mathewhe/aqua_rat huggingface dataset:
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
(A) a) 66.67-x
(B) b) 40-x
(C) c) 80-2x
(D) d) 120-x
(E) e) 40-x/2
Rationale: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of:
R = (100 mi)/(1.5) = 66.67 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 66.67
y = 66.67 - x
Answer =(A)
Answer: (A) a) 66.67-x
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 150 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 2989
(B) 2765
(C) 5800
(D) 2989
(E) 9772
Rationale: Total production of salt by the company in that year
= 5000 + 5150 + 5300 + .... + 6650 = 70050.
Average monthly production of salt for that year
= 70050/12
= 5837.
Answer:C
Answer: (C) 5800
Question: A and B are 90 km apart they start to move each other simultaneously A at speed 10 and B at 5 km/hr if every hour they double their speed what is distance that A pass until he meet B?
(A) 30 km
(B) 40 km
(C) 50 km
(D) 60 km
(E) 70 km
Rationale: in 2 hours a covers (10+20)=30 km
b covers( 5+10)=15 km, total covered=45
in the next hour they have to cover (90-45) km with the speeds 40km/hr and 20 km/hr respectively
let them take another t hrs to meet
so sum of the distance to be covered by both is 45km
(40*t)+(20*t)=45km
gives t= (3/4) hrs
we need to fid out the distance covered by a
which equals to =30+(40*(3/4))=60 km
ANSWER:D
Answer: (D) 60 km
Question: For all numbers u and v, the operation @ is defined by u@v = u^2 - uv. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
(A) II
(B) I and II
(C) I and III
(D) II and III
(E) All of the above
Rationale: u@v = u^2 - uv=u(u-v).... so u@v will be zero if u=v or u=0.. but u cannot be equal to 0.. as per Q, x and y can take any int value except 0...
now lets look at the choices..
when x=y, it will be 0... so ok...
when we put xy=y, it is possible when x=1 and y any integer... so ok again
when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible
only l and ll possible
answer: B
Answer: (B) I and II
Question: If the product of all the unique positive divisors of n, a positive integer which is not a perfect cube, is n^2, then the product of all the unique positive divisors of n^2 is
(A) n^3
(B) n^4
(C) n^6
(D) n^8
(E) n^9
Rationale: the product of factors of a number 'n' would be (n)^(no.of factors/2).given the product of all the unique divisors is n^2.so we can conclude no.of factors for the given number is 4.such numbers would be of the form (p1)^1*(p2)^1 where p1 and p2 are prime numbers.
n=(p1)^1*(p2)^1
n^2=(p1)^2*(p2)^2 .
product of all the factors of n^2 would be (n^2)^(no.of factors of n^2/2)=(n^2)^(3*3/2)=n^9
ANSWER:E
Answer: (E) n^9
Question: Based on this year's costs, an orchard grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to decrease 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be:
(A) 100% less than N
(B) 200% less than N
(C) Equal to N
(D) 100% greater than N
(E) 200% greater than N
Rationale: Correct answer is (D).
This year, the price of a tree is price1=P/N.
If this price decreases by 50% it becomes Price2=P/N*0.5
Then with P dollars, you can grow P/Price2 trees i.e. P/(P/N*0.5) i.e. N/0.5 i.e. 2*N
Which is 100% greater than N.
Answer: (D) 100% greater than N
Question: If S = {1, 2, 3, 4, 5, 6, 7}, how much less is the mean of the numbers in S than the median of the numbers in S?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Mean = (1 + 2 +3 + 4 + 5 + 6 + 7)/7 = 4
Median = 4
Difference = 4-4 = 0
Option A
Answer: (A) 0
Question: If x/y is an integer, which of the following must also be not an integer?
I. xy
II. y/x
III. x
(A) I alone
(B) II alone
(C) III alone
(D) I, II and III
(E) None of the above
Rationale: Let's take X = 4/3 and Y = 2/3
Then X/Y = 2 which is an integer.
But XY = 4/3 * 2/3 = 8/9 --> Not an integer.
Y/X = 2/3 divided by 4/3 = 2/4 = 1/2 Not an integer.
X alone is 4/3. Not an integer.
Hence D.
Answer: (D) I, II and III
Question: In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Chuck and Bob are not seated next to each other?
(A) 24
(B) 48
(C) 72
(D) 74
(E) 96
Rationale: When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....
These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
Answer :C
Answer: (C) 72
Question: Bottle R contains 250 capsules and costs $8.25. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
(A)  $0.25
(B)  $0.01
(C)  $0.05
(D)  $0.03
(E)  $0.002
Rationale: Cost per capsule in R is 8.25/250=0.825/25=0.033
Cost per capsule in T is 2.99/130=0.023
The difference is 0.01
The answer is B
Answer: (B)  $0.01
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(7,2)
D=(3,9)
E=(1,4)
(A) 17
(B) 16.3
(C) 18
(D) 19
(E) 15
Rationale: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as A.
Answer: (A) 17
Question: I bought two books; for Rs.460. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 337.33
(B) 280.33
(C) 299.33
(D) 268.33
(E) 289.33
Rationale: x*(85/100) = (460 - x)119/100
x = 280
Answer: D
Answer: (D) 268.33
Question: The train travels at an average speed of 16km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 8km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip?
(A) 9.6
(B) 10.6
(C) 4.3
(D) 2.5
(E) 5.3
Rationale: Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 16km/hour and 8 km/hour, using a multiple of both 16 and 8 would make the math easiest.
Let's set the Distance up the hill at 64 km.
So, going uphill, we have....
D = (R)(T)
64 = (16)(T)
64/16 = 4 = T
4 hours to go uphill
Going downhill, we have....
D = (R)(T)
60 = (20)(T)
64/8 = 8 = T
8 hours to go downhill
Total Distance = 120 km
Total Time = 4+8 = 12 hours
Average Speed = 128/12 = 10.6 km/hour
B
Answer: (B) 10.6
Question: If 25% of x is 15 less than 15% of 1500, then x is?
(A) 657
(B) 765
(C) 865
(D) 840
(E) 847
Rationale: 25% of x = x/4 ; 15% of 1500
= 15/100 * 1500 = 225
Given that, x/4 = 225 - 15
=> x/4 = 210 => x = 840.
Answer:D
Answer: (D) 840
Question: What is the least number of square tiles required to pave the floor of a room
15 m 17 cm long and 9m 2 cm broad?
(A) 814
(B) 802
(C) 836
(D) 900
(E) 1000
Rationale: L = 15 M 17 CM =1517 CM
B = 9 M 2 CM = 902 CM^2
AREA = 1517 * 902 CM^2
FIND OUT HCF = 41
AREA OF SQUARE = 41 * 41 = 1517 * 902 / 41 * 41 = 37 * 22
=407 * 2 =814
ANSWER A
Answer: (A) 814
Question: 2 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 12/9 days
(B) 30/11 days
(C) 82/8 days
(D) 22/76 days
(E) 22/2 days
Rationale: 2M = 6W ---- 20 days
12M + 8W -----?
36W + 8 W = 44W ---?
6W ---- 20 44 -----?
6 * 20 = 44 * x => x = 30/11 days
Answer:B
Answer: (B) 30/11 days
Question: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days Q will the work get over?
(A) Q=60
(B) Q=70
(C) Q=75
(D) 80
(E) 100
Rationale: We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days)
Answer: (C) Q=75
Question: R-R-R-G-G-G-G-Y-Y-Y-B-R-R-R-G-G-G-G-Y-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
(A) 64
(B) 65
(C) 66
(D) 67
(E) 68
Rationale: The repeated pattern R-R-R-G-G-G-G-Y-Y-Y-B has 11 beads.
But the missing section includes R-R-R-G-G-G-G-Y-Y-Y at the end.
Thus the number of beads in the missing section has the form 11k + 10.
The answer is B.
Answer: (B) 65
Question: If 20 men can build a wall 66 metres long in 10 days, what length of a similar can be built by 86 men in 8 days?
(A) 227.04 mtrs
(B) 378.4 mtrs
(C) 478.4 mtrs
(D) 488.4 mtrs
(E) 578.4 mtrs
Rationale: If 20 men can build a wall 66 metres long in 10 days,
length of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(10*20) = 227.04 mtrs
ANSWER:A
Answer: (A) 227.04 mtrs
Question: Two trains of equal are running on parallel lines in the same direction at 49 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 88
(C) 65
(D) 55
(E) 22
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 49 - 36 = 13 km/hr.
= 13 * 5/18 = 65/18 m/sec.
2x/36 = 65/18 => x = 65.
Answer:C
Answer: (C) 65
Question: Three coworkers P , W , R meet for Dinner. P had 5 sandwiches, W had 3 and R had none. Both PW share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PW, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
(A) a) 5$
(B) b) 3 $
(C) c) 7 $
(D) d) 4 $
(E) e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
W:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: (C) c) 7 $
Question: A company’s four cars running 10 hrs a day consume 1200 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 25% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?
(A) 1200 lt
(B) 1555 lt
(C) 1674 lt
(D) 1728 lt
(E) 4800 lt
Rationale: Given that
4 cars running 10 hrs a day consume 1200 lts. of fuel in 10 days.
1 car consumption per hour per day = 1200 /4 *10 *10 = 3 litre
Now question say new car consume 20% less fuel than the company’s four cars = 75/100 of 3 = 2.25 ( 25 percent less than 3)
Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 2.25 *12 *6*5 =810
similarly = old 4 car consumption for next 6 days for 12 hrs = 3*6*12*4 = 864
hence total is = 810+864 = 1674 lt
Ans is C .
Answer: (C) 1674 lt
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 52,428,800,000 and x + y + z = 17, what is the value of xy/z?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: The number 52,428,800,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is A.
Answer: (A) 0
Question: An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
(A) 1/2
(B) 1/5
(C) 1/5
(D) 3/7
(E) 2/7
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 10/15
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 9 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 9/14
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 10/15 × 9/14 = 3/7
D
Answer: (D) 3/7
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.7
(B) 31.4
(C) 31.6
(D) 31.1
(E) 31.2
Rationale: 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4
= 31.6
Answer:C
Answer: (C) 31.6
Question: Mary's income is 60 percent more than Tim's income, and Tim's income is 60 percent less than Juan's income. What percent of Juan's income is Mary's income?
(A)  64%
(B)  120%
(C)  96%
(D)  80%
(E)  64%
Rationale: Juan's income = 100 (assume);
Tim's income = 40 (60 percent less than Juan's income);
Mary's income = 64 (60 percent more than Tim's income).
Thus, Mary's income (64) is 64% of Juan's income (100).
Answer: A.
Answer: (A)  64%
Question: A work crew of 6 Men takes 8 days to complete one-half of a job. If 9 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?
(A) 2
(B) 3
(C) 3 1/5
(D) 4
(E) 4 4/5
Rationale: Suppose 1 man can do work in X days..
so 4 men will do in ..
6/X=1/8*1/2 as half job is done
X=96
now 9 more are added then
15/96=1/2*1/d for remaining half job
d=3 1/5 Number of days
C
Answer: (C) 3 1/5
Question: George can do a piece of work in 8 hours. Paul can do the same work in 10 hours, Hari can do the same work in 12 hours. George, paul and hari start the same work at 9 am, while george stops at 11 am, the remaining two complete the work. What time will the work complete?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 4
Rationale: Let the total work = 120 units.
As George completes this entire work in 8 hours, his capacity is 15 units /hour
Similarly, the capacity of paul is 12 units / hour
the capacity of Hari is 10 units / hour
All 3 started at 9 am and worked upto 11 am. So total work done upto 11 am = 2 x (15 + 12 + 10) = 74
Remaining work = 120 - 74 = 46
Now this work is to be done by paul and hari. 46 / (12 + 10) = 2 hours (approx)
So work gets completed at 1 pm
Answer:E
Answer: (E) 4
Question: A 2-year certificate of deposit is purchased for K dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
(A) k(1.06)^2
(B) k(1.06)^8
(C) k(1.015)^2
(D) k(1.015)^8
(E) k(1.03)^4
Rationale: term (n) = 2
value of k at the end of 2 yrs, if compounded annually=k(1+r)^n=k(1+0.06)^2
quarterly int. rate (r) = 1.5%
term (n) = 2x4 = 8
value of k at the end of 2 yrs, if compounded qtrly =k(1+r)^n=k(1+0.015)^8
ANSWER:D
Answer: (D) k(1.015)^8
Question: An air conditioner can coo the hall in 20 minutes while another takes 25 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
(A) about 14 minutes
(B) about 12 minutes
(C) about 15 minutes
(D) about 16 minutes
(E) about 17 minutes
Rationale: Take LCM of 20 and 25 = 100
20*5=100/ 25*4=100.
So if both are switched on together , room cooled in 100/(5+4)=100/9=11.11 minutes
11.11 can be round to 12 minutes , so about 12 minutes
ANSWER: B
Answer: (B) about 12 minutes
Question: What is 30% of 210?
(A) 61
(B) 63
(C) 65
(D) 67
(E) 69
Rationale: X/210 = 30/100
100X = 210X30
X =(210X30)/100
X =6300/100
= 63
ANSWER = B = 63
Answer: (B) 63
Question: The sum of 2 numbers is 2000. Their L.C.M. is 21879. Their difference is?
(A) 1845
(B) 1978
(C) 1945
(D) 1862
(E) 1789
Rationale: Let the numbers be x and 2000-x
L.C.M. = x(200-x) = 21879
x^2 - 2000x + 21879 = 0
(x-1989) (x-11) = 0
x = 1989 and x = 11
Difference = 1989-11 = 1978
Answer is B
Answer: (B) 1978
Question: What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?
(A) 277
(B) 278
(C) 120
(D) 276
(E) 298
Rationale: Let the present worth be Rs. x. Then,
S.I. = (132 - x)
(x * 5 * 2) / 100 = (132 - x)
10x = 13200 - 100x
110x = 13200 => x = 120.
Answer:C
Answer: (C) 120
Question: If the selling price is quadrupled,the profit is pentadruple, what is the percentage of profit??
(A) 50%
(B) 100%
(C) 150%
(D) 200%
(E) 250%
Rationale: we can make two equations from the given info..
let selling price be S and cost price be C..
so profit=P=S-C...
if S is doubled profit is tripled..
so 5P=4S-C..
or S=4P...
therefore C=P..
% of profit=P/P=100%
B
Answer: (B) 100%
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 180 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 179
(B) 194
(C) 269
(D) 177
(E) 191
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 â€“ 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x â€“ 180
x + (x - 180) = 208
2x = 388
x = 194 runs
ANSWER: B
Answer: (B) 194
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) 867
(B) 270
(C) 267
(D) 278
(E) 277
Rationale: I = (500*9*6)/100
= 270
Answer: B
Answer: (B) 270
Question: 50% of a number is added to 120, the result is the same number. Find the number?
(A) 300
(B) 277
(C) 240
(D) 99
(E) 121
Rationale: :
(50/100) * X + 120 = X
2X = 480
X = 240
Answer: C
Answer: (C) 240
Question: A labourer was engaged for 25 days on the condition that for every day, he works, he will be paid Rs. 2 and for every day, he is absent he will be fined 50p. If he receives only Rs. 37•50, find the no. of days he was absent is_____
(A) 3 days
(B) 4 days
(C) 5 days
(D) 6 days
(E) 7 days
Rationale: if a labour worked for 25 days he should get 50 Rs.
but in this he is getting 13 Rs less. if he don't go for work for 1 day he will loose 2.5 Rs then
no of days(Absent)=13/2.5=5.2. Means he was absent for 5 days
ANSWER:C
Answer: (C) 5 days
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87, 108and 98
(A) 80
(B) 93.5
(C) 92
(D) 98
(E) 100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98,108
The median quiz score was 93.5 (Four quiz scores were higher than 93.5 and four were lower.)
B
Answer: (B) 93.5
Question: How many numbers are there between 100 and 1000 in which all digits are distinct.
(A) 900
(B) 648
(C) 720
(D) 252
(E) 729
Rationale: We know that numbers between 100 and 1000 will be 3 digit integers.
Let the arrangement be ABC where A,B,C represent distinct digits.
We have 9 options for A (as 0 can not start a 3 digit number), 9 options again for B and 8 for C, giving a total of 9*9*8 = 648 options.
ANSWER B
Answer: (B) 648
Question: How many numbers from 10 to 43 are exactly divisible by 3?
(A) 13
(B) 11
(C) 16
(D) 17
(E) 18
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42.
11 Numbers.
10/3 = 3 and 43/3 = 14 ==> 14 - 3 = 11. Therefore 11 digits
B)
Answer: (B) 11
Question: Statements: Prime school-going children in urban India have now become avid as well as more regular viewers of TV, even in households without a TV. As a result there has been an alarming decline inthe extent of readership of newspapers.
Conclusions:
1) Method of increasing the readership of newspapers should be devised.
2) A team of experts should be sent to other countries to study the impact of TV. on the readership of newspapers.
(A) Only conclusion I follows
(B) Only conclusion II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: The statement concentrates on the increasing viewership of TV. and does not stress either on increasing the readership of newspapers or making studies regarding the same. So, neither I nor II follows.
D
Answer: (D) Neither I nor II follows
Question: If y > 0, (6y)/20 + (3y)/10 is what percent of y?
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: can be reduced to 3y/10+3y/10 =3y/5=60%
C
Answer: (C) 60%
Question: Of the three- digit integers greater than 700, how many have two digits Q that are equal to each other and the remaining digit different from the other two?
(A) 90
(B) 82
(C) 80
(D) 45
(E) 36
Rationale: three-digit integers greater than 700: 701 to 999, inclusive.
possible values for hundreds-digit--> 7,8,9
possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9
when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999
when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999
when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700
Q=27+27+26 = 80
Answer: C
Answer: (C) 80
Question: The average monthly salary of 15 employees in an organisation is Rs. 1800. If the manager's salary is added, then the average salary increases by Rs. 150. What is the manager's monthly salary?
(A) Rs.3601
(B) Rs.3618
(C) Rs.4200
(D) Rs.3619
(E) Rs.3610
Rationale: Manager's monthly salary
= Rs. (1950 * 16 - 1800 * 15)
= Rs. 4200 Answer:C
Answer: (C) Rs.4200
Question: 0, 3, 8, 15, 24, ?
(A) 28
(B) 35
(C) 48
(D) 25
(E) 50
Rationale: The sequence is a series of squares-1
0, 3, 8, 15, 24, 35
Answer : B.
Answer: (B) 35
Question: A rectangular tiled patio is composed of 90 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 90 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
(A) 5
(B) 6
(C) 10
(D) 11
(E) 28
Rationale: r*c=90 and (11+4)(c-2)=90 --> r=11 and c=8.
Answer:D.
Answer: (D) 11
Question: John and Peter are among the seven players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?
(A) 5/11
(B) 8/15
(C) 9/20
(D) 10/21
(E) 11/24
Rationale: The total possible ways of selecting a 5-member team is 7C5 = 21
The possible ways which include John and Peter is 5C3 = 10
The probability of choosing both John and Peter is 10/21
The answer is D.
Answer: (D) 10/21