mathewhe/aqua_rat huggingface dataset:
Question: A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum Z of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?
(A)  5
(B)  7
(C)  9
(D)  10
(E)  14
Rationale: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum Z of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D
Answer: (D)  10
Question: If $0.80 is the commission for sales of $2,000, what percent of the sales amount is the commission?
(A) 4%
(B) 0.4%
(C) 0.04%
(D) 0.004%
(E) 0.0004%
Rationale: % of sales amount of commission
= (Commission/Total Value) *100
= (0.8/2000) * 100
= 0.04%
The answer is C.
Answer: (C) 0.04%
Question: A bookseller sells his books at a 10% markup in price. If he sells a book for $11.00, how much did he pay for it?
(A) $14.40
(B) $14.00
(C) $10.00
(D) $9.60
(E) $5.00
Rationale: Let the cost price of book = x
Selling price of book = 11$
Markup % = 10
(110/100)x = 11
=> x = 10
Answer C
Answer: (C) $10.00
Question: Which of the following could be the sides of an obtuse angled triangle? all values are in degree
I. 19, 29, 39
II. 29, 39, 49
III. 10,110, 60
(A) III only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: obtuse angled triangle means one angle more than 90deg and total 180 deg.. III
A
Answer: (A) III only
Question: With what number must 6.2587 be multiplied in order to obtain the number 625.87?
(A) 1000
(B) 1,0000
(C) 100
(D) 100,000
(E) None of these
Rationale: Explanation: The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.
Answer : (C)
Answer: (C) 100
Question: Students of three different classes appeared in common examination. Pass average of 10 students of first class was 60%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
(A) 74%
(B) 75%
(C) 69%
(D) 70%
(E) None
Rationale: Solution:
Sum of pass students of first, second and third class,
= (60% of 10) + (60% of 15)+ (80% of 25)
= 6+9+20 = 35
Total students appeared,
= 10+15+25 = 50
Pass average,
= 35*100/50 = 70%.
Answer: Option D
Answer: (D) 70%
Question: A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
(A) 7 km/hr
(B) 7.2 km/hr
(C) 7.4 km/hr
(D) 7.8 km/hr
(E) 8.9 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: (B) 7.2 km/hr
Question: Which of the following inequalities is always true for any non-negative real numbers numbers 'x' and 'y'?
(A) (x-y)^2 >= x^2 + y^2
(B) (x+y)^2 <= x^2 + y^2
(C) (x+y)^2 = x^2 + y^2
(D) (x+y)^2 <= x^2 + y^2
(E) (x+y)^2 >= x^2 + y^2
Rationale: Using the concept of superadditivity, we know that for non-negative real numbers the square of the sum of x and y will always be more than the sums of x and y separately; this is a superadditive function. Therefore the answer is E.
Answer: (E) (x+y)^2 >= x^2 + y^2
Question: In a certain sequence, the first term is 2, and each successive term is 2 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
(A) 13/8
(B) 21/13
(C) 58/5
(D) 70/29
(E) 82/13
Rationale: let five terms in the sequence be a,b,c,d,e
a=2
b= 2+1/2=5/2
c=2+2/5= 12/5
d= 2+5/12 = 29/12
e= 2+12/29 = 70/29
hence answer should be D.
Answer: (D) 70/29
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 74 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Total Distance = 74 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 70 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 70 / 10 = 7 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 7 = 28+4 = 32 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 32 /4 = 8 hrs ... Answer E
Answer: (E) 8
Question: The number of roots common between the two equations x3 + 3x2 + 4x + 5 = 0 and x3 + 2x2 + 7x + 3 = 0 is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Explanation :
Let α is the common root.
∴ α3 + 3α2 + 4α + 5 = 0. ............................(i)
α3 + 2α2 + 7α + 3 = 0. .............................(ii)
On subtracting (ii) from (i), we get
α2 - 3α + 2 = 0.
α = 2, α = 1.
But the above values of α do not satisfy any of the equations. Thus, no root is common.
Answer : A
Answer: (A) 0
Question: If 4XZ + YW = 4 and XW + YZ = 8, what is the value of the expression (2X + Y)(2Z + W)?
(A) 22
(B) 20
(C) 24
(D) 26
(E) 28
Rationale: (2x+y)*(2z+w) = 4+2(8) =20
Answer : B
Answer: (B) 20
Question: B completes a work in 7 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?
(A) 3.75 days
(B) 4.11 days
(C) 5.11days
(D) 6.75 days
(E) 7.33 days
Rationale: 1/7 + 1/10 = 17/70
70/17 = 4.11 days
ANSWER:B
Answer: (B) 4.11 days
Question: In one hour, a boat goes 8 km along the stream and 2 km against the stream. the sped of the boat in still water (in km/hr) is :
(A) 3
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: Solution
Speed in still water= 1/2(8+2) km/hr= 5kmph. Answer B
Answer: (B) 5
Question: If x/4 + 24/x = 5, what are the values of 2x - 7?
(A) 8 and 9
(B) 8 and 24
(C) 17 and 21
(D) 12 and 29
(E) 17 and 9
Rationale: I got the same thing E is the answer 9 or 17
Answer: (E) 17 and 9
Question: There are three departments having students 62,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
(A) 72
(B) 74
(C) 75
(D) 76
(E) 77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 62/2 = 31
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 31+12+29 = 72
ANSWER:A
Answer: (A) 72
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 350 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 237
(B) 287
(C) 197
(D) 287
(E) 700
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 350) = 2 + 2(extra)
=> 2x - 700 = x => x = 700.
Answer: E
Answer: (E) 700
Question: P runs 25% faster than Q so P gives Q a 60 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: Let D be the race distance that P ran.
Let T be the time it took to complete the race.
Let V be Q's speed.
T = D/1.25V = (D-60) / V
D=1.25D-75
0.25D=75
D=300 meters.
The answer is C.
Answer: (C) 300
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64500. What is his profit percent?
(A) 22
(B) 77
(C) 17.3
(D) 99
(E) 88
Rationale: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64500
Profit(%) = (64500 - 55000)/55000 * 100 = 17.3%
Answer: C
Answer: (C) 17.3
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 5
(B) 2
(C) 9
(D) 5
(E) 1
Rationale: 1250
= D(100/4)2
D = 2
Answer: B
Answer: (B) 2
Question: Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: For: (2^(3x+3)+3)/3
Let n = 3x + 3
2^n
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....
Rule: x^(m+n) = (x^m)(x^n)
(2^(3x))(2^3)
Rule: x^(mn) = (x^m)^n
((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1.
Answer: B
Answer: (B) 1
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party W. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
(A) 15
(B) 20
(C) 30
(D) 35
(E) 45
Rationale: S=100
not( W and B ) =35
only W=20
(W and B)/B=1/2
let ( W and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Answer: (A) 15
Question: If x < y < z and y-x > 11, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
Rationale: We have:
1) x<y<z
2) y-x>11
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>11, the least value for y-x must be 13, the least value for x must be 2, and, thus, the least possible value for y must be 15 (y-2=13, y=15)
2<15<z, since z is odd, the least possible value for z is 17
z-x=17-2=15
Answer E
Answer: (E) 15
Question: The profit obtained by selling an article for Rs. 66 is the same as the loss obtained by selling it for Rs. 22. What is the cost price of the article?
(A) Rs. 40
(B) Rs. 50
(C) Rs. 49
(D) Rs. 59
(E) Rs.44
Rationale: S.P 1- C.P = C.P – S.P 2
66 - C.P = C.P - 22
2 C.P = 66 + 22;
C.P = 88/2 = 44
ANSWER:E
Answer: (E) Rs.44
Question: If 25% of a number is equal to one-third of another number, what is the ratio of first number to the second number?
(A) 4:3
(B) 1:4
(C) 3:7
(D) 6:11
(E) 2:3
Rationale: Let 25% of A = 1/3 B
then 25A/100 = 1B/3
A/4 = B/3
A/B = 4/3
A:B = 4:3
Answer is A
Answer: (A) 4:3
Question: If 7a - 3b = 10b + 50 = -12b - 2a, what is the value of 9a + 9b?
(A) -9
(B) -6
(C) 0
(D) 6
(E) 9
Rationale: (i) 7a - 13b = 50
(ii) 2a + 22b = -50
Adding (i) and (ii):
9a + 9b = 0
The answer is C.
Answer: (C) 0
Question: A pupil's marks were wrongly entered as 73 instead of 40. Due to the average marks for the class got increased by half. The number of pupils in the class is?
(A) 18
(B) 82
(C) 66
(D) 27
(E) 77
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (73 - 40) => x/2
= 33 => x = 66.
Answer: C
Answer: (C) 66
Question: On a scale that measures the intensity of a certain phenomenon, a reading of a+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of a. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
(A)  5
(B)  50
(C)  10^5
(D)  5^10
(E)  8^10 - 3^10
Rationale: To solve this problem we need to examine the information in the first sentence. We are told that “a reading of a + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of a.”
Let’s practice this idea with some real numbers. Let’s say a is 2. This means that a + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.
Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.
Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.
We have found a pattern, which can be applied to the problem presented in the stem:
3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.
4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.
5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.
We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.
Answer C.
Answer: (C)  10^5
Question: Two family reunions are happening at the same hotel, the Oates reunion and the Yellow reunion. All 100 guests at the hotel attend at least one of the reunions. If 42 people attend the Oates reunion and 65 people attend the Yellow reunion, how many people attend both reunions?
(A)  2
(B)  7
(C)  10
(D)  16
(E)  22
Rationale: No of people in Oates reunion=42
No of people in Yellow reunion=65
Attending both=x
All guests attend at least one.
Therefore, 100=42+65-(Both)
Both=7
Answer B
Answer: (B)  7
Question: Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed?
(A) Tuesday
(B) Wednesday
(C) Saturday
(D) Sunday
(E) Monday
Rationale: This type of story problem is essentially just about a repeating pattern and a 'remainder.'
We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on.
Since the task was supposed to be completed on a Wednesday....
A 1 day postponement would be Thursday
A 2 day postponement would be Friday
A 3 day postponement would be Saturday
A 4 day postponement would be Sunday
A 5 day postponement would be Monday
A 6 day postponement would be Tuesday
A 7 day postponement would be Wednesday
A 8 day postponement would be Thursday
Etc.
So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days.
45/7 = 6 remainder 3
This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday.
C
Answer: (C) Saturday
Question: If abc = ab^3 = 180 where a, b and c are positive integers, what is the value of `c’?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: abc = a(b^3) = 180
on solving abc = a(b^3) we get c = b^2
and for a(b^3) = 180 , there is only one possibility a = 180 and b = 1 so c = 1^2 = 1
ANSWER:B
Answer: (B) 1
Question: Find the number of ways in which 8064 can be resolved as the product of two factors?
(A) 22
(B) 24
(C) 21
(D) 20
(E) 19
Rationale: Solution:
Total number of ways in which 8064 can be resolved as the product of two factors is 24 as below:
(1,8064), (2,4032), (3,2688), (4,2016), (6,1344), (7,1152),(8,1008), (9,896), (12,672), (14,576), (16,504), (18,448), (21,884), (24,336), (28,288), (32,252), (36,224), (42,192), (48,168), (56,144), (63,128), (68,126), (72,112), (84,96).
Answer: Option B
Answer: (B) 24
Question: How many paying stones, each measuring 4 m * 2 m are required to pave a rectangular court yard 40 m long and 20 m board?
(A) 99
(B) 18
(C) 100
(D) 17
(E) 12
Rationale: 40 * 20 = 4 * 2 * x => x
= 100
Answer: C
Answer: (C) 100
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
(A) 2277
(B) 2882
(C) 2800
(D) 2677
(E) 2211
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Answer: C
Answer: (C) 2800
Question: A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 900. How many workers were part of the latter production run?
(A) A)6
(B) B)10
(C) C)11
(D) D)15
(E) E)34
Rationale: The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1
5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 900 .. thus for the current period = 900 -500 = 400
(5n+45)K= 400
k = 400/5n+45........................................2
equate 1 and 2
500/5n+20 = 400 /5n+45
500(5n+45) = 400(5n+20)
25n + 225 = 20n + 80
5n =145
n = 29
thus n+5 = 34
hence E
Answer: (E) E)34
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage?
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 9%
Rationale: The difference of two successive amounts must be the simple interest in 1 year on
the lower amount of money.
S.I = 18522/- - 17640/- = Rs. 882/-
Rate of interest = (882/17640) × (100/1) => 8820/1764 = 5%
Principal = Amount/(1 + R/100)n
= 17640/(1 + 5/100)2
= 17640/(21/20 × 21/20)
= 17640/(1.05 × 1.05)
= 17640/1.1025
= 16000
Thus the principal is Rs.16000/- and the rate of interest is 5%
A
Answer: (A) 5%
Question: An urn contains g green marbles and b blue marbles. If 3 green marbles and 4 blue marbles are added, and then one marble is selected at random from the urn, what is the probability that a blue marble will be drawn?
(A) b/(b+g)
(B) (b+5)/(g+3)
(C) (b+5)/(b+g+8)
(D) (b+4)/(b+g+7)
(E) b/(b+g+5)
Rationale: no of fav outcomes i.e. blue MArbles = b+4
Total no of outcomes i.e. total Marbles = (b+4)+(g+3)= b+g+7
probability = (b+4) /(b+g+7)
Answer D
Answer: (D) (b+4)/(b+g+7)
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.300 when the rate to profit rises from 5 to 7 percent. Find the Capital of C?
(A) 3377
(B) 2899
(C) 3750
(D) 2778
(E) 1991
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 300
C's capital = 22500*1/6 = 3750
Answer: C
Answer: (C) 3750
Question: Walking at 5/6th of its usual speed a cab is 6mnts late. Find its usual time to cover the journey?
(A) 25m
(B) 30m
(C) 32m
(D) 50m
(E) 62m
Rationale: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 6m
UT/5 = 6m
UT = 30m
Answer is B
Answer: (B) 30m
Question: A certain auto manufacturer sold 4% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 63,000
(B) 2,000,000
(C) 2,030,000
(D) 2,040,000
(E) 2,300,000
Rationale: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.
97/100×2100=2037
-->2,037,000 sold in 2007. When rounded to the nearest 10,000 :
2,000,000
B
Answer: (B) 2,000,000
Question: If (12z)/(5 - 6x/y) = 4z then which of the following is true?
(A) 2x = 3y
(B) 3x = 2y
(C) x = 3y
(D) 3x = y
(E) 2x = y
Rationale: (12z)/(5 - 6x/y) = 4z
=> 12zy/(5y - 6x) = 4z
=> 3y/(5y -6x) = 1
=> 3y = 5y - 6x
=> -2y = -6x
=> y = 3x
Hence Ans is D
Answer: (D) 3x = y
Question: The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
(A) 1
(B) 6
(C) 7
(D) 8
(E) 2
Rationale: Explanation:
x + y = 25
xy = 144
(x- y)2 = (x + y)2 â€“ 4xy
(x- y)2 = 625 â€“ 576 => (x â€“ y) = 7
Answer: C
Answer: (C) 7
Question: 76 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 13.25
(B) 38.25
(C) 33.25
(D) 34.25
(E) 31.25
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 76 = 33.25
ANSWER:C
Answer: (C) 33.25
Question: A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
(A) 144
(B) 377
(C) 377
(D) 288
(E) 271
Rationale: Explanation:
Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = Rs. (378 * 8/21) = Rs. 144.
Answer: A) 144
Answer: (A) 144
Question: Of the 50 researchers in a workgroup, 50 percent will be assigned to Team A and the remaining 50 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
(A)  15
(B)  17
(C)  10
(D)  25
(E)  30
Rationale: I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
50 will be in team A
50 will be in team B
The larger diff is
70 want team A so diff is 70-50=20. At least 20 people will NOT get their wish, so for 50 researchers the same number is 10.
Answer choice C
Answer: (C)  10
Question: John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
(A) 66.5%
(B) 96.5%
(C) 56.5%
(D) 46.5%
(E) 26.5%
Rationale: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 402
Let M be the books NOT sold
M = 1200 - N = 1200 - 402 = 798
Percentage
Books not sold / total number of books = 798/1200 = 0.665 = 66.5%
correct answer A
Answer: (A) 66.5%
Question: In a class,9 students like to play Basketball and 8 like to play Cricket. 6 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
(A) 12
(B) 11
(C) 16
(D) 18
(E) 22
Rationale: Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
9 +8 - 6 = 11
B)
Answer: (B) 11
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 5667
(C) 5525
(D) 2466
(E) 2665
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer: Option A
Answer: (A) 3944