > y
(E) x < –y
Rationale: Correct Answer: (E)
Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus –x > y is the same statement as |x| > |y|, and (D) must be true.
Answer: (D) –x > y
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 8 ml
(B) 6 ml
(C) 3 ml
(D) 4 ml
(E) 2 ml
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
Answer: B
Answer: (B) 6 ml
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than or equal to 60% marks is
(A) 4
(B) 3
(C) 2
(D) 1
(E) 5
Rationale: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.
Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.
Hence , there are 3 subject where he secured more that 60 %.
The answer is 3.
B
Answer: (B) 3
Question: 9, 16, 19, 25, 36,49
(A) 9
(B) 16
(C) 19
(D) 25
(E) 36
Rationale: Each of the numbers except 19, is perfect square.
Answer: Option C
Answer: (C) 19
Question: Prizes totaling $ 55,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
(A) (a) $5,000
(B) (b) $10,000
(C) (c) $15,000
(D) (d) $20,000
(E) (e) $65,000
Rationale: The highest prize cannot possibly be less than 1/3rd of 55,000 (because in this case the sum of 3 prizes would be less than 55,000) and cannot be more than 55,000.
Answer: D.
Answer: (D) (d) $20,000
Question: Let f(x) = x4 – 8x3 + 16x2 – 19 and g(x) = x - 5. Find f(x)/g(x)
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Solution:
f(x) = x4 – 8x3 + 16x2 – 19
g(x) = x – 5
f(x)/g(x) = (x4 – 8x3 + 16x2 – 19)/(x - 5)
We first need to rearrange all the terms of the dividend according to descending powers of x. The dividend then becomes x4 – 8x3 + 16x2 – 19, with 1 understood as the coefficient of the first term. No x term is there in the polynomial, but we take a zero as a place holder in the x position, so the dividend is written as x4 – 8x3 + 16x2 + 0x – 19.
We solved the division in both the ways;
(x4 – 8x3 + 16x2 + 0x – 19) ÷ (x - 5) by using synthetic division
Quotient = x3 - 3x2 + x + 5
Remainder = 6
Answer C
Answer: (C) 6
Question: A circular wire of radius 42cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is:
(A) 30cm
(B) 60cm
(C) 72cm
(D) 132cm.
(E) 142cm.
Rationale: Length of wire= circumference of circle of radius 42cm= (2* 22/7* 42)= 264cm.
Therefore, perimeter of rectangle= 264 cm.
Let, length= 6x cm & breadth= 5x cm.
Therefore, 2 (6x+5x)= 264 or x=12.
Therefore, smaller side= 60 cm
ANSWER:B
Answer: (B) 60cm
Question: In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
(A) 2880
(B) 1400
(C) 1200
(D) 3212
(E) None of these
Rationale: Explanation :
In a circle, 5 boys can be arranged in 4! ways
Given that the boys and the girls alternate.
Hence there are 5 places for girls which can be arranged in 5! ways
Total number of ways = 4! x 5! = 24 x 120 = 2880. Answer : Option A
Answer: (A) 2880
Question: Less than half of a committee that is to be formed out of certain group, are to be men. If there are 100 possible ways of forming the committee, then the number of men in the committee can be,
(A) 2
(B) 3
(C) 4
(D) 5
(E) cannot be determined
Rationale: 1. Let there be m men and w women out of which the committee is formed.
2. mCn * wCr = 100, where n is the number of men chosen and r is the number of women chosen
3. The possible products for LHS of (2) are, 100 * 1, 50 * 2, 25 * 4, 20 * 5, 10 * 10
4. Since the number of women is greater than the number of men, the first three products in (3) can be rejected as they would not satisfy this condition.
5. In the case of the fourth product, 20 * 5 may be given by 6C3 * 5C1. Though this may satisfy the condition with 3 women and 1 man, 1 man is not in the choices given.
6. The last product 10 * 10 may be given by 5C2 * 5C3 with 2 men and 3 women. This satisfies the condition and also 2 men is one of the choices given.
Therefore the answer is choice A.
Answer: (A) 2
Question: A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction?
(A) 8%
(B) 9%
(C) 10%
(D) 11%
(E) None
Rationale: Solution
Actual price	= Rs. (25 + 2.50)
= Rs. 27.50
Therefore, saving	= (2.50 / 27.50 ×100)%
= 100 / 11%
= 9×1/11%
= 9%.
Answer B
Answer: (B) 9%
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 5%?
(A) 20%
(B) 29%
(C) 10%
(D) 80%
(E) 42.5%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 95
2/3 SP1 = 95
SP1 = 142.5
100 --- 42.5 => 42.5%
Answer: E
Answer: (E) 42.5%
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 840, what is the least possible value of n?
(A) 5
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 840 = 2 * 2 * 2 * 3 * 5
so the least value forNcan be 5.
A
Answer: (A) 5
Question: a clock hangs on the wall of a railway station,71ft 9in long and 10ft 4in high.those are the dimension of the wall,not the clock!while waiting for a train we noticed that the hands of the clock were pointing in opposite directions,and were parallel to one of the diagonals of the wall,what was the exact time ?
(A) 7:15
(B) 7:5
(C) 7:25
(D) 7:45
(E) 7:55
Rationale: it can have four possiblities
time could be
7:5
1:35
11:25
5:55
ANSWER:B
Answer: (B) 7:5
Question: A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
(A) 46m
(B) 66m
(C) 26m
(D) 56m
(E) 25m
Rationale: Perimeter of the plot = 2(90+50) = 280m
no of poles =280/5 =56m
Answer: D
Answer: (D) 56m
Question: The sector of a circle has radius of 21 cm and central angle 90o. Find its perimeter?
(A) 91.5
(B) 75
(C) 93
(D) 94
(E) 95
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (90/360 * 2 * 22/7 * 21) + 2(21)
= 75 cm
Answer: Option B
Answer: (B) 75
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) 4192 sq m
(B) 4304 sq m
(C) 4312 sq m
(D) 4360 sq m
(E) None of these
Rationale: 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 = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
ANSWER:C
Answer: (C) 4312 sq m
Question: Tom bought 2 shares and sold them for $55 each. If he had a profit of 25% on the sale of one of the shares but a loss of 45% on the sale of the other share, then on the sale of both shares Tom had
(A)  a profit of $44
(B)  a loss of $44
(C)  a profit of $34
(D)  a loss of $34
(E)  neither a profit nor a loss
Rationale: total CP = 5500/125 + 5500/55 = 44 + 100=144
SP=55*2=110
loss= Rs 34/-
Answer: D
Answer: (D)  a loss of $34
Question: Mary and Mike enter into a partnership by investing $600 and $400 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year?
(A) $8500
(B) $9500
(C) $7000
(D) $7500
(E) $6500
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 6 : 4.
i.e., 60% of 2x would go to Mary and 40% of 2x would go to Mike.
Hence, Mary would get (60 - 40)% of 2x more than Mike
Or20% of 2x = $1000
i.e.,(20/100)*2x = 1000
or 2x = 5000.
Hence, the profit made by the company during the year $3x = $7500.
Answer : D
Answer: (D) $7500
Question: A and B together can do a work In 8 days. A alone can do it in 12 days. What time B will take to do the work alone?
(A) 6 days
(B) 8 days
(C) 12 days
(D) 24 days
(E) 25 days
Rationale: Explanation:
A and B 1day's work = 1/8
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/8) - (1/12) = 24 Days
Answer: Option D
Answer: (D) 24 days
Question: The average age of a man and his son is 28 years. The ratio of their ages is 3 :1 respectively. What is the man's age ?
(A) 30 years
(B) 38 years
(C) 44 years
(D) 42 years
(E) None of these
Rationale: Total sum of man’s age & his son’s age =28 × 2 = 56 Now, the Ratio of their ages is 3 : 1.Therefore, Man’s age = (3/4) × 56 = 42
So, the correct answer is option D.
Answer: D
Answer: (D) 42 years
Question: In an election between two candidates, the winner has a margin of 20% of the votes polled. If 3000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election?
(A) 15000
(B) 20000
(C) 30000
(D) 60000
(E) 45000
Rationale: Winner - Looser
60% - 40%
If 3000 people change their mind and vote for the loser:
Winner - Looser
40% - 60%
Thus 3,000 people compose 20% of all voters, which means that the total number of votes is 15,000.
Answer: A
Answer: (A) 15000
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 15 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 28%
(B) 40%
(C) 64.8%
(D) 76.5%
(E) 72%
Rationale: original price = 100
day 1 discount = 10%,price = 100-10 =90
day 2 discount = 10%,price = 90-9=81
day 3 discount = 15%,price = 81-12.15= 68.85
which is 68.85/90 *100 of the sale price on day 1= ~76.5%
Answer D
Answer: (D) 76.5%
Question: A shopkeeper buys mangoes at the rate of 7 a rupee and sells them at 5 a rupee. Find his net profit or loss percent?
(A) 40 %
(B) 90 %
(C) 33 %
(D) 35 %
(E) 30 %
Rationale: The total number of mangoes bought by the shopkeeper be 35.
If he buys 7 a rupee, his CP = 5
He selling at 5 a rupee, his SP = 7
Profit = SP - CP = 7 - 5 = 2
Profit Percent = 2/5 * 100 = 40 %
Answer:A
Answer: (A) 40 %
Question: If x is odd and y is odd, then xy,
(A) Odd
(B) Odd whenever x-y is even
(C) Even whenever x+y is odd
(D) Even
(E) It cannot be determined
Rationale: x is odd and y is odd, then xy is
Let's take x=7 and y=3.
x*y=7*3=21.
x*y=odd.
Option: A
Answer: (A) Odd
Question: find S.P when CP=56.25,gain=20%.
(A) Rs 66.50
(B) Rs 65.50
(C) Rs 67.50
(D) Rs 69.50
(E) Rs 68.50
Rationale: SP =20% of Rs 56.25 ,=Rs{(120/100)*56.25}=Rs67.50
Answer is C
Answer: (C) Rs 67.50
Question: A famous film director thought of an interesting story and he made a film in Hindi, Tamil and Telugu. He release the movie at the same time in all the three languages. The movie had Dhanush, Kamalhasan, Sruthi Hasan and Akdhsay Bachchan in lead role. The collections made was interesting to study. Collections in Hindi to Tamil and Tamil to Telugu was in the ratio 5: 4. If the collection made in language Tamil alone was Rs. 19753080, what was the total collection made.
(A) Rs.60246894
(B) Rs.26024689
(C) Rs.22602468
(D) Rs.22602469
(E) none of these.
Rationale: making them in equal proportion of Hindi:Tamil:Telugu=25:20:16
and given 20x=19753080 so, x=987654
so, total collection is 61*x=60246894
ANSWER:A
Answer: (A) Rs.60246894
Question: A man invests some money partly in 15% stock at 105 and partly in 8% stock at 40.To obtain equal dividends from both,he must invest the money in the ratio :
(A) 3 : 4
(B) 3 : 5
(C) 7 : 5
(D) 16 : 15
(E) None
Rationale: Solution
For an income of Rs. 1 in 15% stock at 105, investment = Rs. (105/15)= Rs. 7.
For an income of Rs. 1 in 8% stock at 40, investment = Rs.(40/8) = Rs. 5.
∴ Ratio of investments = 7:5 =7:5
Answer C
Answer: (C) 7 : 5
Question: John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam three years ago?
(A) 2
(B) 3
(C) 6
(D) 8
(E) 16
Rationale: j= 3s
after 6 years
j +6 = 2(s+6)
j= 2s+6
2s +6 = 3s
s= 6
three years ago
s= 6-3= 3
B is the answer
Answer: (B) 3
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 30% profit on the cost of the item?
(A) 18
(B) 21.6
(C) 22
(D) 25.7
(E) 27
Rationale: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 30% of the final price --> (final price)*0.7 = $18 --> (final price) = $25.7.
Answer: D.
Answer: (D) 25.7
Question: 169, 289, 361, 529, 841, ?, F ind the missing number(?).
(A) 930
(B) 789
(C) 961
(D) 920
(E) 788
Rationale: The series consists of squares of consecutive PRIME numbers.
Answer : C.
Answer: (C) 961
Question: The price of an item is discounted 2 percent on day 1 of a sale. On day 2, the item is discounted another 12 percent, and on day 3, it is discounted an additional 25 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 66%
(B) 67.5%
(C) 69%
(D) 70%
(E) 72%
Rationale: Let initial price be 1000
Price in day 1 after 2% discount = 980
Price in day 2 after 12% discount = 862.4
Price in day 3 after 25% discount = 646.8
So, Price in day 3 as percentage of the sale price on day 1 will be = 646.8/980*100 => 66%
Answer will definitely be (A)
Answer: (A) 66%
Question: How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
(A) 720
(B) 360
(C) 1420
(D) 1680
(E) None of these
Rationale: Explanation :
The first two places can only be filled by 3 and 5 respectively and there is only 1 way
of doing this
Given that no digit appears more than once. Hence we have 8 digits remaining(0,1,2,4,6,7,8,9)
So, the next 4 places can be filled with the remaining 8 digits in 8P4 ways
Total number of ways = 8P4 = 8 x 7 x 6 x 5 = 1680. Answer : Option D
Answer: (D) 1680
Question: A train is 300 meter long is running at a speed of 35 km/hour. In what time will it pass a bridge of 115 meter length?
(A) 29
(B) 23
(C) 47.119
(D) 44.586
(E) 42.686
Rationale: Speed = 35 Km/hr = 35*(5/18) m/sec = 175/18 m/sec
Total distance = 300+115 = 415 meter
Time = Distance/speed
= 415 * (18/175) = 42.686 seconds.
Answer: E
Answer: (E) 42.686
Question: Two employees M and N are paid a total of $572 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
(A) $220
(B) $240
(C) $260
(D) $300
(E) $320
Rationale: 1.2N + N = 572
2.2N = 572
N = 260
The answer is C.
Answer: (C) $260
Question: If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
(A) 9:6:6
(B) 9:7:4
(C) 9:6:6
(D) 9:6:4
(E) 9:3:4
Rationale: A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
Answer: D
Answer: (D) 9:6:4
Question: Two cycles are standing side-by-side. One cycle, which is 2.5 feets tall, casts a shadow that is 5
feets long. The other cycle is 2 feets tall. Compute, in feets, the length of the shadow that
the shorter cycle casts.
(A) 3
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
2.5/5 = 2/x and x = 4 .
correct answer B
Answer: (B) 4
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 677 m
(B) 456 m
(C) 500 m
(D) 663 m
(E) 757 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer: C
Answer: (C) 500 m
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel two times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
(A) 4
(B) 3
(C) 8
(D) 9
(E) 12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/2 and W = 2S
Then we have 1/(2*S) + 1/S = 1/2 <=> 3/(2*S) = 1/2<=> S = 3
ANS: B
Answer: (B) 3
Question: The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement S for his trip along the moving walkway?
(A) 2 feet per second
(B) 2.5 feet per second
(C) 3 feet per second
(D) 4 feet per second
(E) 5 feet per second
Rationale: I get E.
Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.
So we get two equations:
3t=d-120
6t=d
Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.
So, Bill's average rate of movement S is:
He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.
(240+60)/(20+40)= 5 ft/sec=E
Answer: (E) 5 feet per second
Question: A number when divided by a certain divisor left remainder 245, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?
(A) 378
(B) 365
(C) 380
(D) 456
(E) 460
Rationale: Easy solution:
N= Dq1+245
2N = 2Dq1 + 490 - (1)
2N = Dq2 + 112 - (2)
As (1) = (2) = 2N
D*(q2-2q1) = 378
D * Some integer = 378
Checking all options only (A) syncs with it.
Answer A
Answer: (A) 378
Question: The cost price of 20 arƟcles is the same as the selling price of x arƟcles. If the profit is 25%, find out
the value of x
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: Explanation:
Let the Cost Price of one arƟcle = Rs. 1
CP of x articles = Rs. x
CP of 20 articles = 20
Selling price of x articles = 20
Profit = 25% [Given]
⇒
(SP−CPCP)=25100=14
⇒
(20−x)x=14
⇒
80−4x=x
⇒
5x=80
⇒
x=805=16
Answer: D
Answer: (D) 16
Question: In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate
(A) 356000
(B) 356500
(C) 357000
(D) 400000
(E) None of these
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
C)
Answer: (C) 357000
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 276 m
(B) 167 m
(C) 245 m
(D) 167 m
(E) 178 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer:C
Answer: (C) 245 m
Question: What is the area of a square field whose diagonal of length 10 m?
(A) 50
(B) 70
(C) 60
(D) 20
(E) 25
Rationale: d2/2 = (10 * 10)/2
= 50
Answer:A
Answer: (A) 50
Question: In a certain town, there are eight times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
(A) 1 to 4
(B) 1 to 3
(C) 1 to 2
(D) 3 to 4
(E) 8 to 9
Rationale: Town state: 8 times the whole town or country
then ratio will be 8(times)/9 total(times)
So the answer is 8/9.
E
Answer: (E) 8 to 9
Question: Find the sum of all odd numbers up to 100.
(A) 2500
(B) 2400
(C) 2300
(D) 2200
(E) 2100
Rationale: The given numbers are 1, 3, 5, 7, ..., 99.
This is an A.P. with a = 1 and d = 2.
Let it contain n terms. Then,
1 + (n - 1) x 2 = 99 or n = 50.
Required sum = n/2 (first term + last term)
= 50/2 (1 + 99) = 2500.
Answer is A.
Answer: (A) 2500
Question: If xy ≠ 0 and x^2y^2 − 2xy = 8, which of the following could be y in terms of x?
I. 4/x
II. -x/2
III. 3/x
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III
Rationale: (x^2)(y^2) – 2xy - 8 = 0
(xy – 4)(xy + 2) = 0
xy – 4 = 0 or xy + 2 = 0
xy = 4 or xy = -2
Since we need y in terms of x, we can isolate y in both of our equations.
y = 4/x or y = -2/x
Answer: A
Answer: (A) I only
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 560 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 76
(E) 92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 560
Breadth = 28 feet
Area to be fenced = 2B + L = 2 (28) + 20 = 76 feet answer : D
Answer: (D) 76