XAT 2021 — Decision Making Question 12
Read the following scenario and answer the three questions that follow.
The following plot describes the height (in cm), weight (in kg), age (in years) and gender (F for female, M for male) of 20 patients visiting a hospital.
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A person’s body mass index (BMI) is calculated as weight (in kg) divided by squared height (measured in square metres). For example, a person weighing 100 kg and of height 100 cm (1m) will have a BMI of 100. A person with BMI less than or equal to 18.5 is considered as underweight, above 18.5 but less than or equal to 25 as normal weight, above 25 but less than or equal to 30 as overweight, and above 30 as obese.
Zahir and Raman are at the entrance of a dark cave. To enter this cave, they need to open a number lock. Raman sees a note on a rock: “ ... chest of pure diamonds kept for the smart one ... number has six digits ... second last digit is 2, third last is 4 ... divisible by all prime numbers less than 15 ...”. Excited, Zahir and Raman seek your help: which of these can be the first digit of the six digit number that will help them open the lock?
Answer & solution
- A
5
- B
3
- C
9
- D
1
4
Let the 6 digit number be _ _ _ 42_
It is divisible by 2,3,5,7,11,13
Hence, the number is a multiple of 2 × 3 × 5 × 7 × 11 × 13 = 30030
Now, 30030 × k = _ _ _ 4 2 _
Last digit would definitely be 0.
Second last digits which is 2 should be the last digit of 3 × k. Hence, last digit of k should be 4.
âââââââ∴ k = 4 or 14 or 24 and so on.
The only possible value of k from the one's given above satisying the conditions given is 14.
âââââââ∴ 30030 × 14 = 420420
âââââââ∴ The first digit is 4.
Hence, option (e).