divelab/Sys2Bench huggingface dataset:
Question: 8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?
Options:
A)40 Ltrs
B)50
C)60
D)70
E)80
Rationale: Allegation method.
Concentration of Alcohol in original sol - 20%
Concentration of Alcohol in water -- 0%
Concentration of Alcohol in final sol -- 16%
After applying allegation as shown in figure they have to be mixed in 4:1 part
1 part is given as 8 ltr, so total initial volume is 5 part = 5*8 = 40 Ltrs
ANSWER:A
Answer: A
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back, how far is the place?
Options:
A)144km
B)30km
C)48km
D)12km
E)15km
Rationale: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 30
2x+3x = 720
x = 144 km
Answer is A
Answer: A
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 5 years and that for 15 years?
Options:
A)3 : 2
B)1 : 3
C)2 : 3
D)3 : 1
E)2 : 1
Rationale: Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 5 years/Simple Interest for 15 years
=T1/T2
=5/15
=1/3
=1:3
Answer : Option B
Answer: B
Question: Which of the following cannot be the range of a set consisting of 5 odd multiples of 11?
Options:
A)44
B)88
C)45
D)176
E)352
Rationale: Solution: sequence of 11 lets say sequence is 11n, 11(n+1), 11(n+2), 11(n+3), 11(n+4)
so range is 11n+44-11n = 44
if we put the different values of n we will get different but the range will be multiple of 44
and only 45 is not multiple of 44
Answer : C
Answer: C
Question: A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 2 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
Options:
A)11/30
B)29/60
C)17/30
D)19/30
E)7/15
Rationale: I think E - 7/15 is the correct answer.
Here goes:
Lets assume originally the number of beds = x
After the new tower, the total combined no of beds = 2x
So old = x, New = x
Now 1/3 of x are occupied and 1/5 of x are occupied which simplifies to (1/5)x
We are shifting 1/3 of x to the new ward so there will now be:
1/3 of x plus 1/5 of x occupied in the new ward. Add them up to get 8/15 of x
There are x beds in New Tower so ratio is:
(8/15)x / x = 8/15 of x
Subtract that from 15/15 of x and you get the number of un-occupied beds to total capacity of New Towerb=7/15.
E
Answer: E
Question: If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is B:
Options:
A)B=1
B)B=2
C)B=3
D)B=4
E)B=5
Rationale: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.
Hence p/48 should resolve to a integer.
48 -- > 2^4 * 3.
Hence p should have atleast 2^4*3 for p/48 to resolve to a int.
The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
Answer: B
Question: George baked a total of 150 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
Options:
A)5
B)6
C)4
D)3
E)2
Rationale: 3/5 of the 150 pizzas cooked on Saturday = 90 pizzas
3/5 of the remaining pizzas on Sunday = 36 pizzas
We're left with (150-90-36) =24 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W TH F
8 7 6 2 1 =24
W =6
B
Answer: B
Question: Of the people who responded to a market survey, 200 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 4 to 1, how many people responded to the survey?
Options:
A)80
B)160
C)250
D)350
E)480
Rationale: Ratio = 4:1 => 4x respondents preferred Brand X and x preferred Brand Y
Since, no. of respondents who preferred Brand X = 200 => 4x=200 => x=50
Hence Total no. of respondents = 200 + 50 =250
Hence C is the answer.
Answer: C
Question: A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.
Options:
A)14
B)11
C)28
D)26
E)18
Rationale: Explanation:
Distance covered in one revolution = = 88m.
Answer: A) 14
Answer: A
Question: In a group of 800 people, 1/5 play at least one instrument, 128 play two or more. What is the probability that one student play exactly one instrument?
Options:
A)2/125
B)3/125
C)C)2/25
D)3/25
E)1/25
Rationale: P(playing 2 or more instruments) = 128/800 = 4/25.
Then, the probability of playing exactly one instrument is given by:
P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 4/25 = 1/25.
Answer E.
Answer: E
Question: P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 2 days. How many days more will P take to finish the work?
Options:
A)10
B)15
C)42
D)20
E)22
Rationale: Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 2 days = 2 × (1/16) = 2/16 = 1/8
Remaining work = 1 = 1/8 = 7/8
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (7/8) / (1/48) = 42
Option C
Answer: C
Question: Kim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Kim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Kim will win?
Options:
A)5/6
B)2/3
C)1/2
D)5/12
E)1/3
Rationale: 1/3
probability of kim winning is basically the sum of three probabilities:
probability of kim picking rock and renee picking scissors = 1/3*1/3 = 1/9
probability of kim picking scissors and renee picking paper = 1/3*1/3=1/9
probability of kim picking paper and renee picking rock = 1/3*1/3=1/9
1/9 + 1/9 + 1/9 = 3/9 = 1/3=E
Answer: E
Question: If a computer program generates three-digit odd numbers using the numbers 9, 7, 0, 4, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
A. B.
C.
D.
E.
Options:
A)1/2
B)1/3
C)1/5
D)1/6
E)1/7
Rationale: 1) Lets first find TOTAL ways..
a) first/leftmost digit can be any of 5 except 0, so 4 ways
b) middle digit can be any of the 5. so 5 ways
c) the units digit can be ONLY odd- 1,7, and 9- so 3 ways
TOTAL = 4*5*3=60 ways
2) lets now find multiple of 3..
a) Digits not div by 3
7,4 and 1 will each leave remainder of 1 so they can be grouped together to form multiples of 3..
first place - 3 ways, second digit - 3 ways, and units digit ONLY 1 and 7 - 2ways
Total ways = 3*3*2=18
b) digits div by 3
9 and 0- No other digit can be used along with them as no other pair gives us sum of remainder as 3..
first place - 1 way, second digit - 2 ways, and units digit ONLY 9 - 1 way
Total ways = 1*2*1=2
TOTAL= 2+18=20
Prob =2060=132060=13
ANSWER:B
Answer: B
Question: The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#42?
Options:
A)23
B)24
C)25
D)26
E)27
Rationale: 21#42
= 21*24*27*30*33*36*39*42
= 3^11 * 7^2 * 2^7 * 5^1 * 11^1 * 13^1
so total is = 11+2+7+1+1+1=23
Answer A
Answer: A
Question: two watches (non- digital) one gained at the rate of 1 minute and the other lost at the rate of 1 minute daily were se correctly at noon on first january 1988. when will the watches indicate the same time next ?
Options:
A)dec 27 1988 noon
B)dec 27 1988 midnight
C)dec 26 1988 noon
D)dec 25 1988 noon
E)dec 25 1988 midnight
Rationale: every day clock1 is getting one minute gain means it will gain 12 hours lead on 25 dec & similarly every day clock2 is getting one minute loss means it will loss 12 hours lead on 25 dec.
Now from above analysis both the clock will display the same time at dec 25 midnight.
ANSWER:D
Answer: D
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
Options:
A)0
B)9
C)8
D)7
E)6
Rationale: Average of 20 numbers = 0.
Sum of 20 numbers = (0 * 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).
Answer: A
Answer: A
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
Options:
A)2
B)7
C)8
D)6
E)9
Rationale: Explanation:
Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer:A
Answer: A
Question: The time taken by Mr.Dhoni to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 72 kmph, find the speed of the stream?
Options:
A)24 kmph
B)25 kmph
C)26 kmph
D)30 kmph
E)28 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 72/3 = 24 kmph.
Answer: A
Answer: A
Question: P software has coding line 5% more than N, N software has coding line 1/2 more than M. M software has 100 lines of coding. find P lines.
Options:
A)106
B)107
C)108
D)109
E)158
Rationale: M s/w has 100 line of code
N s/w has = 100+100*1/2= 150 line of code
P s/w 5% more N' code 150+7.5=157.5
or
158 line of code
ANSWER:E
Answer: E
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent?
Options:
A)28%
B)25%
C)55%
D)17.6%
E)55%
Rationale: 850 --- 150
100 --- ? => 17.6%
Answer: D
Answer: D
Question: 475.124 x 15.98 ÷ 8.001 + 33.33 = ?
Options:
A)983.578
B)659.121
C)781.189
D)656.112
E)456.512
Rationale: Explanation:
? = 475.124 x (15.98 ÷ 8.001) + 33.33
≈ (475.124 x 16/8) + 33.33 ≈ 950.248 + 33.33 ≈ 983.578
Answer: Option A
Answer: A
Question: Can you deduce the pattern and find the next number in the series?
3, 24,81, 192, __?
Options:
A)276
B)277
C)278
D)279
E)375
Rationale: Solution:
375
Explanation:
3 = 1^1^1 + 1^1^1 + 1^1^1
24 = 2^2^2 + 2^2^2 + 2^2^2
81 = 3^3^3 + 3^3^3 + 3^3^3
192 = 4^4^4 + 4^4^4 + 4^4^4
Thus the next number will be
375 =5^5^5 + 5^5^5 + 5^5^5
Answer E
Answer: E
Question: The value of x.1234 - X = 4234 - 3361
Options:
A)671
B)371
C)361
D)248
E)246
Rationale: 1234-X=4234-3361
X=1234-4234+3361=361
X=361
CORRECT ANSWER : C
Answer: C
Question: If a: b = 17: 5, b: c = 13: 11, find a: b: c?
Options:
A)21: 65: 55
B)121: 65: 55
C)221: 65: 55
D)221: 75: 55
E)221: 65: 45
Rationale: a: b = 17: 5
b: c = 13: 11
a: b: c = 221: 65: 55
ANSWER:C
Answer: C
Question: Of 200 people surveyed, 80 percent own a cellular phone and 45 percent own a pager. If all 200 people surveyed own a cellular phone, or a pager, or both, what percent of those surveyed either do not own a cellular phone or do not own a pager?
Options:
A)35%
B)45%
C)55%
D)65%
E)75%
Rationale: Straight forward answer if you follow 2x2 matrix method.. :)
cell , not cell
Pager - - 90
N. pag - - 110
160 40 200
Required = 110+90 = 150
therefore, 150/200 = 75%.
Answer: E
Answer: E
Question: Two goods trains each 820 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)228
B)27.32
C)76.6
D)78.72
E)21
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 820 + 820 = 1640 m.
Required time = 1640 * 6/125 = 78.72 sec.
Answer:D
Answer: D
Question: A car is traveling 54 kilometers per hour. How many meters does the car travel in one minute?
Options:
A)1,250 meters / minute
B)1,350 meters / minute
C)900 meters / minute
D)950 meters / minute
E)1,650 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
54 kilometers per hour = 54 km/hr
= (54 * 1000 meters) / (60 minutes) = 900 meters / minute
correct answer C
Answer: C
Question: Find the face value of 7 in 942756
Options:
A)7
B)700
C)7000
D)70000
E)70
Rationale: Face value is the value of digit itself
face value of 7 = 7
Answer : A
Answer: A
Question: The mean of 50 observations is 100. But later he found that there is decrements of 13 from each observations. what is the the updated mean is ?
Options:
A)87
B)97
C)67
D)57
E)46
Rationale: 87
Answer is A
Answer: A
Question: What is the probability that the sum of two numbers that are selected randomly from a set of numbers will be greater than 6 if the given set is {2,4,6}
Options:
A)5/3
B)1/7
C)1/2
D)1/4
E)1/3
Rationale: First problem is 3C2 = 6 .. Not 20..
Point 2, your sum should be greater than 6, so these are the following possibilities you have
({2,6},{4,6}) which leads to 2 pairs
So the probability is 2 on 6 or 1/3..
ANSWER:E
Answer: E
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
Options:
A)7% decrease
B)8% decrease
C)9% decrease
D)6% decrease
E)4% decrease
Rationale: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B
Answer: B
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Options:
A)33 1/8%
B)33 7/3%
C)33 1/3%
D)33 8/3%
E)32 1/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer: C
Answer: C
Question: Two-third of a positive number and 64/216 of its reciprocal are equal. The number is:
Options:
A)5/12
B)12/5
C)25/144
D)2/3
E)146/25
Rationale: Let the number be x. Then,
2/3 x = 64/216 * 1/x
x2 = 64/216 * 3/2 = 64/144 = 4/9
x = 2/3
ANSWER:D
Answer: D
Question: In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original purchase price. By what percent did the book value for this car decre ase from 1986 to 1988?
Options:
A)16 2/3 %
B)25 percent
C)33 1/3 %
D)50%
E)75%
Rationale: 1986; 2/3
1988; 1/2
% decrease = change/original * 100
2/3−1/2 / 2/3∗100
1/6∗3/2∗100=14∗100=25
Answer: "B"
Answer: B
Question: In how many ways can the letters of the word, ‘TECHNOLOGY’ be arranged?
Options:
A)1804400
B)1814400
C)1714400
D)1704400
E)1724400
Rationale: The word ‘TECHNOLOGY’ contains 10 letters namely 2O, 1T, 1E, 1C, 1H, 1N, 1L, 1G, 1Y.
Therefore, Required number of ways= 10!/(2!)(1!) (1!) (1!) (1!) (1!) (1!) (1!) (1!)
= 10! / 2!
= 10*9* 8*7*6*5*4*3*2*1/2*1
= 1814400
ANSWER:B
Answer: B
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)45
B)60
C)75
D)90
E)105
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer = D
Answer: D
Question: If f(x) = 3x^4 - 4x^3 - 2x^2 + 5x , then f(-1) =
Options:
A)-4
B)-2
C)0
D)2
E)4
Rationale: f(-1) = 3(-1)^4 - 4(-1)^3 - 2(-1)^2 + 5(-1) = 3+4-2-5 = 0
The answer is C.
Answer: C
Question: The speed of the boat in still water in 12 kmph. It can travel downstream through 45 kms in 3 hrs. In what time would it cover the same distance upstream?
Options:
A)6 hours
B)5 hours
C)9 hours
D)15 hours
E)23 hours
Rationale: Speed of the boat in still water = 12 km/hr
Speed downstream = 45⁄3 = 15 km/hr
Speed of the stream = 15-12 = 3 km/hr
Speed upstream = 12-3 = 9 km/hr
Answer is B
Time taken to cover 45 km upstream = 45⁄9 = 5 hours
Answer: B
Question: I was facing west.I turned 125 degree in the clockwise direction and 10degree in the anticlockwise direction.Which direction am i facing now?
Options:
A)north-west
B)north
C)east
D)north-east
E)west
Rationale: N
W E
S
Clockwise degree - Anti-clockwise degree 115%
90% of W = N
115-90=25 degree . 25 degree of N will lie between N and E = North-East
ANSWER:D
Answer: D
Question: Of 440 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?
Options:
A)20
B)25
C)30
D)35
E)55
Rationale: Say the number of students who read book A is A and the number of students who read book B is B.
Given that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.
Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 440=1.25B+B-0.25B --> B=220, A=1.25B=275 and {Both}=0.25B=55.
The number of students who read only book A is {A}-{Both}=125-25=100;
The number of students who read only book B is {B}-{Both}=275-55-220;
The difference is 220-55=165.
Answer:E.
Answer: E
Question: The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 220 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
Options:
A)44
B)64
C)70
D)80
E)84
Rationale: Let x be the number of new boarders.
The ratio changed from 5:12 up to 1:2 = 6:12.
220 / (220+x) = 5/6
x = 44
The answer is A.
Answer: A
Question: If each side of a square is increased by 20%, find the percentage change in its area?
Options:
A)40%
B)42%
C)46%
D)44%
E)38%
Rationale: let each side of the square be a , then area = a x a
New side = 120a / 100 = 6a / 5
New area =(6a x 6a) / (5 x 5) = (36a²/25)
increased area== (36a²/25) - a²
Increase %= [(11a²/25 ) x (1/a² ) x 100]% = 44%
answer :D
Answer: D
Question: A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son’s head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?
Options:
A)0.9
B)0.75
C)0.6
D)0.45
E)None of these
Rationale: Explanation :
L is the lamp post position, F is father and S is son’s position. X is the point where the shadow falls.
LD = 0.9 = Son’s height , LB = 1.8 = Father’s height.
So AB = 6 – 1.8 = 4.2 Also BC = LF = 2.1
We observe that ∆ABC ~ ∆ADE (two triangles are similar).
Hence, the corresponding sides are proportional.
So, AB/AD = DC/DE.
4.2/5.1 = 2.1/DE.
DE = 5.1*2.1/4.2 = 5.1/2 = 2.55.
LS = DE = 2.55
FS = LS – LF = 2.55 – 2.1 = 0.45.
Answer : D
Answer: D
Question: How long does a train 90 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: D = 90 + 170 = 260 m
S = 60 * 5/18 = 50/3
T = 260 * 3/50 = 15.6 sec
Answer: D
Answer: D
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)77 sec
B)66 sec
C)48 sec
D)55 sec
E)45 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: C
Answer: C
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $300, what were her original savings?
Options:
A)$1200
B)$1300
C)$1400
D)$1800
E)$1900
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $300. So 1 / 4 of her savings is $300. So her original savings are 4 times $300 = $1200
correct answer A
Answer: A
Question: If the number is divided by 3, it reduced by 48. The number is
Options:
A)A)51
B)B)50
C)C)45
D)D)72
E)E)36
Rationale: Explanation:
Let the number be x. Then,
x - (x/3) = 48 => 2x/3 = 48
=> x = 72
Answer: Option D
Answer: D
Question: If a: b = 12: 6, b: c = 9: 7, find a: b: c?
Options:
A)118: 53: 66
B)138: 73: 46
C)128: 43: 36
D)108: 63: 56
E)148: 83: 76
Rationale: a: b = 12: 7
b: c = 9: 8
a: b: c = 108: 63: 56
ANSWER:D
Answer: D
Question: The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.500 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
Options:
A)620
B)720
C)820
D)920
E)1020
Rationale: 500 84
\ /
90
/ \
6 410
3:205
3->12
205->?
820
ANSWER:C
Answer: C
Question: How many different subsets of the set {0, 1, 2, 3} do not contain 0?
Options:
A)A.3
B)B.7
C)C.8
D)D.2
E)E.4
Rationale: Number of subset
Since we have 3 digits other than 0, we can take any numbers from the set of 3 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
3c1+3c2+3c3=7
And one set is the NULL set having no elements in it so
7+1=8.
ANSWER C.
Answer: C
Question: If two numbers are in the ratio 3:4. If 10 is added to both of the numbers then the ratio becomes 4:5 then find the smallest number?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Explanation:
3:4
3x + 10 : 4x + 10 = 4 : 5
5[3x + 10] = 4[4x + 10]
15x + 50 = 16x + 40
16x - 15x = 50 - 40
x = 10
Then smallest number is = 3
3x = 30
Answer: Option C
Answer: C
Question: Triathlete Dan runs along a 4-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
Options:
A)1/8
B)2/15
C)3/15
D)1/4
E)3/8
Rationale: Dan travels 8 miles round trip.
Running part: (4/10 *60 = 24 minutes)
Swimming Part: (4/6 *60 = 40 minutes)
8 miles in (24+40) minutes
8/64 = 1/8 mile per minute
Answer: 1/8 mile per minute
Answer: A
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 40 kg. What is the weight of the new person?
Options:
A)75
B)65
C)85
D)95
E)60
Rationale: Total increase in weight = 8 × 2.5 = 20
If x is the weight of the new person, total increase in weight = x−40
=> 20 = x - 40
=> x = 20 + 40 = 60
Answer is E.
Answer: E
Question: A rectangular box has two sides whose
lengths are 3 centimeters and 9 centimeters
and a volume of 135 cm3. What is the area
of its largest side?
Options:
A)27 cm2*square
B)36 cm2*square
C)39 cm2*square
D)45 centimeter square
E)48 cm2*square
Rationale: The box has dimensions of 3 and 9 and a volume of 135, so plug these values into the
formula for the volume of a box:
V=lwh=>
135=(3)(9)h=>
135=27h=>
5h
So the remaining dimension of the box is 5. The two longest dimensions are 5 and 9, so the
area of the largest side is 5 × 9 = 45
correct answer D)45 cm2*square
Answer: D