Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

Is A>B ?

I. A² + A = ¾ and B² + 2B = 24

II. A² – 3A = -9/4 and B² – 3B = 4

A Statement I alone is sufficient to answer the question.

B Statement II alone is sufficient to answer the question.

C Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

D Either Statement I or Statement II alone is sufficient to answer the question.

E Neither Statement I nor Statement II is sufficient to answer the question.

Solution

Correct Answer: Option E

A² + A = ¾ and B² + 2B = 24

Solving both the quadratic equations to obtain the roots,

A² + A = ¾

We can solve this equation using two methods. One is to use formula \(\frac{{ - b \pm \left( {\sqrt {{b^2} - 4ac} } \right)}}{{2a}}\)

or we can solve it by adding a certain number to both sides such that it makes the LHS a perfect square.

In this case, we add ¼ on both sides to make the LHS of the above equation a perfect square.

⇒ A² + A+ ¼ = ¾ + ¼ ⇒A² + A+ ¼ = 1

A² + A + ¼ = (A + ½)²

⇒ (A + ½)²= 1

⇒ A + ½ = ± 1

⇒ A = +1/2 or -3/2

Similarly, for B² + 2B = 24, we add 1 on both sides,

⇒ B² + 2B+ 1 = 24 + 1 = 25

⇒ (B + 1)² = 25

⇒ B + 1 = ± 5 ⇒B = 4 or – 6

The question cannot be answered by using only these two statements, since each of X and Y have two values.

Hence, statement I is insufficient to answer the question.

From statement II:

A² – 3A = -9/4 and B² – 3B = 4

We solve these equations in a method similar to the one explained previously.

We add 9/4 on both sides

⇒ A² – 3A+ (9/4) = (-9/4) + (9/4)

⇒ A² – 3A+ (9/4) = 0

⇒ (A – (3/2))² = 0

⇒ A = 3/2

Similarly, B² – 3B = 4

We add 9/4 on both sides

B² – 3B+ (9/4) = 4 + (9/4)

⇒ B² – 3B + (9/4) = 25/4

⇒ (B – (3/2))² = 25/4

⇒ B – (3/2) = ± 5/2

⇒ B = 4 or –1

Although the value of A is known, the question cannot be answered since B has 2 values, one less than A and the other greater than A.

Combining the two statements we are not able to reach to a conclusion about values of A and B, and hence the relation between them cannot be determined.

The question can not be answered even if both the statements are combined.

অ্যাপ/ওয়েবসাইটে রুটিনভিত্তিক নিয়মিত লাইভ পরীক্ষা হচ্ছে।

পরীক্ষা – ১১২

কোর্স নামঃ ১৯ তম শিক্ষক নিবন্ধন - লেকচারশীট ভিত্তিক।

টপিকসঃ

সাধারণ জ্ঞান – বাংলাদেশ
বাংলাদেশের জাতিগোষ্ঠী ও উপজাতি সংক্রান্ত বিষয়াদি ষষ্ঠ জনশুমারি ও গৃহগণনা ২০২২। বাংলাদেশের খেলাধুলা বাংলাদেশের কৃষ্টি ও সংস্কৃতি বাংলার সংগীত

পরীক্ষা শুরুঃ ৩য় ব্যাচ শুরু ৫ নভেম্বর, ২০২৫।

রুটিন দেখুন

পরীক্ষা – ৩৮

কোর্স নামঃ প্রাইমারি প্রধান শিক্ষক নিয়োগ প্রস্তুতি (২য় ব্যাচ)

টপিকসঃ

বাংলা: বানান
ইংরেজি: Literary Terms
গণিত: স্থানাঙ্ক জ্যামিতি, সমস্যা সমাধান
সাধারণ জ্ঞান: শিল্প-বাণিজ্য

৫ ফেব্রুয়ারি থেকে শুরু।

রুটিন দেখুন

Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below: Is A>B ? I. A2 + A = ¾ and B2 + 2B = 24 II. A2 – 3A = -9/4 and B2 – 3B = 4

Solution

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