mathewhe/aqua_rat huggingface dataset:
Question: If x+y=5, and x=15/y, what is the value of x^2+y^2?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 10
Rationale: x^2 + y^2 should make you think of these formulas:
(x+y)(x+y) = x^2+y^2+2xy
We already know (x+y) = 5 and x*y = 15
(x+y)(x+y) = (5)(5) = x^2+y^2+2*(15)
x^2+y^2 = 25 - 15 = 10
Answer : E
Answer: (E) 10
Question: If k is the greatest positive integer such that 3^k is a divisor of 24! then k =
(A) 3
(B) 4
(C) 5
(D) 6
(E) 10
Rationale: 24/3=8
24/9=2
8+2 =10
k=10
Answer: E
Answer: (E) 10
Question: The sum of three consecutive multiples of 3 is 72. What is the largest number?
(A) 21
(B) 24
(C) 27
(D) 36
(E) 39
Rationale: Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 72
9x = 63
x = 7
Largest number = 3x + 6 = 27.
ANSWER:C
Answer: (C) 27
Question: 3 boys and 7 girls can complete John work in 10 days . But 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
(A) 10 days
(B) 20 days
(C) 40 days
(D) 56 days
(E) 65 days
Rationale: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Answer: (C) 40 days
Question: What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 4?
(A) n/8
(B) 0.8
(C) 8
(D) 18
(E) π
Rationale: Maximum distance straight line is diameter
d = 2r = 8..
ANS option C.
Answer: (C) 8
Question: The pilot of a small aircraft uses 60 gallons of fuel to fly 300 miles. At this rate, how many gallons of fuel are needed for a 700 mile flight?
(A) 140
(B) 155
(C) 160
(D) 170
(E) 175
Rationale: Number of gallons of fuel per mile = 300 /60 = 5 gallons per mile
Number of gallons of fuel for a 700 mile flight = 700/5 = 140
ANSWER:A
Answer: (A) 140
Question: If the integer n has exactly four positive divisors, including 1 and n, how many positive divisors does n^3 have?
(A) 16
(B) 11
(C) 10
(D) 20
(E) 9
Rationale: take the example of 6...
it has 4 positive divisors (1,2,3,4)
Now, take the example of 216 ...
it has 16 divisors..
so A is the ans
Answer: (A) 16
Question: An escalator moves towards the top level at the rate of 12 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 8 feet per second towards the top level, how much time does he take to cover the entire length.
(A) 10sec
(B) 8sec
(C) 9sec
(D) 7sec
(E) 12sec
Rationale: Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 160/ (12+8) = 8sec
Answer : B
Answer: (B) 8sec
Question: The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to:
(A) 0.04
(B) 0.08
(C) 0.07
(D) 0.06
(E) 0.05
Rationale: = 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749
= 489 x 0.05 x 2/0.09 x 93 x 100
= 489/9 x 93 x 10
= 163/279 x 1/10
= 0.58/10
= 0.058 (or) 0.06.
Answer is D.
Answer: (D) 0.06
Question: The simple form of the ratio 8/5:2/3 is?
(A) 12:5
(B) 12:7
(C) 7:12
(D) 5:7
(E) 4:7
Rationale: 8/5:2/3 = 12:5
Answer: A
Answer: (A) 12:5
Question: John has on his shelf two books of poetry, six novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
(A) 1/2
(B) 2/5
(C) 3/10
(D) 7/20
(E) 4/15
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 6/10*2/9 + 2/10*6/9 = 4/15.
Answer: E.
Answer: (E) 4/15
Question: The cost of 4 bags and 12 purses is Rs.1600, what is the cost of 10 bags and 30 purses?
(A) Rs.3600
(B) Rs.4000
(C) Rs.3800
(D) Rs.3900
(E) None of these
Rationale: Explanation:
Cost of 4 bags + 12 purses = Rs.1600
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.4000.
Answer: Option B
Answer: (B) Rs.4000
Question: When positive integer n is divided by 7, the remainder is 1. When n is divided by 11, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 77?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: n = 7p + 1 = 11q + 5
n+6 = 7p + 7 = 11q + 11
n+6 is a multiple of 7 and 11, so it is a multiple of 77.
The answer is C.
Answer: (C) 6
Question: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and a delta raised to the seventh power?
(A) alpha
(B) beta
(C) gamma
(D) delta
(E) epsilon
Rationale: Let the alpha be 5k and let the delta be 5j+3.
(5k)^7 + (5j+3)^7 which has the form 5k+2, which is a gamma.
The answer is C.
Answer: (C) gamma
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/9
(B) 11 1/4
(C) 19 1/9
(D) 11 1/2
(E) 11 1/41
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer: B
Answer: (B) 11 1/4
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
(A) 60 gallons
(B) 100 gallons
(C) 120 gallons
(D) 180 gallons
(E) 200 gallons
Rationale: Explanation:
Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
ANSWER IS C
Answer: (C) 120 gallons
Question: A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of B.
(A) 250
(B) 450
(C) 750
(D) 800
(E) None of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450
C's share = Rs. [1200 - (300 + 225») = Rs. 150.
Answer is B
Answer: (B) 450
Question: Given two fair dice, what is the probability Q that the sum of their numbers is 4 if exactly one die shows a 3?
(A) a) 2/11
(B) b) 1/18
(C) c) 3/11
(D) d) 2/39
(E) e) 1/5
Rationale: If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.the probability Q that the sum of their numbers is 4 if exactly one die shows a 3
2/11 would be the answer if 'at least one of the die shows a 3'.A
Answer: (A) a) 2/11
Question: 60 + 5 * 12 / (180/3) = ?
(A) 60
(B) 120
(C) 13
(D) 61
(E) 50
Rationale: Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.
ANSWER IS D
Answer: (D) 61
Question: A brick measures 20cm*10cm*7.5cm how many bricks will be requiredfor a wall 25m*2m*0.75m ?
(A) 24000
(B) 23000
(C) 22000
(D) 25000
(E) 27000
Rationale: 25*2*0.75=20/100*10/100*0.75/100*X25=1/100*XX=25000Answer :D
Answer: (D) 25000
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations E of soloists can appear in the liner notes?
(A) 5!
(B) 10!/(5!5!)
(C) 10!/5!
(D) 10!
(E) 10!*5!
Rationale: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations E of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Answer: (B) 10!/(5!5!)
Question: The largest prime number is?
(A) 11
(B) 13
(C) 5
(D) 7
(E) 9
Rationale: The largest prime number is 13.
B)
Answer: (B) 13
Question: A collection of books went on sale, and 2/3 of them were sold for $3 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
(A) $216
(B) $135
(C) $90
(D) $60
(E) $54
Rationale: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($3) or $216. The best answer is therefore A.
Answer: A.
Answer: (A) $216
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
(A) 2/3
(B) 2/9
(C) 1/3
(D) 1/9
(E) 2/5
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 × 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)=4/36=1/9
Answer is E
Answer: (E) 2/5
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 278
(B) 166
(C) 151
(D) 270
(E) 109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer:D
Answer: (D) 270
Question: One of the following numbers can be marked out as the odd one out. can you find which one?
1) 680986879
2) 716089780
3) 820670987
4) 932967879
(A) The odd number is 680986879
(B) The odd number is 820670987
(C) The odd number is 716089780
(D) The odd number is 932967879
(E) None
Rationale: Correct Answer : B
if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987
Answer: (B) The odd number is 820670987
Question: At an M&M factory, two types of M&Ms are produced, red and blue. The M&Ms are transported
individually on a conveyor belt. Anna is watching the conveyor belt, and has determined that
four out of every five red M&Ms are followed by a blue one, while one out of every six blue
M&Ms is followed by a red one. What proportion of the M&Ms are red?
(A) 1/29
(B) 2/29
(C) 3/29
(D) 4/29
(E) 5/29
Rationale: Suppose that the fraction of red M&Ms is fr and the fraction of blue M&Ms
is fb. Then the probability that Anna sees a red one emerge next is fr. This probabil-
ity can also be expressed using conditional probabilities as fr = P(blue)P(red after blue) +
P(red)P(red after red), or fr = fb(1=6) + fr(1=5). Likewise, we find fb = fr(4=5) + fb(5=6).
Solving the system of equations gives fb = 24
29 and fr =5/29
correct answer E
Answer: (E) 5/29
Question: If 5x + 3 = 10x – 22, what is the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: solve for x:
5x+3=10x-22
25=5x
5=x
correct answer E)5
Answer: (E) 5
Question: If each term in the sum R=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12=R => 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
Hence C.
Answer: (C) 40
Question: The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 32,000 locusts?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: - 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
Answer : C
Answer: (C) 6
Question: The price of a book is increased from $300 to $330. What is the % of increase in its price?
(A) 10%
(B) 20%
(C) 30%
(D) 35%
(E) 45%
Rationale: Explanation: Change in the price = Rs 330 – Rs 300
= Rs 30
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 30 / 300
) *100 = 10%
A
Answer: (A) 10%
Question: The 44 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=44
solving for x you get 4
Answer A
Answer: (A) 4
Question: A and B together can do a piece of work in 2 days. If A alone can do the same work in 22 days, then B alone can do the same work in?
(A) 0.35 days
(B) 0.45 days
(C) 0.55 days
(D) 0.25 days
(E) 0.15 days
Rationale: B = 1/2 – 1/22 =0.45 days
ANSWER:B
Answer: (B) 0.45 days
Question: A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.
(A) 20 m * 58 m
(B) 20 m * 7 m
(C) 20 m * 5 m
(D) 80 m * 5 m
(E) 20 m * 1 m
Rationale: From the question, 2b+l = 30
=> l = 30-2b
Area=100m2=>l×b=100=>b(30−2b)=100b2−15b+50=0=>(b−10)(b−5)=0
Area=100m2=>l×b=100=>b(30−2b)=100b2−15b+50=0=>(b−10)(b−5)=0
b = 10 or b = 5
when b = 10 then l = 10
when b = 5 then l = 20
Since the garden is rectangular so we will take value of breadth 5.
So its dimensions are 20 m * 5 m
Answer: C
Answer: (C) 20 m * 5 m
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 27
(B) 82
(C) 245
(D) 288
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer:C
Answer: (C) 245
Question: A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 27,000, then what is B's share in the profit?
(A) Rs. 2000
(B) Rs. 3000
(C) Rs. 4000
(D) Rs. 5000
(E) None of these
Rationale: Explanation :
Ratio of the initial investment = 7/2 : 4/3 : 6/5
= 105 : 40 : 36
From this ratio, we can assume that actual initial investments of A, B and C
are 105x, 40x and 36x respectively
A increases his share 50% after 4 months. Hence the ratio of their investments =
(105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12
= 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3
= 105 * 4 : 40 *3 : 36 * 3
= 35 * 4 : 40 : 36
= 35 : 10 : 9
B's share = total profit * (10/54) = 27,000 * 10/54 = 5000. Answer : Option D
Answer: (D) Rs. 5000
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 A. 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: Assume the total pool of registered voters = 100, so 35 of the country’s registered voters had an unfavorable impression of both of that state’s major political parties and 20 had a favorable impression only of Party A
let x = # of voters with a favorable impression of both parties
let 2x = # of voters with a favorable impression only of Party B
so unfavorable A and favorable B # of voters = 2x-x = x
35+x = number of unfavorable A
20+ 35+x = 100
55+x=100
x=45
ANSWER:E
Answer: (E) 45
Question: In 16 minutes, the minute hand gains over the hour hand by
(A) 16°
(B) 80°
(C) 88°
(D) 96°
(E) None of these
Rationale: In 1 hour, the minute hand gains 330° over the hour hand.
i.e. in 60 minute, the minute hand gains 330° over the hour hand.
∴ In 16 minutes, the minute hand gains over the hour hand by 330°⁄60 × 16° = 88°
Answer C
Answer: (C) 88°
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 11
(B) 18
(C) 19
(D) 12
(E) 15
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Answer: (B) 18
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(A) 10 days
(B) 12 days
(C) 15 days
(D) 20 days
(E) 25 days
Rationale: A's 2 day's work = 1	x 2 =	1	.
20	10
(A + B + C)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.
20	30	60	60	10
Work done in 3 days = 1	+	1 =	1	.
10	10	5
Now,	1	work is done in 3 days.
5
Whole work will be done in (3 x 5) = 15 days.
Option C
Answer: (C) 15 days
Question: What is the greatest positive integer E such that 3^E is a factor of 9^10?
(A) E=5
(B) E=9
(C) E=10
(D) E=20
(E) 30
Rationale: What is the greatest positive integer E such that 3^E is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20
Answer: (D) E=20
Question: A parking garage rents parking spaces for $10 per week or $35 per month. How much does a person save in a year by renting by the month rather than by the week?
(A)  $100
(B)  $160
(C)  $220
(D)  $240
(E)  $260
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
35$ per month!
An year has 12 months.
Annual charges per year = 12 * 35 = 420$
520 - 420 = 100
Ans A
Answer: (A)  $100
Question: How many arrangements of the letters of the word CONTINUES can be made, without changing the place of the vowels in the word?
(A) 130
(B) 140
(C) 150
(D) 120
(E) 110
Rationale: O,I,E,U fixed. Consonants can be arrangements in 5P5 = 5! = 120 ways
Option 'D'
Answer: (D) 120
Question: A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John ( he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike?
(A) 2534 s
(B) 5435 s
(C) 7645 s
(D) 7456 s
(E) 3576 s
Rationale: Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then
---------- (i)
and ---------(ii)
From eq.(i) and (ii)
3(R - A ) = 2 (R + K)
R = 3A + 2K
In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram
= 1800 ( R - A) - 24 ( A + K)
Time required =
= (3600 - 24) = 3576 s
E
Answer: (E) 3576 s
Question: A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 476 m
(B) 420 m
(C) 440 m
(D) 407 m
(E) 402 m
Rationale: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 15
x + 300 = 720
x =420 m.
Answer: B
Answer: (B) 420 m
Question: What was the day of the week on 17th June 1998?
(A) Monday
(B) Sunday
(C) Wednesday
(D) Friday
(E) Tuesday
Rationale: Explanation:
17 Jun 1998 = (1997 years + period from 1-Jan-1998 to 17-Jun-1998)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
Number of odd days in the period 1601-1900
= Number of odd days in 300 years
= 5 x 3 = 15 = 1
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 1901-1997
= 73 normal years + 24 leap year
= 73 x 1 + 24 x 2 = 73 + 48 = 121 = (121 - 7 x 17) = 2 odd days
Number of days from 1-Jan-1998 to 17-Jun-1998
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 17(Jun)
= 168 = 0 odd day
Total number of odd days = (0 + 1 + 2 + 0) = 3
3 odd days = Wednesday
Hence 17th June 1998 is Wednesday.
Answer: Option C
Answer: (C) Wednesday
Question: If p is an odd integer and q is an even integer, which of the following must be an even integer?
(A) 2q-p
(B) 3p+q
(C) 2p+3q
(D) 4(p+q)
(E) p+q^2
Rationale: p is odd; for this assume p=1
q is even; for this assume q = 2
(2*2)-1 = 3 Odd
(3*1)+2 = 5 Odd
(2*1)+(3*2) = 9 Odd
4(1+2) = 12 Even
1+(2^2) = 5 Odd
Answer:D
Answer: (D) 4(p+q)
Question: Which of the following cannot be the sum of 2 different prime numbers?
(A) 10
(B) 13
(C) 14
(D) 15
(E) 19
Rationale: Option A: 10 = 7 + 3. Sum of 2 different prime numbers.
Option B: 13 = 11 + 2. sum of 2 different prime numbers
Option C: 4 = This is not a sum of 2 different prime numbers.
Option D: 15 = 13 + 2. Sum of 2 different prime numbers
Option E: 19 = 17 + 2. Sum of 2 different prime numbers
Correct Option: C
Answer: (C) 14
Question: A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares?
(A) 37.5
(B) 40
(C) 50
(D) 48
(E) 52
Rationale: Dividend on 1 share = $(10/100*50)
=$5
$12.5 is an income on an investment of $100
$5 is an income on an investment of $(100*2/25*5)=40
Thus, cost of 1 share =$40
ANSWER B
Answer: (B) 40
Question: All of the stocks on the over-the-counter market are designated by either a 6-letter or a 7-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
(A) a. 2(26^5)
(B) b. 26(26^4)
(C) c. 27(26^4)
(D) d. 26(26^5)
(E) e. 27(26^6)
Rationale: no of different stocks for 6-letter code = 26^6
no of different stocks for 7-letter code = 26^7
total = 26^6 + 26^7 = 26^6(26+1) = 27(26^6)
[Reveal]Spoiler:
Option E
Answer: (E) e. 27(26^6)
Question: There are 418 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
(A) 152
(B) 209
(C) 242
(D) 171
(E) 181
Rationale: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 418 = 242
ANSWER:C
Answer: (C) 242
Question: Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number?
(A) 9
(B) 12
(C) 14
(D) 16
(E) 20
Rationale: Explanation:
We have, 2/3 * 2/5 * 3/4 * X = 36
X = 180
Now, 4/5 * X = 4/5 * 180 = 144
√144 = 12
ANSWER: B
Answer: (B) 12
Question: A grocer has a sale of Rs. 5921, Rs. 5468, Rs. 5568, Rs. 6088 and Rs. 6433 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5900?
(A) 4902
(B) 4922
(C) 5922
(D) 5924
(E) 5928
Rationale: Total sale for 5 months = Rs. (5921 + 5468 + 5568 + 6088 + 6433) = Rs. 29478.
Required sale = Rs. [ (5900 x 6) - 29478 ]
= Rs. (35400 - 29478)
= Rs. 5922.
ANSWER:C
Answer: (C) 5922