divelab/Sys2Bench huggingface dataset:
Question: Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature Q in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
Options:
A)29
B)30
C)30.5
D)31
E)32
Rationale: to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median will be==>mean of 15 and 16 th place temperature Q===>(30+30)/2=30
hence B
Answer: B
Question: A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is
Options:
A)2 km/hr
B)4 km/hr
C)5 km/hr
D)10.5 km/hr
E)None
Rationale: Sol.
Speed of stream = 1/2(28-10) kmph = 4 kmph.
Answer B
Answer: B
Question: Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed T?
Options:
A) 6
B) 8
C) 10
D) 12
E) 16
Rationale: Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)
As per question, 96/(x-4) - 96/1.5x = 16
Solving this T we get x = 8.
B.
Answer: B
Question: A certain stock exchange designates each stock with a two-letter or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes using only the vowels A, E, I, O, or U?
Options:
A)110
B)120
C)130
D)140
E)150
Rationale: The number of two-letter codes is 5*5=25.
The number of three-letter codes is 5*5*5=125.
The total number of codes is 25+125=150.
The answer is E.
Answer: E
Question: Which of the following must be true if b=x^5
I. b is positive.
II. x is non-negative.
III. If x is positive then b is positive.
Options:
A)I only
B)II and III only
C)II only
D)I and III only
E)III only
Rationale: I. b is negative --> true
II. b is non-negative. b can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If x is positive then b is positive.
Answer: D (I and III only).
Answer: D
Question: If 2 >p > 1> q > 1, which of the following must be greater than 1?
I.	p/q
II.	pq
III.	p-q
Options:
A)I and II
B)I and III
C)I only
D)II only
E)III only
Rationale: We could solve this easily using counter examples.
I is true since p>q and both are positive
II is false. Take p=4/3, q=3/4. pq=1
III is false. Take p=1.2, q=0.3. p-q=0.9
So, the answer is A
Answer: A
Question: The average of 9 numbers is 104. Average of the first 5 of them is 99 and that of the last 5 is 100. Find the 5th number?
Options:
A)46
B)59
C)63
D)75
E)88
Rationale: Sum of all the 9 numbers = 9 * 104 = 936Sum of the first 5 of them = 5 * 99 = 495Sum of the last 5 of them = 5 * 100 = 500So, the 5th number = 495 + 500 - 936= 59.Answer: B
Answer: B
Question: There are 28 stations between Kolkatta and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)870
B)970
C)1070
D)1000
E)800
Rationale: The total number of stations = 30
From 30 stations we have to choose any two stations and the direction of travel (i.e., Kolkatta to Chennai is different from Chennai to Kolkatta) in 30P2 ways.
30P2= 30 * 29 = 870
ANSWER: A
Answer: A
Question: A student,after his teacher's question, chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
Options:
A)344
B)251
C)411
D)212
E)120
Rationale: Let x be the number he chose, then
2⋅x−138=102
2x=240
x=120
correct answer is E)120
Answer: E
Question: If Y > X and XM < YM, what must be true?
Options:
A)M > 0.
B)M < Y.
C)X < 0.
D)M < 0.
E)Y < 0.
Rationale: X<Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when ve is multiplied on both sides. That means M is ve
A is the answer
Answer: A
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
Options:
A)8
B)6
C)5
D)5
E)4
Rationale: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer:B
Answer: B
Question: A simple interest amount of rs 5000 for six month is rs 200. what is the anual rate of interest?
Options:
A)10%
B)6%
C)8%
D)9%
E)7%
Rationale: S.I=P*N*R/100
200=5000*0.5*R/100
R=200*100/(5000*0.5)
R=8%
ANSWER:C
Answer: C
Question: f n = 3^5 - 2^5, which of the following is NOT a factor of n?
Options:
A)211
B)422
C)633
D)100
E)844
Rationale: =243-32 =211 is prime number.any number not a factor of 211
D
Answer: D
Question: In how many ways can be 6 boys and 6 girls sit around circular table so that no two boys sit next to each other?
Options:
A)(5!)^2
B)(6!)^2
C)5!6!
D)11!
E)(5!)^2*6!
Rationale: first fix one boy and place other 5 in alt seats so total ways is 5!
now place each girl between a pair of boys... total ways of seating arrangement of girls 6!
total is 5!*6!
ANS C
Answer: C
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
Options:
A)Rs.109
B)Rs.108
C)Rs.100
D)Rs.103
E)Rs.102
Rationale: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x = 100 Rs.
Answer:C
Answer: C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)200 m
B)225 m
C)245 m
D)250 m
E)270 m
Rationale: Let the length of the bridge:L
The equation now is L+130/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =245m
ANSWER:C
Answer: C
Question: A car owner buys petrol at 7.50, 8.00 and 8.50 per litre for three successive years. What approximately is his average cost per litre of petrol if he spends 4000 each year?
Options:
A)8
B)9
C)7.98
D)8.50
E)None of these
Rationale: Let average cost of petrol per litre be x
Then x = 12000 /4000/7.5+4000/8+4000/8.5
= 3 /2/15+1/8+2/17=6120/767= Rs. 7.98 per litre
Answer C
Answer: C
Question: 128% of 5/8 =
Options:
A)0.2
B)0.5
C)0.6
D)0.8
E)1.0
Rationale: Should be simple.
1.28*5/8 = 6.4/8= 0.8
Correct Option : D
Answer: D
Question: 0, 1, 2, 4, 6, 9, 12, 16, ?
What number should replace the question mark?
Options:
A)24
B)20
C)19
D)26
E)47
Rationale: B
20
add 1, 1, 2, 2, 3, 3, 4, 4.
Answer: B
Question: The product of x and y is a constant. If the value of x is increased by 60%, by what percentage must the value of y be decreased?
Options:
A)30%
B)32%
C)35%
D)37.5%
E)40%
Rationale: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.6x (120)
i.e. 160*New 'y' = 10000
i.e. New 'y' = 10000/160 = 62.5
i.e. y decreases from 100 to 62.5 i.e. Decrease of 37.5%
Answer: option D
Answer: D
Question: Two trains 300 m and 450 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.6
B)27
C)10.4
D)10.8
E)10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 300 + 450 = 750 m.
Required time = 700 * 9/250 = 27 sec.
Answer: B
Answer: B
Question: By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .
Options:
A)12%
B)25%
C)30%
D)45%
E)50%
Rationale: Sol:
(SP of 33m)-(CP of 33m)=Gain=SP of 11m
SP of 22m = CP of 33m
Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.
Gain%=[(11/22)*100]%=50%
Ans: E
Answer: E
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 30%?
Options:
A)1/2
B)2/6
C)3/6
D)9/6
E)15/2
Rationale: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 180% of Re. 1 = Rs. 9/5
For Rs. 9/5 , toffees sold = 6.
For Re. 1, toffees sold = 9 x 5 /6 =15/2.
Answer E
Answer: E
Question: a, b, c are non negitive integers such that 28a+30b+31c = 365. a + b + c = ?
Options:
A)22
B)12
C)88
D)73
E)92
Rationale: In a calender,
Number of months having 28 days = 1
Number of months having 30 days = 4
Number of months having 31 days = 7
28 x 1 + 30 x 4 + 31 x 7 = 365
Here, a = 1, b = 4, c = 7.
a+b+c = 12
Answer:B
Answer: B
Question: Write 880,000,000,000 in scientific notation.
Options:
A)8.8 * 10^11
B)800.900 * 10^11
C)8.900 * 10^11
D)80.9000* 10^11
E)08.900 * 10^11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
880,000,000,000 = 8.8* 100,000,000,000 = 8.8 * 10 11**
correct answer A
Answer: A
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Options:
A)20 %
B)10 %
C)15 %
D)22 1/2%
E)21%
Rationale: Explanation:
9 = (1*40*R)/100
R = 22 1/2 %
ANSWER IS D
Answer: D
Question: If n is a prime number, which of the following could be true
Options:
A)n^n/4 = 1^(n-1)
B)n^2/4= is even
C)(n)(n^n) = is negative
D)n^2+n^3= n^5
E)n^n=n
Rationale: A should be the answer.
2^2/4 = 1^(2-1)
Answer: A
Question: How many multiples of 4 are there between 20 and 112, inclusive?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: The multiples of 4 are from 4*5 up to 4*28.
28-5+1 = 24.
The answer is D.
Answer: D
Question: If w is 40 percent less than u,u is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?
Options:
A)4%
B)18%
C)36%
D)40%
E)50%
Rationale: GIven w= 0.6u, u=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. E is the correct answer.
Answer: E
Question: A certain company’s profit in 1996 was 20 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
Options:
A)5%
B)18%
C)33%
D)44%
E)38%
Rationale: Profit in 1995 - 100
Profit in 1996 - 120
%increae Profit in 1997 in comparison to 1995 = 20 + 120*20%= 44
Correct Option : D
Answer: D
Question: Pat's watch gains an extra 10 seconds every 3 hours. Kim's watch loses 4 seconds every 2 hours. If both watches are set to correct time at 8 o'clock in the morning and run without interruption, after 36 hours, what will be the difference in time between Pat's watch and Kim's watch?
Options:
A) 3 min 16 sec
B) 3 min 15 sec
C) 3 min 14 sec
D) 3 min 13 sec
E) 3 min 12 sec
Rationale: In 36 hours Pat's watch will gain an extra 36/3*10 = 120 seconds.
In 36 hours Kim's watch will lose 36/2*4 = 72 seconds.
Hence the difference will be 120 + 72 = 192 seconds.
Answer: E.
Answer: E
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 50 paisa and Z gets 40 paisa. If the share of X is RS. 30, what is the total amount?
Options:
A)67
B)55
C)62
D)47
E)57
Rationale: x:y:z = 100:50:40
10:5:4
10 --- 30
19 --- ? => 57
Answer: E
Answer: E
Question: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
Options:
A) 4
B) 6
C) 9
D) 5
E) 12
Rationale: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides and added top , hence 4+1 = 5.
D
Answer: D
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $240, what were her original savings?
Options:
A)$900
B)$800
C)$960
D)$700
E)$1500
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 $240. So 1 / 4 of her savings is $240. So her original savings are 4 times $240 = $960
correct answer C
Answer: C
Question: A apple costs Rs 20 each and a watermelon costs Rs. 7 each. If I spend Rs 47 on total what is the number of apple I purchased?
Options:
A)5
B)6
C)2
D)7
E)8
Rationale: 2 * 20 +7 = 47
Answer : 2 apple
Answer : C
Answer: C
Question: Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 30 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
Options:
A)81
B)159
C)166
D)285
E)304
Rationale: I solve it using the tough luck technique:
According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.
80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=100>80
Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books
What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.
We picked:
50 Botany Books
65 Zoology Books
30 Geology Books
Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!
Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick
79*2+1 books
Because, we could have picked the books in following order;
1st book picked: Physics
2nd book picked: Chemistry
3rd book picked: Physics
Thus, Total= 50+65+30+79*2+1=145+1+158=304
Ans:E
Answer: E
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
Options:
A)10.6 km/hr
B)10.8 km/hr
C)18.8 km/hr
D)80.8 km/hr
E)10.1 km/hr
Rationale: Total distance traveled = 10 + 12
= 22 km /hr.
Total time taken = 10/12 + 12/10
= 61/30 hrs.
Average speed = 22 * 30/61
= 10.8 km/hr.
Answer: B
Answer: B
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 3000. The difference between the profit shares of A and C is?
Options:
A)621
B)276
C)236
D)600
E)1200
Rationale: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 3000
=> 5 parts out of 15 parts is Rs. 3000
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (3000) = Rs. 1200
Answer: E
Answer: E
Question: In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 5 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?
Options:
A) 18.6
B) 9.3
C) 1.2
D) 3.1
E) 1.6
Rationale: number of
passengers using Kennedy airport = 37/3 =~12.43
Passengers using Miami airport = 12.43/2=~6.2
passengers using logan airport = 6.2/5 =~1.24
so C
Answer: C
Question: What will come in place of the x in the following Number series? 5, 10, 20, x , 55
Options:
A)33
B)37
C)55
D)50
E)43
Rationale: (C)
The pattern is + 5, + 10, + 15, +20 â€¦â€¦â€¦..
So the missing term is = 20 + 15 = 55
Answer: C
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
Options:
A)400
B)625
C)1250
D)2500
E)10 000
Rationale: If x is total number of fish in the pond :
4 = 50/x * 100
=> x = 1250
So answer is C
Answer: C
Question: A man had to make 3 trips to the store because he kept forgetting items his wife had requested. The store was 500 meters from his home. It took the man 45 minutes to complete the store run. What was the man's speed in kilometers per hour.
Options:
A)2
B)1.5
C)2.25
D)3
E)1.75
Rationale: The distance between the man's home and the store is 500 meters.
3 times means that the man made the 500 meter trip 6 times in total.
6 * 500 = 3000 meters or 3 km.
Since the man's total time was 45 min, we need to multiply 3000 by 3/4 or .075.
Correct answer is 2.25 km per hour
Answer: C
Question: Triangle STV has sides ST = TV = 13, and SV = 10. What is the area?
Options:
A)60
B)100
C)120
D)136
E)165
Rationale: Let the base B of the triangle be SV = 10. Then we need to find the height H.
H^2 = 13^2 - 5^2 = 144 and then H = 12.
The area is (1/2)*B*H = 5*12 = 60
The answer is A.
Answer: A
Question: A student committee that must consists of 6 members is to be formed from a pool of 8 candidates. How many different committees are possible
Options:
A)5
B)28
C)40
D)56
E)336
Rationale: Out of 8 people, any 6 can be selected for a committee. So 8c6= 28 is the answer.
B
Answer: B
Question: 2^1 + 2^1 + 2^1 + 2^1 =
Options:
A)2^2
B)4^6
C)4^8
D)4^9
E)4^12
Rationale: Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
2^1 + 2^1 + 2^1 + 2^1 =
Now, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...
X + X + X + X =
What would the sum be?
Clearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...
2^1 + 2^1 + 2^1 + 2^1 =
2(2^1)
This can be re-written as...
(2^1)(2^1)
...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...
(2^1)(2^1) = 2^2
Final Answer:
A
Answer: A
Question: If M = 2N+1 where M is an Integer then which of the following is true?
Options:
A)M is even if N is a non integer and a multiple of 0.5
B)M is always Even
C)M is a non multiple of 2
D)M= 1
E)M IS ODD
Rationale: A
Answer: A
Question: A man purchases 2 watches for $ 500. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
Options:
A)$ 260 and $ 300
B)$200 and $ 300
C)$224 and $336
D)$560 and $560
E)$224 and $ 350
Rationale: x + y = 500 --- (1)
1.15x + 0.9y = 500 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*100)/(3*100) = 200/300
Answer: B
Answer: B
Question: A man can row downstream at the rate of 10 Km/hr and upstream at 6 Km/hr. Find man's rate in still water and the rate of current?
Options:
A)9,6
B)8,2
C)9,3
D)6,6
E)None of these
Rationale: Explanation:
Rate of still water = 1/2 (10 + 6) = 8 Km/hr
Rate of current = 1/2 (10-6) = 2 Km/hr
Answer: Option B
Answer: B
Question: In the youth summer village there are 300 people, 200 of them are not working,100 of them have families and 125 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
Options:
A)150
B)125
C)175
D)200
E)100
Rationale: total =300
not working =200
having family=100
like to sing in shower = 125
working=300-200=100
not having family = 300-100=200
like to sing in shower = 125
largest possible number is the lowest possible among the above
Thus 100
E
Answer: E
Question: The price of cooking oil has increased by 25%. The percentage of reduction that a family should effect in the use of cooking oil so as not to increase the expenditure on this account is?
Options:
A)25%
B)20%
C)23%
D)24%
E)none of these
Rationale: Reduction in consumption
= [(P/(100 + P)] X 100)%
= [(25/(100 + 25)] X 100)%
= 20%
ANSWER:B
Answer: B
Question: In the quiet town ofNothintodothere are 600 inhabitants, 400 are unemployed and 200 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
Options:
A)50.
B)100.
C)150.
D)200.
E)300.
Rationale: Total = 600
unemployed=400
employed=600-400=200
som=200
unemployed som = 200/2=100
employed som = 100
employed that are not som = 200-100=100
Answer : B
Answer: B
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 35.
Options:
A)324
B)350
C)384
D)444
E)256
Rationale: Number of odd numbers between 1 and 35 is (35+1)/2=18
Therefore Sum of odd numbers 18*18= 324
ANSWER: A
Answer: A
Question: A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?
Options:
A)1:2:8
B)1:2:0
C)1:2:5
D)1:2:4
E)1:2:1
Rationale: WC of A: B = 1:2
B: C = 1:2
---------------------
A: B: C = 1:2:4
Answer:D
Answer: D
Question: The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 20 positive perfect squares?
Options:
A)1,010
B)1,164
C)1,240
D)2,316
E)2,870
Rationale: First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.
Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.
Plug values of n = 20 and c = 1/2 into the equation and simplify to get the answer 2870.
Option E.
Answer: E
Question: A rectangular photograph is surrounded by a border that is 3 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 6 inches wide on each side, the total area would have been (M + 178) square inches. What is the perimeter of the photograph, in inches?
Options:
A)34
B)36
C)38
D)40
E)20
Rationale: Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)
According to the question:
(L+6)(B+6) = m ----(2)
and
(L+12)(B+12) = m + 178 ---------> (L+12)(B+12) - 178 = m ------(3)
Equating (2) and (3)
(L+6)(B+6) = (L+12)(B+12) - 178
LB + 6L + 6B +36 = LB + 12L + 12B + 144 -168
Simplify
6L + 6B = 60 ------> 2(L+B) = 20 (Check eq (1))
Answer is E
Answer: E
Question: The price of 357 mangoes is Rs. 1517.25 what will be the approximate price of 9 dozens of such mangoes ?
Options:
A)Rs. 3000
B)Rs. 3500
C)Rs. 4000
D)Rs. 2500
E)None of these
Rationale: Solution
Let the required price be Rs. x. Then, More mangoes, More price
∴ 357 : (49 × 12) : : 1517.25 : x
⇔ 357 x = (49 × 12 × 1517.25) ⇔ x = 49x12x1517.25/357⇔ x = 2499.
Hence, the approximate price is Rs. 2500 . Answer D
Answer: D
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is even
II. (x+z)/y is an integer
III. xz is even
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: x, y, and z are consecutive integers ⇒
Y = X+2
Z = X+4
1- x+y is even - Correct: sum of any 2 odd integers is even
2- (x+z)/y is an integer - Correct: x+z = x+x+4 = 2x+4 = 2(x+2)
and x+z/y = 2(x+2)/x+2 = 2 ⇒ integer
3- xz is even - Not Correct: multiplication of any 2 odd integers is always odd
Answer: D
Answer: D
Question: If a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?
Options:
A)6
B)18
C)20
D)108
E)216
Rationale: 1st member can be selected in 6 ways
2nd can be selected in 5 ways
3rd can be selected in 4 ways
So total ways : 120
But to avoid the similar scenarios 120/3!=20
ANS:C
Answer: C
Question: If m is not equal to zero, and m+1/m = 1, then what is the value of m^4 + (1/m)^4?
Options:
A)-5
B)-4
C)-3
D)-2
E)-1
Rationale: m + 1/m=1
we square both sides so we have m^2 + 1/m^2 +2 = 1
or m^2 + 1/m^2= -1
squaring again we have m^4 + 1/m^4 + 2 = 1
or m^4 + 1/m^4 = -1
answer =-1 (E)
Answer: E