mathewhe/aqua_rat huggingface dataset:
Question: If the average of 9 consecutive number is T. How much will the average increase by if the next 3 consecutive numbers are also added?
(A) 3
(B) 1.5
(C) 2.5
(D) Can’t be determined
(E) None of these
Rationale: DETAILED SOLUTION
Let the numbers be n, n+1, n+2……………….n+8
Average of these numbers = n + 4
When n +9, n+10, n+11 are added, the difference of these numbers from the earlier average = 5, 6, 7 respectively = 18
This 18 will increase the average by 18/15 = 1.5
CORRECT ANSWER B
Answer: (B) 1.5
Question: Two pipes A and B can fill a tank in 40 and 120 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 30
(B) 35
(C) 25
(D) 82
(E) 22
Rationale: Part filled by A in 1 min. = 1/40
Part filled by B in 1 min. = 1/120
part filled by (A + B) in 1 min. = 1/40 + 1/120 = 1/30.
Both the pipes can fill the tank in 30 minutes.
Answer: A
Answer: (A) 30
Question: 100 oranges were bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. What is the percentage of profit or loss?
(A) 19 2/7%
(B) 17 2/7%
(C) 14 2/7%
(D) 15 2/7%
(E) 5 15/17%
Rationale: 100*48/12*350-1)100=1/7*100=14 2/7%
i.e., profit percentage =14 2/7%
Answer : C
Answer: (C) 14 2/7%
Question: Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is?
(A) 2987
(B) 2000
(C) 2789
(D) 7999
(E) 7389
Rationale: Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each horse
= Rs.2000.
Answer: B
Answer: (B) 2000
Question: The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees.
(A) $2291.7
(B) $1546.8
(C) $2546.5
(D) $1879.3
(E) $3125.3
Rationale: mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7
Answer is A
Answer: (A) $2291.7
Question: If q and d are both integers, q>d, and -3q>19, then the largest value of d would be?
(A) -5
(B) -6
(C) -7
(D) -8
(E) -10
Rationale: No, your thinking is incorrect. When we know that q>d and q<-6.33, the largest value of q can be -7 while if q=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.
You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.
Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:
.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).
So, as per the question if d<q and q = -7 , then d's largest 'possible' value has to be -8.
-10 is smaller than -8=D
Answer: (D) -8
Question: A waitress's income consists of her salary and tips.During one week ,her tips were 7/4 of her salary.What fraction of her income for the week came from tips?
(A) 1/9
(B) 1/6
(C) 2/3
(D) 4/9
(E) 7/11
Rationale: Her tips were 7/4 of her salary.
Let's say her salary =$4
This mean her tips = (7/4)($4) =$7
So, her TOTAL INCOME =$4+$7=$11
What fraction of her income for the week came from tips
$7/$11= 7/11
= E
Answer: (E) 7/11
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 800 per sq. metre.
(A) Rs. 15000
(B) Rs. 15550
(C) Rs. 15600
(D) Rs. 16500
(E) None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (800 × 20.625) = 16500. Answer D
Answer: (D) Rs. 16500
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARIT', if repetition of letters is not allowed?
(A) 690
(B) 210
(C) 740
(D) 760
(E) 780
Rationale: The word 'LOGARIT' has 7 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 7P3
=
7
×
6×
5
=
210
Option B
Answer: (B) 210
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
(A) 1
(B) 2
(C) 5
(D) 6
(E) 8
Rationale: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Answer: (B) 2
Question: . A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit . For how long B’s money was used.
(A) 33
(B) 27
(C) 10
(D) 8
(E) 82
Rationale: Explanation:
B received 2/3 of the profit ⇒Their profits ratio = A : B = 1 : 2
Let the total capital = 4 units
Then A's capital = 1
B's capital = 3
Assume B's money was used for b months
Then A : B = 1 × 15 : 3 × b = 1 : 2
⇒ 15 : 3b = 1 : 2
⇒ 153b=12153b=12
⇒ b = 10
Answer: C
Answer: (C) 10
Question: Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ?
(A) 97.959%
(B) 98.959%
(C) 99.959%
(D) 96.959%
(E) 95.959%
Rationale: let the number be x
the right number is 7x
the wrong number is x/7
error is(7x-x/7)=48x/7
percentage of error is((48x/7)/7x)*100=97.959%
ANSWER:A
Answer: (A) 97.959%
Question: A certain ski shop sells pairs of gloves in 9 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?
(A) 1/144
(B) 1/143
(C) 1/24
(D) 1/23
(E) 1/17
Rationale: there are 9 different colours sothere are 9 pairs of gloves dropped..
first can be any of 18..so 18/18..
second has to be its pair, which will be just one out of remaining 17.. 1/17..
overall prob=18/18*1/17= 1/17..
E
Answer: (E) 1/17
Question: If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is :
(A) 4.25 kmph
(B) 6 kmph
(C) 6.5 kmph
(D) 8.5 kmph
(E) None of these
Rationale: Solution
Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C
Answer: (C) 6.5 kmph
Question: If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 75 percent of the test takers answered the second question correctly, and 15 percent of the test takers answered neither question correctly, what percent answered both correctly?
(A) 60 %
(B) 65 %
(C) 70%
(D) 75%
(E) 80%
Rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 75 - {Both correctly} + 15
{Both correctly} = 75.
Answer: D.
Answer: (D) 75%
Question: The unit digit in the product (635 * 767 * 984 * 489) is:
(A) 0
(B) 8
(C) 3
(D) 2
(E) 1
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (5*7*4*9) = 0
ANSWER: A
Answer: (A) 0
Question: If b does not equal zero, and ab = b/8, what is the value of a?
(A) A)1/8
(B) B)1/4
(C) C)1/3
(D) D)1/2
(E) of the above
Rationale: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/8
(ab)/b = (b/8)/b
a = (b/8)*1/b
a = 1/8
Answer: (A).
Answer: (A) A)1/8
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 11
(B) 22
(C) 44
(D) 55
(E) 79
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer:C
Answer: (C) 44
Question: The average weight of 8 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) kg
(B) 70 kg
(C) 80 kg
(D) 90 kg
(E) 93 kg
Rationale: Total weight increased = (8 x 3.5) kg = 28 kg.
Weight of new person = (65 + 28) kg = 93 kg.
E)
Answer: (E) 93 kg
Question: Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 80 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?
(A) 110
(B) 112
(C) 116
(D) 118
(E) 122
Rationale: This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/4)*(4x/5) is an integer
Or x/5 is an integer.
Hence we need the lowest multiple of 5 from the given options.
Let us start from the lowest value:
Option A: 110. This is a multiple of 5 Hence the correct answer.
Correct Option: A
Answer: (A) 110
Question: Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 70% of Mary and John’s combined income?
(A)  $3,000
(B)  $4,000
(C)  $7,000
(D)  $11,000
(E)  $27,000
Rationale: Let Mary's income increase by x, then the equation will be
15,000 + x= (70/100)* (15,000 + x + 18000 )
15,000 + x = (14/20) * (33,000 + x)
300,000 + 20x = 14x + 462,000
6x = 162,000
x = 27,000
So, Answer will be E
Answer: (E)  $27,000
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
(A) 610
(B) 720
(C) 825
(D) 920
(E) None of these
Rationale: Explanation :
The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels
should always come together. Hence these three vowels can be grouped and considered as a
single letter. That is, PTCL(OIA).
Hence we can assume total letters as 5. and all these letters are different.
Number of ways to arrange these letters = 5! = [5 x 4 x 3 x 2 x 1] = 120
All The 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves = 3! = [3 x 2 x 1] = 6
Hence, required number of ways = 120 x 6 = 720. Answer : Option B
Answer: (B) 720
Question: A rectangular plot measuring 15 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) 26m
(C) 26m
(D) 56m
(E) 25m
Rationale: Perimeter of the plot = 2(15+50) = 130m
no of poles =130/5 =26m
Answer: B
Answer: (B) 26m
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 50
(B) 99
(C) 88
(D) 77
(E) 51
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
Answer: (A) 50
Question: In the manufacture of a certain product, 9 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
(A) 0.125%
(B) 0.36%
(C) 0.8%
(D) 1.25%
(E) 2.0%
Rationale: Percent of defective produced = 9%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(9/100)*100%
= (36/10000)*100%
= (36/100)%
= .36 %
Answer B
Answer: (B) 0.36%
Question: If Janice was 21 years old z years ago and Lisa will be 19 years old in p years, what was the average (arithmetic mean) of their ages 8 years ago?
(A) (z + p)/2
(B) (z - p + 24)/4
(C) (z - p + 14)/4
(D) (z + p + 34)/2
(E) (z - p + 24)/2
Rationale: Today, J = z+21 and L = 19-p
8 years ago, J = z+13 and L = 11-p
The average of their ages was (z-p+24) / 2
The answer is E.
Answer: (E) (z - p + 24)/2
Question: Find all positive integers n such that n^2
+ 1 is divisible by n+ 1.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: There is only one such positive integer : n = 1.
In fact, n^2+1= n(n+1)-(n-1);
thus, if n+1|n^2+1, then n+1|n-1 which for positive integer n is possible only if n-1 = 0,
hence if n = 1.
Answer is 1
Answer: (A) 1
Question: 5 men are equal to as many women as are equal to 7 boys. All of them earn Rs.90 only. Men’s wages are?
(A) 8Rs.
(B) 7Rs.
(C) 6Rs.
(D) 4Rs.
(E) 5Rs.
Rationale: 5M = xW = 7B
5M + xW + 7B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
ANSWER:C
Answer: (C) 6Rs.
Question: The height of the wall is 6 times its width and length of the wall is 7 times its height .if the volume of the wall be 6804 cu.m.its width is
(A) 3m
(B) 5m
(C) 6m
(D) 7m
(E) 8m
Rationale: Explanation:
Let width = x
Then, height=6x and length=42x
42x Ã— 6x Ã— x = 6804
x = 3
Answer: A
Answer: (A) 3m
Question: In a village, there are four tribes located at different distances from each other. Tribe R is 60 miles away from Tribe P; Tribe S 40 miles away from Tribe B and Tribe R is 10 miles nearer to the Tribe S than it is to Tribe Q.
How far is the Tribe S located from the tribe P ?
(A) 23 km
(B) 24 km
(C) 25 km
(D) 26 km
(E) 27
Rationale: Solution:
25
Distance between Tribe Q and Tribe S = 40km
=> Distance between Tribe Q and Tribe R + Distance between Tribe R and Tribe S = 40km
=> Distance between Tribe Q and Tribe R + (Distance between Tribe Q and Tribe R - 10) = 40 km
=> 2 * Distance between Tribe Q and Tribe R = 50km
=> Distance between Tribe Q and Tribe R = 25km
Answer C
Answer: (C) 25 km
Question: A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 168 km downstream.
(A) 4 hours
(B) 5 hours
(C) 6 hours
(D) 7 hours
(E) 8 hours
Rationale: Explanation:
It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph
Time = distance/speed = 168/21 = 8 hours
Option E
Answer: (E) 8 hours
Question: In 1991, there are 28 days in February and there are 365 days in the year. In 1992, there are 29 days in February and there are 366 days in the year. If the date March 15, 1995 is a Tuesday, then which one of the following would the date March 15, 1996 be?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) Monday
Rationale: From the information given,March 15, 1992 is 366 days after March 15, 1991.
366 days = 52 weeks and 2 more days. Therefore if March 15, 1995 is a Tuesday, then March 15, 1996 is Tuesday + 2 days = Thursday
Answer: A
Answer: (A) Thursday
Question: IF
20= W
21= W
22= W
23= W
24= W
THEN 25=?
(A) I
(B) J
(C) W
(D) L
(E) M
Rationale: IF
21= W... Second letter of twenty one
22= W.... Second letter of Twenty two
23= W
24= W
25= W
THEN 26=W... Second letter of Twenty six
ANSWER:C
Answer: (C) W
Question: Look at this series: U32, V29, __, X23, Y20, ... What number should fill the blank?
(A) M43
(B) D14
(C) W26
(D) F24
(E) K81
Rationale: C
W26
In this series, the letters progress by 1; the numbers decrease by 3.
Answer: (C) W26
Question: If the length of the longest chord of a certain circle is 22, what is the radius of that certain circle?
(A) 11
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: Longest chord of a circle is the diameter of the circle
diameter = 2 * radius
If diameter of the circle is given as 22 = 2 * 11
so radius of the circle = 11
correct answer - A
Answer: (A) 11
Question: What is the smallest number Y which when increased by 5 is completely divisible by 8, 11 and 24?
(A) 264
(B) 259
(C) 269
(D) 270
(E) 282
Rationale: This question includes a number of great Number Property shortcuts that you can take advantage of:
1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.
2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.
3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.
The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.
Final Answer:
B
Answer: (B) 259
Question: The average monthly salary of 25 employees in an organisation is Rs. 2500. If the manager's salary is added, then the average salary increases by Rs. 200. What is the manager's monthly salary?
(A) Rs.7700
(B) Rs.3618
(C) Rs.3600
(D) Rs.3619
(E) Rs.3610
Rationale: Manager's monthly salary
= Rs. (2700 * 26 - 2500 * 25)
= Rs. 7700 Answer:A
Answer: (A) Rs.7700
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked three times as much as much chestnuts than Peter. Lucy picked 4 kg more than Peter. Together the three of them picked 29 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
(A) 9, 5 and 15
(B) 5, 15 and 9
(C) 15, 5 and 9
(D) 9, 15 and 5
(E) 5, 9 and 15
Rationale: M = 3P
L = P+4
M + P + L = 29
3P + P + (P+4) = 29
P = 5, M = 15, L = 9
Therefore, Mary, Peter, and Lucy picked 15, 5, and 9 kg, respectively.
The answer is C.
Answer: (C) 15, 5 and 9
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 18 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 17 books, how many shelves does the bookcase have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
11x - 18 = 7(x-1) + 17
4x = 28
x= 7
The answer is C.
Answer: (C) 7
Question: A company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 7 persons for the position of sales manager, 5 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hirings of these three people are possible?
(A) 7 + 5 + 10
(B) 7 × 5 × 10
(C) 21 × 20 × 19
(D) 7! + 5! + 10!
(E) 7! × 5! × 10!
Rationale: 1 sales manager can be selected out of 7 in 7 ways
1 clerk can be selected out of 5 in 5 ways
1 receptionist can be selected out of 10 in 10 ways
total no. of ways these 3 can be selected = 7 *4 * 10
Ans. B) 7 × 5 × 10
Answer: (B) 7 × 5 × 10
Question: Eight animals of a circus has to be placed inside in eight cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
(A) A.604
(B) B.2880
(C) C.502450
(D) D.784200
(E) E.302400
Rationale: ways for cages that are too small = 5*4*3*2=120
since we have 4 cages and 4 animal left therefore ways for 4 cages =4!
total ways =120*4!=2880
Answer B
Answer: (B) B.2880
Question: Sum of the squares of three numbers is 414 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 22
(C) 25
(D) 26
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 414 + 2* 131
a + b + c = √676 = 26
D
Answer: (D) 26
Question: A certain animal shelter has 26 horses and 36 cows. How many horses must be taken away from the animal shelter so that 75 percent of the animals in the shelter will be cows?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Suppose x horses need to be removed from the shelter.
After x horses are removed, the shelter shall have (26 - x) horses and the same 36 cows; and the total number of animals shall be (26 - x) + 36 = 62 - x
Now we want the 75 percent of animals in the shelter to be cows.
This means 75 percent of (62 - x) should be equal to the number of cows which is 36.
This means,
75 % of (62 - x) = 36
Solving above equation we get x = 14
x=14
Ans C
Answer: (C) 14
Question: Walking 7/6 of his usual rate, a boy reaches his school 2 min early. Find his usual time to reach the school?
(A) 14
(B) 28
(C) 99
(D) 77
(E) 66
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
2 --------- ? 14 m
Answer:A
Answer: (A) 14
Question: Company Z has 61 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
(A) 6
(B) 7
(C) 13
(D) 9
(E) 12
Rationale: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y =61.
Now, plug options for x. Only C and E give an integer value for y. But only for C x > y as needed.
Answer: C.
Answer: (C) 13
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 four years ago?
(A) 2
(B) 4
(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
four years ago
s= 6-4= 2
A is the answer
Answer: (A) 2
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
(A) 120 m
(B) 190 m
(C) 115 m
(D) 110 m
(E) 250 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 250 m
Answer: E
Answer: (E) 250 m
Question: In 2008, the profits of Company M were 5 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 124%
(D) 240%
(E) 138%
Rationale: the profit 0f 2009 in terms of 2008 = 0.8*15/5*100=240%
D
Answer: (D) 240%
Question: The speed of a car is 85 km in the first hour and 45 km in the second hour. What is the average speed of the car?
(A) 72 kmph
(B) 65 kmph
(C) 30 kmph
(D) 80 kmph
(E) 82 kmph
Rationale: S = (85 + 45)/2
= 65 kmph
ANSWER:B
Answer: (B) 65 kmph
Question: A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 64 ounces of nuts, representing a mixture of both brands, and 14 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
(A)  14
(B)  20
(C)  32
(D)  44
(E)  48
Rationale: lets say x ounces of P is mixed with Q.
=> 64-x ounces of Q is present in the mixture (as the total = 64 ounces)
given total almond weight = 14 ounces
(20x/100)+(25/100)(64-x) = 14
=> x = 40
=> 64-40 = 14 ounces of Q is present in the mixture.
Answer is A.
Answer: (A)  14
Question: If x is a prime number, and x-1 is the median of the set {x-1, 3x+3, 2x-4}, then what is the average (arithmetic mean) of the set?
(A) 2
(B) 5/3
(C) 3
(D) 10/3
(E) 14/3
Rationale: If x is a prime number, and x-1 is the median of the set {x-1, 3x+3, 2x-4}, then what is the average (arithmetic mean) of the set?
A. 2
B. 5/3
C. 3
D. 10/3
E. 14/3
Solution:
x-1 is the median of the set, implies if we arrange the set in ascending order, the set would be [2x-4, x-1, 3x+3]. This means that:
2x-4<x-2<3x+3
solving inequality gives x>-2 and x<3. Since x is prime number and the only prime number <3 is 2, so put x=2.
Hence set becomes: [ 0, 1, 9] and avg = 10/3.D
Answer: (D) 10/3
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 60, find the other?
(A) 100
(B) 240
(C) 120
(D) 200
(E) 150
Rationale: Other number = 12*600/60= 120
Answer is C
Answer: (C) 120
Question: A car salesman earns a base salary of $1,000 per month plus a commission of $200 for each car he sells. If the car salesman earned $2000 in March, how many cars does he need to sell in April in order to double his March earnings?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 1000+200x=4000
x=15 cars.
The answer is B.
Answer: (B) 15
Question: The average weight of a group of boys is 30 kg. After a boy of weight 37 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) 6
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 37 kg joins the group, total weight of boys = 30x + 37
So 30x + 37 + 31(x + 1) = > x = 6.
Answer: E
Answer: (E) 6