mathewhe/aqua_rat huggingface dataset:
Question: An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of B?
(A) 360
(B) 358
(C) 356
(D) 514
(E) 504
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of B = 4/13 * 1638 = Rs. 504
Answer: E
Answer: (E) 504
Question: A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
(A) $200
(B) $333.33
(C) $100.25
(D) $277.78
(E) $377.00
Rationale: Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 )
$25000 is 60% of total amount.
So total amount = 25000 * 100/60
Remaining amount is 40% of total amount.
40% of total amount = 25000 * (100/60) * (40/100) = 50000/3
This amount has to be divided by 50( remaining people are 50 )
So per head amount is 50000/3 / 50 = 32000/180 = 333.33;
ANSWER:B
Answer: (B) $333.33
Question: In a company of 11 employees, 5 employees earn $32,000, 4 employees earn $45,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 11 employees is $48,000, what is the annual salary for each of the highest-paid employees?
(A) $90,000
(B) $94,000
(C) $98,000
(D) $102,000
(E) $106,000
Rationale: 5*32,000+4*45,000+2x=11*48,000
2x=528,000-160,000-180,000
2x=188,000
x=94,000
The answer is B.
Answer: (B) $94,000
Question: (1000)7÷(10)16=?
(A) 10
(B) 100
(C) 1000
(D) 100000
(E) None of these
Rationale: Explanation:
=(103)7/(10)16
=(10)21/(10)16=10(5)=100000
Option D
Answer: (D) 100000
Question: Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 54
(B) 59
(C) 63
(D) 71
(E) 62
Rationale: Total = 70
Thrower = 46
Rest = 70 - 46 = 24
Left Handed = 24/3 = 8
Right handed = 16
If all Thrower are right handed then total right handed is 46 + 16 = 62
so E. 62 is the right answer
Answer: (E) 62
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:
(A) 70 km/hr
(B) 75 km/hr
(C) 84 km/hr
(D) 87.5 km/hr
(E) 77.5 km/hr
Rationale: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours,
then the speed of the first train = 400/4= 100 kms/hr
then the speed of the first train is:100*7/8 = 700/8 = 87.5 km/hr
ANSWER:D
Answer: (D) 87.5 km/hr
Question: One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?
(A) 11 km
(B) 13 km
(C) 16 km
(D) 18 km
(E) 19 km
Rationale: Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9
4 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
C
Answer: (C) 16 km
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
(A) 9
(B) 12
(C) 14
(D) 15
(E) 60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
=3*20=60
E. 60
Answer: (E) 60
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability R that at least one will be orange?
(A) R=7/10
(B) R=3/5
(C) R=2/5
(D) R=3/10
(E) 1/10
Rationale: Method 1
Probability R that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Answer: (A) R=7/10
Question: Which of the following options is an arithmetic sequence?
I. m-9, n-5, o-9,p-9, q-9, r-9
II. m^5, n^5, o^5, p^5, q^5
III. 4m,4n,4o,4p,4q
(A) I only
(B) I and II
(C) I and III
(D) II and III
(E) III only
Rationale: lets look at the three choices...
I. m-9, n-5, o-9,p-9, q-9, r-9
since the difference is not constant, it is not an arithmetic sequence...
II. m^5, n^5, o^5, p^5, q^5
since the difference is not constant, it is not an arithmetic sequence
III. 4m,4n,4o,4p,4q
since the difference is constant it is an arithmetic sequence...
The answer is E)
Answer: (E) III only
Question: Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
(A) Rs. 692.80
(B) Rs. 905
(C) Rs. 990
(D) Rs. 1385
(E) None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 735 x 3 - 650 x 2 Rs.
= 905 Rs.
Correct Option: B
Answer: (B) Rs. 905
Question: In how many ways the word "RITUAL" can be arranged?
(A) 120
(B) 240
(C) 720
(D) None
(E) Cannot be determined
Rationale: Explanation :
The required number of ways = 6!
= 720
Answer : C
Answer: (C) 720
Question: 210 reputed college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
(A) 25
(B) 40
(C) 50
(D) 60
(E) 75
Rationale: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: (B) 40
Question: 5 identical snow plows can clear an iced parking lot in 24 hours. How long would it take 6 such snow plows to clear the same parking lot?
(A) 1 hour, 15 minutes
(B) 2 hours, 30 minutes
(C) 3 hours
(D) 7 hours, 30 minutes
(E) 20 hourss
Rationale: 6/5 as many plows will take 5/6 as many hours --> 24*5/6=20 hours.
Answer: E.
Answer: (E) 20 hourss
Question: If |q|=−q, which of the following must be true?
(A) q≥0
(B) q≤0
(C) q2>x
(D) x3<0
(E) 2x<x
Rationale: |q| =-q means absolute value of q is equal to negative of q. Since absolute value cannot be negative hence negative of q should result in a non negative number. It means q is a non positive number i.e. q<0. Answer is B
Answer: (B) q≤0
Question: If a whole number n is divided by 4, we will get 3 as remainder. What will be the remainder if 2n is divided by 4 ?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Explanation:
Let n ÷ 4 = p , remainder = 3
=> n = 4p + 3
2n = 2(4p + 3)
= 8p + 6
= 8p + 4 + 2
= 4(2p + 1) + 2
Hence, if 2n is divided by 4, we will get 2 as remainder.
Answer: C
Answer: (C) 2
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
(A) 27 sec
(B) 87 sec
(C) 67 sec
(D) 47 sec
(E) 37 sec
Rationale: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300x 18 / 40 x 5 = 27 seconds.
Answer: A
Answer: (A) 27 sec
Question: How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.
(A) 648
(B) 720
(C) 890
(D) 980
(E) None of these
Rationale: Explanation :
Since, there is no repetition, numbers 1 to 6 will always be present in the 6 digit number.
We will go through this step by step.
Divisible by 1 and 1 at the unit place:
_ _ _ _ _ 1
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 2 and 2 at the unit place:
_ _ _ _ _ 2
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 3 and 3 at the unit place:
_ _ _ _ _ 3
Since, any number will have all the digits from 1 to 6 and the sum 1 + 2 + 3 + 4 + 5 + 6 = 21 is divisible by 3
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 4 and 4 at the unit place:
_ _ _ _ _ 4
Here, there are two cases
_ _ _ _ 2 4
This gives 4 x 3 x 2 x 1 = 24 numbers.
_ _ _ _ 6 4
This gives 4 x 3 x 2 x 1 = 24 numbers.
This gives us total of 24 + 24 = 48 numbers.
Divisible by 5 and 5 at the unit place:
_ _ _ _ _ 5
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 6 and 6 at the unit place:
_ _ _ _ _ 6
As all 6 digit numbers formed with 1 to 6 digits(without repetition) are divisible by 3 and numbers with 6 at the unit place are even.
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
None of these cases will have numbers overlapping with each other.
So, Total numbers = 120 + 120 + 120 + 48 + 120 + 120 = 648
Answer : A
Answer: (A) 648
Question: One year ago, Priya was four times as old as her daughter Sneha. Six years hence, Priya’s age will exeed her daughter’s age by 9 years. The ratio of the present ages of Priya and her daughter is :
(A) 9 : 2
(B) 11 : 3
(C) 12 : 5
(D) 13 : 4
(E) 13 : 6
Rationale: Let the ages of Priya and Sneha 1 year ago be 4x and x years respectively.
Then, [(4x + 1) + 6] - [(x + 1) + 6] = 9
3x = 9
x = 3
Required ratio = (4x + 1) : (x + 1) = 13 : 4
ANSWER:D
Answer: (D) 13 : 4
Question: A car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Let T be the total time of the trip.
35*4 + 44(T-4) = 38T
6T = 176-140
T = 6
The answer is A.
Answer: (A) 6
Question: A store sells a certain product at a fixed price per unit. At the product's current price, v units cost a total of exactly $300. If the price were lowered by $5 from its current value, then v + 2n units would cost exactly $300; if the price were raised by $5, then v – n units would cost exactly $300. What is the value of v?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p v pv = 300
p-5 v+2n (p-5)(v+2n) = 300
p+5 v-n (p+5)(v-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So v = 20 satisfies all equations!!
Answer: (C) 20
Question: It would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
(A) 72/17
(B) 17/72
(C) 14/24
(D) 24/56
(E) 34/56
Rationale: The rate of the first machine is 1/9 job per hour;
The rate of the second machine is 1/8 job per hour;
Thus, the combined rate of the machines is 1/9+1/8=17/72 job per hour, which means that it takes 1/(17/72)=72/17 hours both machines to do the job.
Answer: A.
Answer: (A) 72/17
Question: find the average of first 20 multiples of 7?
(A) 73.5
(B) 70.5
(C) 63.5
(D) 54.5
(E) 40.5
Rationale: Required average =7(1+2+3+…….+20)/20
(7*20*21)/(20*2)
(147/2)=73.5.
ANSWER A 73.5
Answer: (A) 73.5
Question: Out of 8 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
(A) 7/8
(B) 9/10
(C) 11/12
(D) 13/14
(E) 15/16
Rationale: P(no graduates) = 4C3 / 8C3 = 4/56 = 1/14
P(at least one graduate) = 1- 1/14 = 13/14
The answer is D.
Answer: (D) 13/14
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.51 more than Jane, what was the original price of the dish?
(A)  24
(B)  34
(C)  37.8
(D)  42
(E)  84
Rationale: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.51--> 15p - 13.5p = 51 --> p = 34.
Answer: B.
Answer: (B)  34
Question: Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
(A) y + 3z
(B) (y +z) / 4
(C) 5y + 3z
(D) 3y + z
(E) 3y + 4.5z
Rationale: Soln:
The resulting equation is
=> (.01x + .05y + .03z)/(x+y+z) = 1.5/100
=> x + 5y + 3z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 5y + 3z
Ans is C
Answer: (C) 5y + 3z
Question: If x is divisible by 3, 14, and 15, which of the following must be the least multiple of x?
(A) 308
(B) 210
(C) 200
(D) 120
(E) 100
Rationale: If x is divisible by 3, 14, and 15, then x must be a multiple of 3,14 and 5.
Hence,the least multiple of x will be 3*14*5=210.
ANSWER:B
Answer: (B) 210
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1450?
(A) Rs.1000
(B) Rs.1250
(C) Rs.1010
(D) Rs.10000
(E) None of these
Rationale: Explanation:
1450 = P [1 + (5*16/5)/100]
P= 1250
Answer: Option B
Answer: (B) Rs.1250
Question: How many different section of 4 books can be made from 10 different books if two particular books are always selected?
(A) 36
(B) 38/
(C) 26
(D) 28
(E) 24
Rationale: This means two books are seclected out of the remaining 8 books. Required number of ways = 8C2= 8!/6!x2!=28. Ans: D.
Answer: (D) 28
Question: 4 couples are seating at a round tables how many ways can the 4 women sit together
(A) 4!*4!
(B) 3!*4!
(C) 4!*3!
(D) 5!*4!
(E) 6!*4!
Rationale: 4 men can be arranged around a table in (4-1)!=3! ways;
Now, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways.
So, total # of ways is 3!*4*4!=4!*4!
ANS:A
Answer: (A) 4!*4!
Question: 417 + 4.017 + 0.417 + 4.0017 = ?
(A) 425.4357
(B) 423.7563
(C) 629.6357
(D) 425.5637
(E) 629.6753
Rationale: 417
4.017
0.417
+ 4.0017
--------
425.4357
---------
Answer is A
Answer: (A) 425.4357
Question: If the radius of a circle is increased by 60% then the area is increased by:
(A) 44%
(B) 120%
(C) 156%
(D) 40%
(E) None of the above
Rationale: initially A=pi*r2
now R2=160/100r
then area=Pi*(160R/100)2
area=256R/100
that is area increases from 100 to 256=increase in area=156%
ANSWER:C
Answer: (C) 156%
Question: A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?
(A) (5y-1)/(755-y)
(B) 5/(755+y)
(C) 5y/(755+y)-1
(D) 5y/(755+y)
(E) 5y
Rationale: The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y).
Answer: B.
Answer: (B) 5/(755+y)
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the
probability that it is neither blue nor green?
(A) 2/3
(B) 8/21
(C) 3/7
(D) 9/22
(E) None of these
Rationale: Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: B
Answer: (B) 8/21
Question: From a pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ?
(A) 1/212
(B) 1/223
(C) 1/221
(D) 2/213
(E) 3/313
Rationale: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Answer: (C) 1/221
Question: When p is divided by 9, the remainder is 8. All of the following are possible values of p, except for which of the following?
(A) 17
(B) 35
(C) 53
(D) 61
(E) 71
Rationale: Four of these numbers can be expressed in the form of 9x+8, where x can be 0,1,2,3,4....
However, 61 = 9(6) + 7
The answer is D.
Answer: (D) 61
Question: A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?
(A) 30%
(B) 40%
(C) 50%
(D) 65%
(E) 72%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% = 10 × 100 = 50%
20
Profit of 50 % was made by the merchant.
C
Answer: (C) 50%
Question: The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is:
(A) 111 cm2
(B) 148cm2
(C) 154cm2
(D) 259cm2
(E) 269cm2
Rationale: 2πr-r=37 or (2π-1)r=37.
Or (2* 22/7 -1)r=37 or 37r/7=37 or r=7.
Therefore, Area= πr2= (22/7 *7*7)= 154 cm2
ANSWER:C
Answer: (C) 154cm2
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) Rs.3919
(B) Rs.3910
(C) Rs.3997
(D) Rs.3900
(E) Rs.3902
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer:D
Answer: (D) Rs.3900
Question: There are three prizes to be distributed among nine students. If no students gets more than one prize, then this can be done in?
(A) 10
(B) 45
(C) 5
(D) 84
(E) None of these
Rationale: Explanation :
3 prize among 9 students can be distributed in 9C3 ways = 84 ways.
Answer : D
Answer: (D) 84
Question: What percentage of numbers from 1 to 70 have squares that end in the digit 1?
(A) 90%
(B) 28%
(C) 20%
(D) 23%
(E) 12%
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such numbers = 14.
Required percentage = (14/70 * 100) =20%
Answer:C
Answer: (C) 20%
Question: Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1265
(C) 1350
(D) 1467
(E) 1647
Rationale: Let the smaller number be x. Then larger number = (x + 1375).
x + 1375 = 6x + 15
5x = 1360
x = 272
Large number = 272+1375 = 1647
E
Answer: (E) 1647
Question: An ant walks an average of 1000 meters in 30 minutes. A beetle walks 10% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?
(A) 1.8
(B) 1.6
(C) 2.775.
(D) 1.9
(E) 3.5.
Rationale: the ant walks an average of 1000 meters in 30 minutes
1000 meters in 1/2 hours
the beetle walks 10% less distance = 1000-10=900 meters in 30 minutes
0.900 km in 30/60 = 1/2 hours
speed = 0.900*2= 1.8 km/h
I guess option A should be 1.8
Answer: (A) 1.8
Question: A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days.If they get Rs 1500 for the whole work, the daily wages of B and C are?
(A) 225
(B) 276
(C) 126
(D) 187
(E) 1267
Rationale: Explanation:
Let the total work = 30 units.
Then capacity of A = 3 units, B = 2 units. Now they worked for 5 days. So they must have completed 25 units. Rest of the work 5 units done by C in 2 days. So C capacity = 5/2 = 2.5 units.
Given that toatal wages are Rs.1500 for 30 units. So for 1 unit of work they get Rs.50. Now B and C per day work = (2 + 2.5) = 4.5 units. So their daily wages = 4.5 × 50 = Rs.225
Answer:A
Answer: (A) 225
Question: In a nationwide poll, N people were interviewed. If 1/5 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
(A) N/8
(B) 6N/7
(C) 4N/15
(D) 7N/15
(E) 14N/15
Rationale: The number of people who answered yes to both questions is (1/3)(1/5)N = N/15
The number of people who did not answer yes to both is 1 - N/15 = 14N/15
The answer is E.
Answer: (E) 14N/15
Question: Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?
(A) $6.80
(B) $8.40
(C) $7.70
(D) $4.70
(E) $3.90
Rationale: Linda spent
1.20 ? 3 = $3.60 on notebooks
The total amount of money that Linda spent is equal to
3.60 + 1.50 + 1.70 = $6.80
correct answer A
Answer: (A) $6.80
Question: The present ages of three persons are in proportions 4:7:9.Thirteen years ago, the sum of their ages was 81. Find their present ages.
(A) 24, 42
(B) 28, 36
(C) 35, 45
(D) 35, 55
(E) of these
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 13) + (7x - 13) + (9x - 13) = 81
20x = 120 => x = 6
Their present ages are 24, 42 and 54 years respectively.
ANSWER:A
Answer: (A) 24, 42
Question: 57+58=115. How many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: since 2+3=5 & 7+8=15
any combination with these no be will give u desirable result...
so total no in 100 will be 20 & that's why in 1000,it will be 20X15=300.
ANSWER:C
Answer: (C) 300
Question: The average (arithmetic mean) monthly income of four workers is $1,000. After one worker’s income increases by 50 percent the new average income is $1,200. What was the original income of the worker whose monthly income increased?
(A) $1,800
(B) $1,500
(C) $1,300
(D) $1,600
(E) $1,100
Rationale: Increase in total income was 200*4=$800, we know that this increase was 50% (1/2) of the workers original income, thus his/her original income was 800*2=$1,600.
Answer: D
Answer: (D) $1,600
Question: What is the largest 4 digit number exactly divisible by 35?
(A) 4676
(B) 4678
(C) 9975
(D) 9504
(E) 9936
Rationale: Largest 4 digit number = 9999
9999 ÷ 35 = 285, remainder = 24
Hence largest 4 digit number exactly divisible by 88
= 9999 - 24 = 9975
answer :C
Answer: (C) 9975
Question: The sum of 3 consecutive numbers is definitely
(A) Positive.
(B) Divisible by 2.
(C) Divisible by 4.
(D) Divisible by 3.
(E) Divisible by 5.
Rationale: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: D
Answer: (D) Divisible by 3.