If a and b are two real numbers, is ab

Question

If a and b are two real numbers, is ab < 6?

(1) |a-2| < 1

(2) |b+3| < 5

chetan2u · Answer

We require values of both a and b as there are no restrictions on them. Clearly, both the statements individually are insufficient. 1) |a-2|<1 a-2<1…..a<3 2-a<1…..a>1 So, the range is 1-8 So, the range is -8

JerryAtDreamScore · Answer

Breaking Down the Info: We have to be careful of the signs of a and b. Two very negative numbers will make a*b > 6. Statement 1 Alone: Nothing on b so this is insufficient. Opening the absolute value gives us -1 < a - 2 < 1 and 1 < a < 3 so we at least know a is positive. Statement 2 Alone: Nothing on a so this is insufficient. Opening the absolute value gives us -5 < b + 3 < 5 and -8 < b < 2 . Both Statements Combined: Since a cannot be negative, we can only attempt to get a*b > 6 by multiplying the two biggest positive values of each. The biggest value of a*b is near 3*2 = 6, so a*b must be less than 6. Thus by combining statements it is sufficient. Answer: C

ktzsikka · Answer

Here is the  OE

Solution:
Step 1: Analyse Question Stem
a and b are two real numbers.
We need to find if a* b < 6 or not.
We don’t know anything about a and b, so let’s analyse each statement and see if we can find if a* b < 6 or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: |a – 2| < 1

⟹ -1 < a – 2 < 1

⟹ -1 + 2 < a – 2 +2 < 1 + 2

⟹ 1 < a < 3

We know the range of a, however, don’t know anything about b. Hence, statement 1 is not sufficient and we can eliminate answer options A and D.

Statement 2: |b + 3| < 5

⟹ -5 < b + 3 < 5

⟹ -5 – 3 < b + 3 – 3 < 5 - 3

⟹ -8 < b < 2

We know the range of b, however, don’t know anything about a. Hence, statement 2 is also not sufficient and we can eliminate answer B.

Step 3: Analyse Statements by Combining
From statement 1: 1 < a < 3

From statement 2: -8 < b < 2

Multiplying the extreme values of a and b, we get

1 x – 8 = -8

1 x 2 = 2

3 x -8 = -24

3 x 2 = 6

Thus, the range of a*b will be:

-24 < a*b < 6

We can clearly see that the value of a*b is always less than 6. Hence the correct answer is  Option C.

bumpbot · Answer

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If a and b are two real numbers, is ab < 6? (1) |a-2| < 1 (2) |b+3|

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