mathewhe/aqua_rat huggingface dataset:
Question: If M = 2N+1 where M is an Integer then which of the following is true?
(A) M is even if N is a non integer and a multiple of 0.5
(B) M is always Even
(C) M is a non multiple of 2
(D) M= 1
(E) M IS ODD
Rationale: A
Answer: (A) M is even if N is a non integer and a multiple of 0.5
Question: A man purchases 2 watches for $ 500. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 260 and $ 300
(B) $200 and $ 300
(C) $224 and $336
(D) $560 and $560
(E) $224 and $ 350
Rationale: x + y = 500 --- (1)
1.15x + 0.9y = 500 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*100)/(3*100) = 200/300
Answer: B
Answer: (B) $200 and $ 300
Question: A man can row downstream at the rate of 10 Km/hr and upstream at 6 Km/hr. Find man's rate in still water and the rate of current?
(A) 9,6
(B) 8,2
(C) 9,3
(D) 6,6
(E) None of these
Rationale: Explanation:
Rate of still water = 1/2 (10 + 6) = 8 Km/hr
Rate of current = 1/2 (10-6) = 2 Km/hr
Answer: Option B
Answer: (B) 8,2
Question: In the youth summer village there are 300 people, 200 of them are not working,100 of them have families and 125 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
(A) 150
(B) 125
(C) 175
(D) 200
(E) 100
Rationale: total =300
not working =200
having family=100
like to sing in shower = 125
working=300-200=100
not having family = 300-100=200
like to sing in shower = 125
largest possible number is the lowest possible among the above
Thus 100
E
Answer: (E) 100
Question: The price of cooking oil has increased by 25%. The percentage of reduction that a family should effect in the use of cooking oil so as not to increase the expenditure on this account is?
(A) 25%
(B) 20%
(C) 23%
(D) 24%
(E) none of these
Rationale: Reduction in consumption
= [(P/(100 + P)] X 100)%
= [(25/(100 + 25)] X 100)%
= 20%
ANSWER:B
Answer: (B) 20%
Question: In the quiet town ofNothintodothere are 600 inhabitants, 400 are unemployed and 200 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
(A) 50.
(B) 100.
(C) 150.
(D) 200.
(E) 300.
Rationale: Total = 600
unemployed=400
employed=600-400=200
som=200
unemployed som = 200/2=100
employed som = 100
employed that are not som = 200-100=100
Answer : B
Answer: (B) 100.
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 35.
(A) 324
(B) 350
(C) 384
(D) 444
(E) 256
Rationale: Number of odd numbers between 1 and 35 is (35+1)/2=18
Therefore Sum of odd numbers 18*18= 324
ANSWER: A
Answer: (A) 324
Question: A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?
(A) 1:2:8
(B) 1:2:0
(C) 1:2:5
(D) 1:2:4
(E) 1:2:1
Rationale: WC of A: B = 1:2
B: C = 1:2
---------------------
A: B: C = 1:2:4
Answer:D
Answer: (D) 1:2:4
Question: The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 20 positive perfect squares?
(A) 1,010
(B) 1,164
(C) 1,240
(D) 2,316
(E) 2,870
Rationale: First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.
Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.
Plug values of n = 20 and c = 1/2 into the equation and simplify to get the answer 2870.
Option E.
Answer: (E) 2,870
Question: A rectangular photograph is surrounded by a border that is 3 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 6 inches wide on each side, the total area would have been (M + 178) square inches. What is the perimeter of the photograph, in inches?
(A) 34
(B) 36
(C) 38
(D) 40
(E) 20
Rationale: Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)
According to the question:
(L+6)(B+6) = m ----(2)
and
(L+12)(B+12) = m + 178 ---------> (L+12)(B+12) - 178 = m ------(3)
Equating (2) and (3)
(L+6)(B+6) = (L+12)(B+12) - 178
LB + 6L + 6B +36 = LB + 12L + 12B + 144 -168
Simplify
6L + 6B = 60 ------> 2(L+B) = 20 (Check eq (1))
Answer is E
Answer: (E) 20
Question: The price of 357 mangoes is Rs. 1517.25 what will be the approximate price of 9 dozens of such mangoes ?
(A) Rs. 3000
(B) Rs. 3500
(C) Rs. 4000
(D) Rs. 2500
(E) None of these
Rationale: Solution
Let the required price be Rs. x. Then, More mangoes, More price
∴ 357 : (49 × 12) : : 1517.25 : x
⇔ 357 x = (49 × 12 × 1517.25) ⇔ x = 49x12x1517.25/357⇔ x = 2499.
Hence, the approximate price is Rs. 2500 . Answer D
Answer: (D) Rs. 2500
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is even
II. (x+z)/y is an integer
III. xz is even
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: x, y, and z are consecutive integers ⇒
Y = X+2
Z = X+4
1- x+y is even - Correct: sum of any 2 odd integers is even
2- (x+z)/y is an integer - Correct: x+z = x+x+4 = 2x+4 = 2(x+2)
and x+z/y = 2(x+2)/x+2 = 2 ⇒ integer
3- xz is even - Not Correct: multiplication of any 2 odd integers is always odd
Answer: D
Answer: (D) I and II only
Question: If a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?
(A) 6
(B) 18
(C) 20
(D) 108
(E) 216
Rationale: 1st member can be selected in 6 ways
2nd can be selected in 5 ways
3rd can be selected in 4 ways
So total ways : 120
But to avoid the similar scenarios 120/3!=20
ANS:C
Answer: (C) 20
Question: If m is not equal to zero, and m+1/m = 1, then what is the value of m^4 + (1/m)^4?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1
Rationale: m + 1/m=1
we square both sides so we have m^2 + 1/m^2 +2 = 1
or m^2 + 1/m^2= -1
squaring again we have m^4 + 1/m^4 + 2 = 1
or m^4 + 1/m^4 = -1
answer =-1 (E)
Answer: (E) -1
Question: A girl has 12 jeans and 15 tops. In how many different ways can she select a jeans and a tops?
(A) 108
(B) 200
(C) 90
(D) 120
(E) 180
Rationale: The girl can select one jeans in 12 ways.
The girl can select one top in 15 ways.
The number of ways in which she can select one jeans and one top is 12*15=180
Answer:E
Answer: (E) 180
Question: If a person allocates 20 percent of his budget to house rent, 30 percent to food, and 25 percent to clothes, what fraction of his budget remains for other allocations?
(A) 3/5
(B) 4/5
(C) 1/2
(D) 1/3
(E) 1/4
Rationale: 100%-(20%+30%+25%)=25% remains for other allocations --> 25% = 25/100 = 1/4.
Answer: E.
Answer: (E) 1/4
Question: If a committee of 3 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
(A) 20
(B) 32
(C) 54
(D) 80
(E) 120
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
8*6*4 / 6 = 32. Answer B.
Answer: (B) 32
Question: If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 284 pounds. What is Jake’s present weight, in pounds?
(A) 176
(B) 180
(C) 184
(D) 188
(E) 192
Rationale: J + K = 284 and so K = 284 - J
J - 8 = 2K
J - 8 = 2(284-J)
3J = 576
J = 192
The answer is E.
Answer: (E) 192
Question: A and B complete a work in 80 days. A alone can do it in 40 days. If both together can do the work in how many days?
(A) 1.0875 days
(B) 0.1875 days
(C) 0.0675 days
(D) 0.0375 days
(E) 0.0775 days
Rationale: 1/80 + 1/40 = 0.0375 days
ANSWER:D
Answer: (D) 0.0375 days
Question: A composer’s guild is planning its spring concert, and eight pieces have been submitted for consideration. The director of the guild knows that they will only have time to present five of them. If the pieces can be played in any order, how many combinations of pieces are possible?
(A) 56
(B) 21
(C) 10
(D) 50
(E) 19
Rationale: Combination question..
8C5 = 56..
IMO option A is correct..
Answer: (A) 56
Question: Line k is in the rectangular coordinate system. If the f-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?
(A) -3f + 2y = 6
(B) 3f + 2y = -6
(C) 3f - 2y = 6
(D) 2f - 3y = 6
(E) -2f - 3y = 6
Rationale: This question can be solved in much simpler way.
To find the f intercept
Put y=0 in the equation of the line.
To find the y-intercept
Put f=0 in the equation of the line.
So
Sub f=0 in the answer choices check whether you are getting y=3.
A. -3f + 2y = 6 --- y = 3
B. 3f + 2y = -6 --- y = -3
C. 3f - 2y = 6 ----- y = -3
D. 2f - 3y = 6 --- y = -2
E. -2f - 3y = 6 --- y =-2
Eliminate answer B,C,D and E.
So the answer is A.
Answer: (A) -3f + 2y = 6
Question: John's annual salary after a raise of 15% is $45,000. What was his salary before the raise?
(A) $49,007
(B) $31,876
(C) $54,765
(D) $39,130
(E) $42,123
Rationale: Let x be the salary before the increase. Hence x + 15% x = $45,000
Solve for x to find x = $39,130
correct answer D)$39,130
Answer: (D) $39,130
Question: The marks of 10 students of a class are 46,51,62,70,35,x,50,83,65,52. If the average marks is 55, find x.
(A) 36
(B) 34
(C) 42
(D) 46
(E) 52
Rationale: Average =( 46+51+62+70+35+x+50+83+65+52 )/10 = 55 Therefore x = 550- 514 =36 Answer : A
Answer: (A) 36
Question: The population of a town increases 20% and 25% respectively in two consecutive years. After the growth the present population of the town is 1500. Then what is the population of the town 2 years ago?
(A) A)1000
(B) B)1100
(C) C)1200
(D) D)1300
(E) E)1400
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
1500 * 100/120 * 100/125 = 1000
Answer: Option A
Answer: (A) A)1000
Question: If 21!/3^x is an integer, what is the greatest possible value of x?
(A) 3
(B) 4
(C) 5
(D) D
(E) 7
Rationale: 21 - 7 *3
18 - 3*3*2
15 - 5*3
12 - 4*3
9 - 3*3
6 - 2*3
3 - 1*3
Hence max of 3^9 is allowed. IMO D.
Answer: (D) D
Question: Max bungee jumps from the top of a building straight to the ground at a constant speed. 5 seconds after he starts plummeting he passes the 10th floor. 10 seconds after he starts plummeting he passes the 5th floor. Each floor is 5 meters high. What is Mr. Wayne's speed in meters per second?
(A) 5
(B) 6
(C) 10
(D) 15
(E) 12
Rationale: 10 Floors * 5 Meter/Floor = 50 Meters
Time= 10 sec
Rate * 10 = 50
Rate= 50/10
=5
Answer is A
Answer: (A) 5
Question: In how many different number of ways 7 men and 2 women can sit on a shopa which can accommodate persons?
(A) 200
(B) 210
(C) 230
(D) 250
(E) 15120
Rationale: 9p5 = 9 X 8 X 7 Ã— 6 Ã— 5 = 15120
E)
Answer: (E) 15120
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 65 liters
(B) 88 liters
(C) 10 liters water
(D) 45 liters
(E) 8 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters. Answer: C
Answer: (C) 10 liters water
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, then how old is B?
(A) 17 years
(B) 19 years
(C) 29 years
(D) 8 years
(E) 12 years
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
5x = 20 => x = 4
Hence, B's age = 2x = 8 years.
Answer: D
Answer: (D) 8 years
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 5 percent, but profits were 10 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 120%
(D) 124.2%
(E) 95%
Rationale: the profit 0f 2009 interms of 2008 = 0.95*10/10*100=95%
E
Answer: (E) 95%
Question: A person can swim in still water at 10 km/h. If the speed of water 4 km/h, how many hours will the man take to swim back against the current for 12 km?
(A) 2
(B) 7
(C) 5
(D) 9
(E) 6
Rationale: M = 10
S = 4
US =10 - 4 = 6
D = 12
T = 12/6 = 2
Answer: A
Answer: (A) 2
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) 6620
(B) 9278
(C) 2782
(D) 5772
(E) 5286
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: (A) 6620
Question: In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
(A) 1/4
(B) 1/6
(C) 7/12
(D) 5/36
(E) 11/36
Rationale: n(S)36
n(E)=5
P(E)=5/36
ANSWER D 5/36
Answer: (D) 5/36
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 38 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
(A) 2
(B) 4
(C) 8
(D) 12
(E) 32
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 38 + 40 + 10 - (12) - 2x
x = 8
So, answer will be C
Answer: (C) 8
Question: The set X = {10,11,12,13,14}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?
(A) 7/20
(B) 3/20
(C) 7/10
(D) 3/10
(E) 3/5
Rationale: The total number of x and y pairs is 5*4=20.
There are six pairs such that x / y is an integer.
The probability that x / y is an integer is 6/20=3/10.
The answer is D.
Answer: (D) 3/10
Question: The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers?
(A) 7 and 12
(B) 8 and 12
(C) 9 and 12
(D) 10 and 12
(E) None of these
Rationale: Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by
x = 2y - 4
We use the sum of the two numbers to write a second equation.
x + y = 20
Substitute x by 2y - 4 in x + y = 20 to obtain
2y - 4 + y = 20
Solve for y to find
y = 8 and x = 2y - 4 = 12
Answer B
Answer: (B) 8 and 12
Question: Average between two sets of numbers is closer to the set with morenumbers?
(A) 70
(B) 80
(C) 85
(D) 90
(E) 95
Rationale: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Answer: (B) 80
Question: A can finish a work in 12days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
(A) 10days
(B) 12days
(C) 6days
(D) 7days
(E) 5days
Rationale: B+C 1day work = 1/9 + 1/12 = 7/36
work done by B and C in 3days = 7/36 * 3 = 7/12
Remaining work = 1 - 7/12 = 5/12
1/24 work is done by A in 1day
5/12 work is done by A in 12*5/12 = 5days
Answer is E
Answer: (E) 5days
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
(A) 29777
(B) 37500
(C) 27889
(D) 2776
(E) 29971
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 39/4 * 1/100)
(9x + 1100000 - 11x)/100 = 39000/4 = 9750
x = 62500
Sum invested at 9% = Rs. 62500
Sum invested at 11% = Rs. (100000 - 62500) = Rs. 37500.
Answer: B
Answer: (B) 37500
Question: If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
(A) 16 2/3%
(B) 16 2/8%
(C) 16 2/1%
(D) 16 1/3%
(E) 16 2/7%
Rationale: Let the price of the article be Rs. 100.
20% of 100 = 20.
New price = 100 + 20 = Rs. 120
Required percentage = (120 - 100)/120 * 100
= 20/120 * 100 = 50/3 = 16 2/3%.
Answer:A
Answer: (A) 16 2/3%
Question: The average of 25 results is 8. The average of first 12 of them is 14 and that of last 12 is 17. Find the 13 result?
(A) 52
(B) 68
(C) 78
(D) 92
(E) 65
Rationale: 13th result = sum of 25results - sum of 24 results
18*25-14*12+17*12 = 78
Answer is D
Answer: (D) 92
Question: How many integers between 300 and 1400 are there such that their unit digit is odd?
(A) 350
(B) 450
(C) 550
(D) 650
(E) 750
Rationale: There are 1100 numbers from 301 to 1400 (inclusive).
Half of the numbers are odd, so there are 550 odd numbers.
The answer is C.
Answer: (C) 550
Question: Caleb spends $64.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?
(A) 29
(B) 10
(C) 20
(D) 40
(E) 45
Rationale: Solution -
Lets say, Single hamburgersxand Double hamburgersy
Given that,
x+y=50 and 1x+1.5y=64.50. By solving the equations y=29. ANS A.
Answer: (A) 29
Question: 5b2 is a three-digit number with b as a missing digit. If the number is divisible by 6, the missing digit is:
(A) 2
(B) 3
(C) 6
(D) 7
(E) 8
Rationale: Let the number be 5b2. Clearly, it is divisible by 2.
Now, 5+b+2= (7+b) must be divisible by 3. So, b= 2.
ANSWER:A
Answer: (A) 2
Question: The average salary of 16 people in the shipping department at a certain firm is $20,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 each. What is the average salary of the remaining employees?
(A)  $18,714
(B)  $18,500
(C)  $18,000
(D)  $15,850
(E)  $12,300
Rationale: total salary... 16*20k=320k
5 emp @ 25k =125k
4 emp @ 16k =64k
remaing 7 emp sal = 320k-125k-64k =131k
average=131k/7 = 18714
Ans :A
Answer: (A)  $18,714
Question: If 314,314 bottles of water need to be placed in boxes and each box can contain at most 9 bottles of water. How many bottles of water will be in the last unfilled box?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 10
Rationale: The number of bottles of water that can be placed in boxes of 9 bottles is the first number that is divisible by 9 that occurs before 314,314.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 314,314 = 16 and 9 is divisible by 9.
Hence, we need to remove 7 to this number for it to be divisible by 9
Correct Option: D
Answer: (D) 7
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 166
(B) 105
(C) 178
(D) 177
(E) 169
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Answer: (B) 105
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 460?
(A) 18%
(B) 21%
(C) 25.9%
(D) 19%
(E) None of these
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 460, Discount = 621 - 460 = 161
Discount % = 161/621 * 100 = 25.9%
ANSWER:C
Answer: (C) 25.9%
Question: The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher.
(A) 40 yrs
(B) 42 yrs
(C) 45 yrs
(D) 46 yrs
(E) 47 yrs
Rationale: The average age of 30 boys of a class is equal to 14 yrs:
i.e Sum of all boys:30*14
include class teacher:31 candidates in a class
& avg age is:15 yr
i.e. sum of all:31*15(include class teacher)=465
so,the age of the class teacher:465-420=45yr
answer will be 45 yrs
ANSWER:C
Answer: (C) 45 yrs
Question: In how many years, Rs. 150 will produce the same interest at 6% as Rs. 400 produce in 2 years at 4½% ?
(A) 4 years
(B) 6 years
(C) 8 years
(D) 9 years
(E) 12 years
Rationale: Explanation :
Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.400 at 4½ % for 2 years
150×6×n/100=400×9/2×2/100
150×6×n=400×9/2×2
150×6×n=400×9
n=4 years
Answer : Option A
Answer: (A) 4 years
Question: If P = k^3 – k, where k and P are positive integers, and k is given by the expression k=(10x)n+54k=(10x)n+54, where x and n are positive integers, then what is the remainder when P is divided by 4 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) cannot be determined
Rationale: p=k^3-k
=k(k^2-1)
=(k-1)k(k+1)
as can be seen, p is a product of three consecutive integers. now k can be both even and odd.
now look into the given expression of k
k=(10x)n+54k=(10x)n+54
5454 will always be odd. and (10x)n(10x)n will always be even
thus k= even + odd =odd
Also, k =1 is not possible ( because p is a positive integer)
so lets try k=3
p=(3-1)(3)(3+1)
=2*3*4
ANSWER:A
Answer: (A) 0
Question: If a store adds 50 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 40%, what will the new inventory of chairs be?
(A) 40
(B) 60
(C) 100
(D) 140
(E) 160
Rationale: Explanation:
Let’s say t = total current inventory of chairs. The first sentence states that 50 + t = (3/2)t. First solve for the current inventory:
50 + t = (3/2)t
50 = (3/2)t − t
50 = (1/2)t
100 = t
The manager wants to increase this by 40%.
40% of 100 is 40, so the new inventory will be 140.
Answer: (D).
Answer: (D) 140
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent Q of the distribution is less than m +d ?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
Rationale: D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, Q=(68+16)% or (100-16)% of the population is less than m+d.
Answer: (D) 84%
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 8 m wide at the top and 6 m wide at the bottom and the area of cross-section is 700 sq m, the depth of cannel is?
(A) 76
(B) 100
(C) 27
(D) 80
(E) 25
Rationale: 1/2 * d (8+ 6) = 700
d = 100
Answer: B
Answer: (B) 100
Question: Given 3^n, for any real integer of n, which of the following is a possible resultant?
(A) 242
(B) 244
(C) 243
(D) 254
(E) 245
Rationale: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 3^n has a cycle of 4.
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
Observe that the last digit of the resultant of 3^1 and 3^5 is 3. If we continue 3^n, the last digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, .... So, all we need look for is the last digit in the pattern.
Cycle of 4, the answer with last digit 3.
Answer: C
Answer: (C) 243
Question: Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 8, when a # b = 100?
(A) 5
(B) 8
(C) 10
(D) 13
(E) 17
Rationale: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 8 = 10/2 + 8 = 13.
The correct answer is D
Answer: (D) 13