**Data Sufficiency Answer Set-1**

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**1.**From st. a x is prime factor of 42

42 can be written as 6.7, 21.2, 14.3, and 42.1

In the above list (6,7), (21,2) and (14,3) are co-primes

From st. b the range of x is given 5 £ x £ 11

Prime no. in this range is 7

Hence the value of x using both statements is 7.

**2.**From st. a 7 4x – 1 = 343

7 4x – 1 = 73

4x – 1 = 3

4x = 4

x = 1

From st. b 7 x+y = 49 4

7 x+y = 7 8

x + y = 8

using value of x = 1 in then y = 8 – 1 = 7

the value of y – x = 7 – 1 = 6.

Using both sts. We can get the answer.

**3.**St. a is not required in this case as square of any no. is positive

hence we will consider st. b given x3 < 0 which implies x < 0

here we could answer the question.

st. b is enough to answer.

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**4.**St. a AC = 40

St. b AB = BC

AC2 = AB2 + BC2

2AB2 = 402

AB2 = 800

AB = 20Ö2

Area can be calculated.

Hence both the sts are required

**5.**st. a

B = 1

G + 10

B = G + 10

st. b

B + 20 = 3

G 1

Using both G + 10 + 20 = 3G

2G = 30

G = 15

B = 15 + 10

Hence both the sts are required.

**6.**st. a area = 289p

pr2 = 289p

r = 17

st. b

r + w = 23

using both sts

17 + w = 23

w= 6

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**7.**st. a A = C + 4

st. b 3A + 5C = 92

using both sts

3( C + 4 ) + 5C = 92

8 C = 80

C = 10

A = 14

Amount of 40 Adults and 50 Children can be calculated

Hence both the sts are required.

**8.**The question gives x + y + z = 45

st. a no.s are positive

st. b all the no.s are consecutive odd no.s

Using both the sts. By trial and error x, y, and z are 13, 15, and 17

Hence both sts. are required

**9.**st. a total balls are 36

st. b ratio of red and black is given as 2 : 1

No information of green balls is given.

Hence neither of the sts. are sufficient.

**10.**st. a 9x – 5y = 21

st. b 3x – 5y = 7

3

9x – 5y = 21

only one equation is given

hence neither of the sts. are sufficient.

**11.**st. a the wt of the packet is given as 800gms

st. b the cost of 500gms is Rs.75 and each additional 50gms costs

Rs.5 using both the sts. cost of the packet = 75 + 6.5 = 105

hence both the sts. are sufficient

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**12.**st. a gives the ratio of a : b : c = 4 : 5 : 6

st. b gives the semi perimeter (a + b + c) /2= 22.5

We can find out the area. Hence using both the sts. we can get the area.

Note: In data sufficiency there is no need to get exact answer. We should see whether we can get the answer using data given in both the sts.

**13.**st. a gives the sides of the triangle 17, 15, and 12

st. b gives the perimeter of the triangle as 44

to get the ratio a check should be done, when sides in st. a are

added can be the perimeter given in st. b

17 + 15 + 12 = 44

using area of triangle = s.r

and s = ( a + b + c )/2

we can find the ratio of semi perimeter and the in radius.

Hence both the sts. are required

**14.**st. a Vc = Vs 2

st. b radius of sphere is 9

using both the sts.

volume of sphere can be calculated and we can calculate the volume of cylinder.

Hence both the sts. are required.

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**15.**st. a C finished second

st. b D,E, and F are disqualified

but no data about A and B is not given.

Hence neither of the sts. are sufficient.

**16.**st. a W consumes more carbohydrates

st. b X and Y consume more proteins

who is heaviest can’t be determined.

Hence neither of the sts. are sufficient.

**17.**st. a Christmas is celebrated on 25th Dec

st. b day after tomorrow is 26th Dec

using both sts. we can answer the question

Hence both the sts. are sufficient.

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**18.**st. a the height of the wall is given

st. b the angle made by the ladder and the floor is given

using both the sts. we can be

using sin q = opposite /hypotenuse will give the length of the ladder. Hence both the sts. are sufficient.

**19.**st. a Area of rectangle = 180

st. b change of length, breath and corresponding perimeter of rectangle is given.

Using both the sts. % change in area can be calculated.

Hence both the sts. are required.

**20.**st. a 3cm snowfall for first fifteen days in January

st. b 4cm snowfall for the following fifteen days in January

using both sts. the information is for 30days ,where as January has 31 days

we can’t determine the average snowfall.

Hence neither of the sts. are sufficient.

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