Ronny uses a 5-digit key for a combination lock, where 5 digits need to be entered in a fixed sequence. While he remembers that the 5 digits are 9, 8, 7, 5, and 4, he has forgotten the sequence he uses. He also remembers that the sum of the first three digits is a multiple of 3, and so is the sum of the last three digits. Further, the sum of the last four digits is a multiple of 4.
Which of the following is DEFINITELY FALSE?
Which of the following is DEFINITELY FALSE?
Show Hint
- 9 is the third digit of the key
- 8 is the second digit of the key
- 8 is the fourth digit of the key
- 4 is the fourth digit of the key
- 4 is the second digit of the key
The Correct Option is C
Solution and Explanation
The 5 digits are 9, 8, 7, 5, and 4, but their sequence is unknown.
Step 2: Analyze the conditions.
- The sum of the first three digits must be a multiple of 3. - The sum of the last three digits must be a multiple of 3. - The sum of the last four digits must be a multiple of 4.
Step 3: Check each option.
We know that: - The sum of the last four digits must be a multiple of 4. The sum of the four digits is \( 9 + 8 + 7 + 5 = 29 \), and we must check if this sum fits the condition. This doesn't work, so the combination where 8 is the fourth digit will be impossible.
Step 4: Conclusion.
The correct answer is (C) because having 8 as the fourth digit does not satisfy the conditions.
Top Questions on Geometry
- During Durga Puja, for the purpose of lighting, one puja pandal in Kolkata used many identical structures made of wooden sticks. The design of the structures was as follows: each structure was constructed with the help of six wooden sticks by combining an isosceles triangular structure, and a square structure, with the bases of both structures being the same. Let us take one such structure. Call the triangle PAB, with PA = PB, and the square ABCD, with AB being the same wooden stick as a common base for the triangle and the square. To make the structure strong, the two equal sides of the triangular structure were tied with the opposite side of square’s base, i.e., CD, at points E and F, in such a way that CE = EF = FD. The structure was hung from P.
If AB = 0.5m (meter), the total length of wooden sticks required for twenty such structures is:
- Rajan is a fruit seller. On any day, he sells only one kind of fruit. On the first day, he buys 9 kg of blueberries. On the second day, he buys 22 kg of kiwis. On the third day, he buys mangoes at Rs. 35/kg and spends Rs. 15 less than any of the previous three days.
If he then sells all the mangoes at Rs. 50/kg, what is his MINIMUM possible profit on the fourth day?
- During Durga Pooja, six wooden sticks are used to create a structure to be used in a Pandal. First, an isosceles triangle is created using three sticks. Let this triangle be \(PAB\) with \(PA = PB\). Then a square \(ABCD\) is completed using the common base \(AB\). To strengthen this structure, the equal sides \(PA\) and \(PB\) are also joined to points \(E\) and \(F\) on side \(CD\) such that \(CE = EF = FD\). What is the total length of sticks used to create 20 such structures if \(AB = 0.5\) meters?
- Two equal circles of radius 5 cm are touching each other at point \(P\). A common tangent to the circles touches them at points \(Q\) and \(R\). A square is drawn inside triangle \(PQR\) such that one of its sides is resting on this common tangent and the other two vertices touch the two circles. Find the area of the square.
- Let the three sides of a triangle ABC be given by the vectors $$ 2\hat{i} - \hat{j} + \hat{k}, \quad \hat{i} - 3\hat{j} - 5\hat{k}, \quad \text{and} \quad 3\hat{i} - 4\hat{j} - 4\hat{k}. $$ Let G be the centroid of the triangle ABC. Then $$ 6 \left( |\vec{AG}|^2 + |\vec{BG}|^2 + |\vec{CG}|^2 \right) \text{ is equal to}$$ _______
Questions Asked in XAT exam
- Arrange the following generations from the oldest to the youngest:
1. Generation X
2. Silent Generation
3. Generation Alpha
4. Baby Boomers
5. Millennials
- XAT - 2026
- Current Affairs
- Read the following scenario and answer the THREE questions that follow.
Brijbhushan, a microfinancier, lends money at the rate of Rs.10 per square meter to small farmers at a village. He charges an annual interest rate of 10%. All the farming plots in that village are rectangular, with areas varying between a minimum of 1000 square meters and a maximum of 10,000 square meters.
This year, Brijbhushan has lent money only to five farmers: Aditya, Binod, Chhuttan, Dabloo and Govind. The perimeter of Chhuttan’s plot is 250 meters, with the length and width being at a ratio of 4:1. Aditya’s plot has an area three times the area of Govind’s plot. The area of Aditya’s plot is also the average of the areas of Govind’s plot and Dabloo’s plot. The plots belonging to Aditya, Binod and Dabloo are of the same width, but of different lengths. Moreover, the length of Binod’s plot is the sum of the lengths of Aditya’s plot and Dabloo’s plot.- XAT - 2026
- Mensuration
Light Chemicals is an industrial paint supplier with presence in three locations: Mumbai, Hyderabad and Bengaluru. The sunburst chart below shows the distribution of the number of employees of different departments of Light Chemicals. There are four departments: Finance, IT, HR and Sales. The employees are deployed in four ranks: junior, mid, senior and executive. The chart shows four levels: location, department, rank and gender (M: male, F: female). At every level, the number of employees at a location/department/rank/gender are proportional to the corresponding area of the region represented in the chart.
Due to some issues with the software, the data on junior female employees have gone missing. Notice that there are junior female employees in Mumbai HR, Sales and IT departments, Hyderabad HR department, and Bengaluru IT and Finance departments. The corresponding missing numbers are marked u, v, w, x, y and z in the diagram, respectively.
It is also known that:
a) Light Chemicals has a total of 210 junior employees.
b) Light Chemicals has a total of 146 employees in the IT department.
c) Light Chemicals has a total of 777 employees in the Hyderabad office.
d) In the Mumbai office, the number of female employees is 55.
- XAT - 2026
- Pie Charts
An investment company, Win Lose, recruit's employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:
1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.
Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.
Ratan, Shri, Tamal and Upanshu started working for Win Lose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits (in Rs. ‘000’) over the 12-month period, where x, y and z are masked information.
Note:
• A negative profit value indicates a loss.
• The value in any cell is an integer.
Illustration: As Upanshu is continuing after March, that means his total profit during January-March (2z +2z +0) ≥
Rs.20,000. Similarly, as he is continuing after June, his total profit during January − June ≥
Rs.10,000, as well as his total profit during April-June ≥ Rs.10,000.
- XAT - 2026
- Logical and Analytical Reasoning Skills
Business schools’ (B schools) curriculums are filled with group assignments and case competitions. Even when students have just joined the B schools, corporate houses try 38 to catch good talent early by promising them internships based on case competitions. These competitions involve solving the problems presented by the organizations, analyzing the challenges they currently face, and presenting solutions in a manner that convinces the organizations’ representatives.
For students who are just joining a B school, the capability to actually solve such problems is quite limited. Because of that, the corporate houses generally are more focused on the presentations made by groups. Hence, the groups that communicate better, most often, win these competitions.
Abirami joins MBS, a B school. As a fresher, she believes she needs to learn a lot about how organizations work and wants to work with others who have joined MBS and have work experience.- XAT - 2026
- Statements and Assumptions