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# Data Sufficiency Problem 1

 Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question.
 Mark A If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone. Mark B If the question can be answered by using either statement alone. Mark C If the question can be answered by using both statements together, but cannot be answered by using the either statement alone. Mark D If the question cannot be answered even by using both the statements together.
 1. What are the ages of two individuals, X and Y ? (I)  The age difference between them is 6 yr. (II) The Product of their ages is divisible by 6. (a) A (b) B (c) C (d) D
 2. Is x + y – z + t even ? (I)  x + y + t is even. (II) t and z are odd. (a) A (b) B (c) C (d) D
 3. What is the number X ? (I)  The LCM of X and 18 is 36. (II) The HCF of x and 18 is 2. (a) A (b) B (c) C (d) D
 4. What is the length of the rectangle ABCD ? (I)  Area of rectangle is 48 sq. unit. (II) Length of diagonal is 10 unit. (a) A (b) B (c) C (d) D
 5. What is the first term of an arithmetic progression of positive integers ? (I)  Sum of the squares of the first and the second term is 116. (II)The fifth term is divisible by 7. (a) A (b) B (c) C (d) D
 6. What is the price of bananas ? (I)  With Rs 84, I can buy 14 bananas and 35 oranges. (II) If price of bananas is reduced by 50%,then we can buy 48 bananas in Rs 12. (a) A (b) B (c) C (d) D
 7. What is the area of the triangle ? (I)  Two sides are 41 cm each. (II) The altitude to the third side is 9 cm long. (a) A (b) B (c) C (d) D
 8. What is the profit percentage ? (I)  The cost price is 80% of the selling price. (II) The profit is Rs 50. (a) A (b) B (c) C (d) D
 9. What is the value of x, if x and y are consecutive positive even integers ? (I)  (x – y)2 = 4 (II) (x + y)2≤ 100 (a) A (b) B (c) C (d) D
 10 If x, y and z are real numbers, is z-x is even or odd ? (I)  xyz is odd. (II) xy + yz + zx is even. (a) A (b) B (c) C (d) D

 1 D 2 C 3 C 4 C 5 A 6 A 7 C 8 A 9 D 10 A

Detailed Solution

1. ElitmusZone Post author

Hello Deepak,
Statement (1) (x =2, y = 4), (x = 4, y = 6), (x = 6, y = 8)
Statement (2) (x = 2, y = 4), (x = 4, y = 6)
Statemeat (1) and Statement (2) x={2, 4}
We have to find the unique value of x.

the ans for ques 9 is A cause we get the unique value of x in statement 2 . where it is said (a+b)^2 <100
and only one case fits here i.e X=2,Y=4 rather the value X=4,Y=6 gives the value 100 where it doesnt suit the question cause the condition says the value cant be equal or greater than 100

Abhishek !
Plz read statement 2 again it bcoz says (x+y)^2 <= 100 implies x+y <= 10
so x=4, y=6 or fit for this inequality.

for Q 5 :
statement 1 gives a=10 or -10 and b = 4 or -4
we don’t know that from which term will be first and second term…
so if we use statement 2 then we can be sure about first and second bcoz we have info about 5th term

so answer should be option C

1. ElitmusZone Post author

In Q No. 05, It is clearly mentioned that arithmetic Progression of POSITIVE INTEGER. Please don’t consider the negative numbers.
Further, Arithmetic Progression will be 4, 10, ……..

2. Shujayat Ali

Let the first term be a, and the difference between 2 consecutive terms be b.

(1) : a^2 + (a+b)^2 = 116
Both terms are positive integers, so we can try different values of a, to see the possible combinations of a^2 and (a+b)^2
(1,115)
(4,112)
(9,107)
(16,100)
(25,91)
(36,80)
(49,67)
(64,52)
(81,35)
(100,16)
Of these 100,16 is the only pair that satisfies the sum 116 and are squares of 2 integers.
Also, we know the progression is all positive integers, so it has to be an increasing progession
Means a=4 & a+b=10
Hence, (1) is sufficient

3. Sujata Malakar

But in this question they told about only positive integers. So only 1st statement is enough to tell the answer.

1. Mukul

No neha, It must be c. You are saying that Statement II is enough to give ans, as t and z are odd => t-z=even, so being even of x+y+t-z will depend on the sum of x+y (as t-z is even already from statement II) but statement II is not saying about the sum of x and y. So, it may be possible that sum of x and y become odd one time and become even next time. So, we cant judge about the x+y+t-z from II statement alone.

1. aishwary

in question 7 …the height of altitude is given but length of base is not given …so how can we find the area…altitude is drawn on the third line

3. Akash Singh

In question 4 we have a equation of l2+b2=100 where we remove one variable using l*b=48
Putting b=48/l in first eqn we get a four degree equation whose solution is

4. Akash Singh

In question 4 we have a equation of l2+b2=100 where we remove one variable using l*b=48
Putting b=48/l in first eqn we get a four degree equation whose solution is
l2=64, 72

from there we get two solutions one with l=sqrt(72) and l=8
then why the answer is C it should be D
because we are not getting a unique solution

1. Shivam Rawat

(Question no 4 ans is wrong)

In question 4.. What is the length of the rectangle ABCD ?
(I) Area of rectangle is 48 sq. unit.
(2)II) Length of diagonal is 10 unit.

solution:

(I) Area of rectangle is 48 sq. uni

POSSIBLE VALUES {(1,48),(2,24),(3,16),(4,12),(6,8),(12,4),(24,2)}
(not sufficient)

(II) Length of diagonal is 10 unit.

NOT SUFFICIENT ALONE

Let us take both statements together:

possible set of values satisfying both conditions { (8,6),(6,8)}

Even using both we cannot asnwer because there will be ambiguity as what should be value of length of rectangle as it can be 6 or 8.Hence,we didn’t get UNIQUE SOLUTION…

HENCE…Question cannot be answered even using both statements altogether

5. vaish

Q1 can b solved by using both d statement together..statmnt1: x-y=6
statmt 2 xy/6.. so x=12 n y=6.. diff is 6 n d product is divisible by 6..
tel me where m going wrong?

6. pawan

Answer for Q 10 should be B i.e solve by either of the statement.
In 1st case x,y,z value must me odd so we will get the result as odd.
In 2nd case x,y,z value must be even so we will get the result as even.

7. charan kumar

PLEASE explain q 2 as we can not answer the question by using with statement 1 and statement 2 so then how the answer will be c according to me the answer is d as c means (If the question can be answered by using both statements together, but cannot be answered by using the either statement alone.) but by using both we can not answer the question x+Y+T- z? according to statement 1 x+y+t is even means in order to obtain x+Y-z+t to be even then z should be even as even – even = even. but in statement 2 t and z are given odd it means we cant say that x+y will be even so in my point of view so how the answer is c my answer is d

8. Srijeeta Guha

no 10 should be marked as B because we can get the ans from both the statement.
From statement 1) we get the value of z-x is even.
from 2) z-x is odd.
the question was if z-x is even or odd! so we can get the ans from either the statement.
So the ans will be B

1. PRODABS

In 10, ans is ‘A’ because xy+yz+zx has to be even but value of z and x can b even *odd or even*even which is not certain therefore z-x cannot be determined.

9. Bhavya Mehta

Ans for question 5 is C.
An = A1 + (n-1)D
Therefore, 5th term =
A1+4D which is divisible by 7
(A1+4D)/7 = 0
therfore
lets say A1 = 2 then D = 6
lets say A1 = 3 then D = 15

and may be more so 1st term can not be determined by any one statement.

10. akanksha

in question 7 by using the first option we can find out the area.
since it is an isosceles triangle so they have equal angle i.e, 45. by using sin 45= height/ hyp we can find the hieght and then find the base. Please let me know if i m wrong

11. Niketan Moon

A1 + 4D = 7K;
where K is a constant variable.
It can only be solved by statement 1.
I hope this clears your doubt.

12. rahul jaiswal

bro the answer of 1st Q ans must be B.. here is the explation…
1st statement :- diff btw a and b is 6
2nd statement :- product of their ages is divigible by 6

if we get a=6 and b=12… diff btw both is 6 then
then the product of their age 72 and its divigible by 6

so i think its must be C

13. Shivam

in que it is not given that x,y,z are integer