mathewhe/aqua_rat huggingface dataset:
Question: Set X consists of 5 integers and has median of 20 and a range of 20. What is the value of the greatest possible integer that can be present in the set?
(A) 20
(B) 37
(C) C.40
(D) 43
(E) 50
Rationale: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20
This is possible. Hence it is the greatest such number.
Answer (A)
Answer: (A) 20
Question: A train is running at a speed of 40 km/hr and it crosses a post in 25.2 seconds. What is the length of the train?
(A) 190 metres
(B) 160 metres
(C) 280 metres
(D) 120 metres
(E) 250 metres
Rationale: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 25.2 s
Distance Covered, d = vt = (400/36)Ã— 25.2 = 280 m
Distance covered is equal to the length of the train = 280 m
Correct answer is 280 metres
C
Answer: (C) 280 metres
Question: A circular path of 19 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
(A) rs.49.25
(B) rs.40.50
(C) rs.44.20
(D) rs.62.85
(E) rs.43.10
Rationale: Explanation:
π (21^2 - 19^2) = 22/7 * (441-361) = 251.43
251.43 * 1/4 = Rs.62.85
Answer: Option D
Answer: (D) rs.62.85
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 4 as quotient and the 15 as remainder
(A) 1235
(B) 1346
(C) 1378
(D) 1635
(E) 1815
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 4x + 15
3x = 1350
x = 450
Large number = 450+1365 = 1815
E
Answer: (E) 1815
Question: Rahul went to a shop and bought things worth Rs. 26, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19.7
(B) 20.7
(C) 22
(D) 21.4
(E) 21.5
Rationale: Total cost of the items he purchased = Rs.26
Given that out of this Rs.26, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (26−30/100−x)6/100 = 30/100
⇒ 6(26 −0.3 −x) = 30
⇒ (26 − 0.3 − x) = 5
⇒ x = 26 − 0.3 − 5 = 20.7
B
Answer: (B) 20.7
Question: The average weight of a group of boys is 30 kg. After a boy of weight 38 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 8
(C) 5
(D) 2
(E) 7
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 38 kg joins the group, total weight of boys = 30x + 38
So 30x + 38 + 31(x + 1) = > x = 7.
Answer: E
Answer: (E) 7
Question: How many of the positive divisors of 480 are also multiples of 4 not including 480?
(A) 15
(B) 16
(C) 19
(D) 20
(E) 24
Rationale: 480 = 2^6 * 3 * 5 = (4) * 2^3 * 3 * 5
Besides (4), the exponents of 2, 3, and 5 are 3, 1, and 1.
There are (3+1)(1+1)(1+1) = 16 ways to make multiples of 4.
We must subtract 1 because one of these multiples is 480.
The answer is A.
Answer: (A) 15
Question: .
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
(A) 0
(B) 3
(C) 5
(D) 8
(E) 11
Rationale: Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
Required remainder = 5.
Answer: Option C
Answer: (C) 5
Question: x percent of y percent of z is decreased by y percent. find the result?
(A) (xz - y) / 100
(B) (100xyz - xy^2z) /1,000,000
(C) (xz - y) / 10,000
(D) (xyz - 2y) / 100
(E) (xyz - 2y) / 10,000
Rationale: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.
IF....
X = 10
Y = 50
Z = 100
First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5
So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.
Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5
Anwer is B
Answer: (B) (100xyz - xy^2z) /1,000,000
Question: There are 7 boxes numbered from 1 to 7. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: 1 green ball: 7 ways
2 green balls: 6 ways
3 green balls: 5 ways
4 green balls: 4 ways
5 green balls: 3 ways
6 green balls: 2 ways
7 green balls: 1 way
The total number of ways is 7*8/2=28
The answer is B.
Answer: (B) 28
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7, 8}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
(A) 28/243
(B) 31/243
(C) 35/729
(D) 83/729
(E) 101/729
Rationale: The number of ways to select w, x, and y is: 9*9*9=729
The number of ways to choose three different numbers from the set is 9C3=84.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
The probability that w < x < y is 84/729 = 28/243
The answer is A.
Answer: (A) 28/243
Question: A boat moves down stream at the rate of 1 km in 6 minutes and
upstream at the rate of 1 km in 10 minutes. The speed of current is
(A) 2 kmph
(B) 3 kmph
(C) 4 kmph
(D) 5 kmph
(E) 6 kmph
Rationale: If speed(in kmph) of the boat=b and current=c, then
In downstream time taken(in hrs.)=1/(b+c)=6/60=1/10 or b+c=10 ---(i) &
In upstream time taken(in hrs.)=1/(b-c)=10/60=1/6 or b-c=6 ---(ii)
From (i) & (ii), b=8, c=2
ANSWER:A
Answer: (A) 2 kmph
Question: If a, b, w are integers, 33 = abw, and a < b < w, what is the smallest possible value of a?
(A) -33
(B) -3
(C) 1
(D) 3
(E) 11
Rationale: Given : a * b * w = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.
Correct answer is A
Answer: (A) -33
Question: If you multiply two integers together and
then add 4, the result is 40. Which of the
following could NOT be the sum of the
two numbers?
(A) 12
(B) 13
(C) 15
(D) 18
(E) 20
Rationale: Let the two integers equal x and y, and then create the following equation and simplify:
xy + 4 = 40
xy = 36
So x and y are a pair of integers that equal 36. Try adding all possible combinations of two
integers that multiply out to 36:
1 × 36 = 36 1 + 36 = 37
2 × 18 = 36 2 + 18 = 20
3 × 12 = 36 3 + 12 = 15
4 × 9 = 36 4 + 9 = 13
6 × 6 = 36 6 + 6 = 12
This list of sums includes 12, 13, 15, and 20, but not 18. Thus, no pair of integers both
satisfies the original equation and adds up to 18
correct answer D)18
Answer: (D) 18
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio A of men to women?
(A)  5:2
(B)  5:1
(C)  4:3
(D)  4:1
(E)  3:1
Rationale: (A) A=184 x 5 + 170 x 2 = 1260.A
Answer: (A)  5:2
Question: Find the arithmetic mean P of all roots of the following equation- see an attachment.
(A) 2
(B) 1
(C) 0.5
(D) -1/3
(E) 0.3
Rationale: arithmetic mean P your answer C and E are same, can you correct one of them please. thanks.C
Answer: (C) 0.5
Question: The product of two numbers is 336 and the sum of their squares is 289. The sum of the number is?
(A) A)23
(B) B)25
(C) C)27
(D) D)31
(E) E)35
Rationale: Let the numbers be x and y.
Then, xy = 336 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 336) = 961
x + y =31.
Option D
Answer: (D) D)31
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 5 hours. How long would it take Taimour to paint the fence alone?
(A) 6 hours
(B) 8 hours
(C) 15 hours
(D) 24 hours
(E) 32 hours
Rationale: I believe the answer is C. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 5 => 1/15
Working alone Taimour can do the job in 1 = 1/15* hours => 15
Answer C
Answer: (C) 15 hours
Question: Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 35% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?
(A) $20
(B) $65
(C) $50
(D) $80
(E) $100
Rationale: Deargoodyear2013,
I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.
Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.
They had this same selling price, $100, before they made the change, and had a profit of 35%, so the manufacturing must have been $65. Answer = (B).
Answer: (B) $65
Question: There are 2 sections A and B in a class, consisting of 50 and 70 students respectively. If the average weight of section A is 50kg and that of section B is 70kg, Find the average of the whole class?
(A) 50.78kg
(B) 49.32kg
(C) 61.67kg
(D) 69.15kg
(E) 70.89kg
Rationale: Total weight of 50+70 students = 50*50 + 70*70 = 7400
Average weight of the class is = 7400/120 = 61.67 kg
Answer is C
Answer: (C) 61.67kg
Question: The sum of two consecutive numbers is 37. What are they?
(A) 18 and 19
(B) 18 and 21
(C) 18 and 23
(D) 19 and 20
(E) None
Rationale: Two consecutive numbers are like 8 and 9, or 51 and 52.
Let x, then, be the first number. Then the number after it is x + 1.
The problem states that their sum is 37:
word problem = 37
2x = 37 − 1
= 36.
x = 36
2
= 18.
The two numbers are 18 and 19.
Option is A
Answer: (A) 18 and 19
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/8. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
(A) 134
(B) 146
(C) 152
(D) 162
(E) 170
Rationale: The probability of survival for each of the first 3 months of life is 1-1/8= 7/8, so of 200 newborn 200*7/8*7/8*7/8=~134 is expected to survive.
Answer: A.
Answer: (A) 134
Question: Calculate the value of u: 16u^2-7u+2 = 125
(A) 5
(B) 2
(C) 4
(D) 1
(E) 3
Rationale: Using the elimination method substitute options for x and find the correct option.
Answer: E
Answer: (E) 3
Question: In a class of 50 students, 20 play Tennis, 15 play Cricket and 11 play Football. 7 play both Tennis and Cricket, 4 play Cricket and Football and 5 play Tennis and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
(A) 10
(B) 20
(C) 25
(D) 30
(E) 40
Rationale: {Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer A
Answer: (A) 10
Question: Bradley owns b video game cartridges. If Bradley’s total is one-ninth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) 37b / 4
(B) 39b / 4
(C) 41b / 4
(D) 43b / 4
(E) 45b / 4
Rationale: b = Bradley’s total
9b = Andrew’s total
b/4 = Charlie’s total
The total number of cartridges is:
b + 9b+ b/4 = (4b + 36b + b) / 4 = 41b / 4
The answer is C.
Answer: (C) 41b / 4
Question: According to a survey, at least 65% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
(A) 15%
(B) 20%
(C) 25%
(D) 0%
(E) 35%
Rationale: To minimize the percentage who like all three, let's maximize the percentage who like 2 out of 3.
80% like cherries and 20% don't like cherries.
Let's combine this with the people who like bananas.
20% don't like cherries but do like bananas.
55% like cherries and bananas.
25% like cherries but not bananas.
Now let's distribute the people who like apples.
20% like bananas and apples, but not cherries.
25% like cherries and apples, but not bananas.
20% like all three.
35% like cherries and bananas, but not apples.
The answer is B.
Answer: (B) 20%
Question: Find the two digit number, such that the ratio is 7/4 of original number to the number formed by reversing the digits.
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: here ratio is 7/4.
so lets check one by one.
for 1 : 7*1/4*1 = 7/4
for 2 : 7*2/4*2 = 14/8 ,which doesn't satisfy the conditions.
for 3 : 7*3/4*3 = 21/12
ANSWER:B
Answer: (B) 21
Question: A soccer team played 140 games and won 50 percent of them. How many games did it win?
(A) 140
(B) 94
(C) 104
(D) 70
(E) 80
Rationale: 50% of 140 =x
0.50*140 = x
70=x
answer :D
Answer: (D) 70
Question: Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 2.5. What value is exactly 2 standard deviations less than the mean?
(A)  8.5
(B)  11
(C)  11.5
(D)  12
(E)  12.5
Rationale: The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*2.5=8.5.
Answer: A.
Answer: (A)  8.5
Question: A ladies hostel had provision of food for 300 women for 45 days. After 10 days, 275 women left the hostel. The number of days for which the remaining food will last is:
(A) 420
(B) 430
(C) 450
(D) 480
(E) 425
Rationale: Explanation :
After 10 days : 300 women had food for 35 days.
Suppose 25 women had food for x days.
Now, Less women, More days (Indirect Proportion)
25 : 300 :: 35 : x
=> 25 x x = 300 x 35
=> x = 300 x 35 / 25
=> x = 420
Answer : A
Answer: (A) 420
Question: An auction house charges a commission of 17% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
(A) $115,000
(B) $160,000
(C) $205,000
(D) $240,000
(E) $365,000
Rationale: Say the price of the house was $x, then 0.17*50,000+0.1*(x-50,000)=24,000 --> x=$205,000 (17% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: C.
Answer: (C) $205,000
Question: In a certain corporation, there are 300 male employees and 150 female employees. It is known that 10% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
(A) 1/5
(B) 5/15
(C) 6/15
(D) 3/10
(E) 4/15
Rationale: P(female) = 150/450 = 1/3
P(male with advanced degree) = 0.1*300/450 = 30/450 = 1/15
The sum of the probabilities is 6/15 = 2/5
The answer is C.
Answer: (C) 6/15
Question: At a speed of 40 miles per hour, a certain car uses 1 gallon of gasoline every 40 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour, the amount of gasoline used would be what fraction of a full tank?
(A) 3/25
(B) 5/12
(C) 7/12
(D) 2/3
(E) 25/36
Rationale: Gas used = (5 hours)*(40 miles/hour)*(1 gallon/40 miles) = 5 gallons
Portion used = (5) / 12 = 5/12
Ans B
Answer: (B) 5/12
Question: If x ≠ 1 and if yx/(y - x) = 1, what is the value of y in terms of x?
(A) (1-x)/x
(B) (x - 1)/x
(C) x/(x + 1)
(D) (x + 1)/x
(E) x/(1-x)
Rationale: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
E
Answer: (E) x/(1-x)
Question: A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 250 items for $150 each, what will her monthly salary be?
(A) $1,500
(B) $1,800
(C) $3,250
(D) $2,500
(E) $2,800
Rationale: Ans : 1000+ 7.5 % * 150 * (250-50) = $ 3250
ANSWER:C
Answer: (C) $3,250
Question: What least number must be subtracted from 427751 so that remaining no.is divisible by 10
(A) 3
(B) 1
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
On dividing 427751 by 10 we get the remainder 1, so 1 should be subtracted
Option B
Answer: (B) 1
Question: Which of the following inequalities has (have) a finite range of values of "x" satisfying it (them)?
(A) x^2 + 5x + 6 > 0
(B) |x + 2| > 4
(C) 9x - 7 < 3x + 14
(D) x^2 - 4x + 3 < 0
(E) (B) and (D)
Rationale: Factorizing x^2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0.
This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative.
Evaluating both the options, we get 1 < x < 3. i.e., a finite range of values for "x".
ANSWER : D
Answer: (D) x^2 - 4x + 3 < 0
Question: P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
(A) 16 days
(B) 17 days
(C) 19 days
(D) 14 days
(E) 10 days
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days.
Answer:A
Answer: (A) 16 days
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings?
(A) 3600
(B) 3607
(C) 3608
(D) 3602
(E) 3603
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 18000 => x = 3600
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3600.
Answer:A
Answer: (A) 3600
Question: There are 12 yes or no questions. How many ways can these be answered?
(A) 1254
(B) 3624
(C) 4578
(D) 4096
(E) 3265
Rationale: Each of the questions can be answered in 2 ways (yes or no)
Therefore, no. of ways of answering 12 questions = 212 = 4096 ways.
Ans: D
Answer: (D) 4096
Question: Simplify: 0.3*0.8+0.1*0.5
(A) 0.52
(B) 0.29
(C) 0.48
(D) 0.64
(E) 0.46
Rationale: Given exp. = 0.3*0.8+(0.1*0.5) = 0.24+0.05 = 0.29
Answer is B.
Answer: (B) 0.29
Question: There is a train and car. The ratio btw the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 480km in 8h. The speed of the bus is 3/4th of the speed of the train. How much distance will the car cover in 6h?
(A) 300 km
(B) 400 km
(C) 420 km
(D) 430 km
(E) 450 km
Rationale: Sol. Speed of bus = 480/8 = 60km/ h
Speed of train = (60*4)/3=80 km / h
Speed of train : Speed of car = 16 : 15
Speed of car =80/16 * 15 = 75 km/ h
Distance covered by car in 6 hr = 75 × 6 = 450 km
E
Answer: (E) 450 km
Question: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination. How many miles did John drive?
(A) 235 miles.
(B) 245 miles.
(C) 225 miles.
(D) 265 miles.
(E) 275 miles.
Rationale: The total distance D traveled by John is given by
D = 45 * 2 + 3 * 45 = 225 miles.
Answer C
Answer: (C) 225 miles.
Question: If k, (k+200), (k+350), and 15*K are all multiples of A, then A could equal which of the following ?
(A) 20
(B) A=25
(C) 75
(D) 100
(E) 150
Rationale: {Multiple of A} - {Multiple of A} = {Multiple of A}.
(K+200) - k = 200 = {Multiple of A}.
(K+350) - k = 350 = {Multiple of A}.
Both 200 and 350 are multiples of only option B.
Answer: B.
Answer: (B) A=25
Question: In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M?
(A) 278
(B) 2890
(C) 270
(D) 2702
(E) 1050
Rationale: 504/M = 384/800
(504 * 800) / 384 = M
M = 1050
Answer:E
Answer: (E) 1050
Question: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,071 bacteria each. How many bacteria are there approximately?
(A) 10^7
(B) 10^11
(C) 10^9
(D) 10^10
(E) 10^8
Rationale: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,071 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 79=80, 48=50, 25,071=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is E.
Answer: (E) 10^8
Question: The average of four positive integers is 67. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
(A) 72
(B) 78
(C) 80
(D) 82
(E) 84
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 268 - (A + D) = 268 - 132 = 136.
B + B -28 = 136
B = (136 + 28)/2 = 82
ANSWER:D
Answer: (D) 82
Question: If 1+2+3+...+n=n (n+1), then
2 (1+3+5+....+99)=?
(A) 6000
(B) 5000
(C) 2500
(D) 6500
(E) None of these
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 99=1+(n-1)2
=> n=50
Use value of n in (1)
then,
Sn = (50/2)(1+99) = 2500
Ans:- 2(Sn) = 5000
Hence (B) is correct
Answer : B
Answer: (B) 5000
Question: 3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is:
(A) 2/9
(B) 1/9
(C) 8/9
(D) 7/9
(E) 6/9
Rationale: let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house
there will be 1 case when x,y,z will buy house a
another when they buy house b
and another when they buy house c
so the prob that they buy same house is 3*1/27=1/9
ANSWER:B
Answer: (B) 1/9
Question: Find the highest common factor of 36 and 84.
(A) 4 years
(B) 6
(C) 7
(D) 8
(E) 12
Rationale: 36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.
Answer: Option E
Answer: (E) 12