1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
2. The number of satellites serving all three of B, C, and S is 100.
3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B.
What best can be said about the number of satellites serving C?
Must be between 450 and 725
- Cannot be more than 800
- Must be between 400 and 800
- Must be at least 100
The Correct Option is C
Solution and Explanation
The correct answer is (C):
The number of satellites serving region C is given by:
\[ \text{Satellites serving C} = z + 0.3x + 100 + y \]
Substitute the values from the equations:
\[ z = 550 - 5y,\quad x = 5y + 250 \] \[ \Rightarrow \text{Satellites serving C} = (550 - 5y) + 0.3(5y + 250) + 100 + y \]
Simplify:
\[ = 550 - 5y + 1.5y + 75 + 100 + y = 725 - 2.5y \]
This expression is maximum when \( y \) is minimum. Minimum value of \( y = 0 \), so:
\[ \text{Maximum satellites serving C} = 725 - 2.5 \times 0 = 725 \]
From equation (3):
\[ z = 550 - 5y \] Since the number of satellites cannot be negative, we must have: \[ z \geq 0 \Rightarrow 550 - 5y \geq 0 \Rightarrow y \leq 110 \]
Now, the maximum possible value of \( y \) is 110.
When \( y = 110 \):
\[ \text{Satellites serving C} = 725 - 2.5 \times 110 = 725 - 275 = 450 \]
Therefore, the number of satellites serving C lies between 450 and 725.
What is the minimum possible number of satellites serving B exclusively?
- 100
- 200
- 500
- 250
The Correct Option is D
Solution and Explanation
Given the problem, we need to determine the minimum number of satellites serving B exclusively. Let's break down the information:
Let B = 2x, C = x, and S = x based on the ratio 2:1:1.
The number of satellites serving all three (B ∩ C ∩ S) is 100.
Let Be, Ce, and Se be the satellites serving exclusively B, C, and S, respectively. Given Ce = Se = 0.3Be.
The number of satellites serving others (O) is the same as the number serving C and S but not B, let's denote this as C ∩ S - B.
Using these, we can set up equations based on the total number of satellites:
• Total satellites: B + C + S + O = 1600 (1)
• B = Be + C ∩ B - S + C ∩ B ∩ S + B ∩ S - C (2)
• C = Ce + C ∩ B - S + C ∩ B ∩ S + C ∩ S - B (3)
• S = Se + C ∩ S - B + C ∩ B ∩ S + B ∩ S - C (4)
• B ∩ C ∩ S = 100 (5)
• Ce = 0.3Be (6)
• Se = 0.3Be (7)
Based on equation 6 and 7, suppose Be = 1000, then Ce = Se = 0.3 × 1000 = 300.
Hence, equations (2), (3), (4) become:
B = 2x = Be + D
C = x = Ce + E
S = x = Se + F
Substituting the known values: B = 2x = 1000 + D, C = x = 300 + E, S = x = 300 + F, where D = E = F = H, which satisfy total 1600 condition.
If D + E + F + O = 1600 - (Be + Ce + Se + B ∩ C ∩ S = 1900), so D + 100 + O = 600.
Thus, O = C ∩ S - B = Ce + Se + 100.
If Be is minimised to 250, solving directly from equilibrated conditions where B: 2x, hence deductions confirm Be = 250 (since other conditions uphold a 4_ratio in disparity between C/S/B linked-exclusive constraints).
| Satellite | Count |
|---|---|
| Bexclusive | 250 |
| Ce = Se | 75 |
| B ∩ C ∩ S | 100 |
The minimum possible number of satellites serving B exclusively is confirmed as 250.
If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
At most 475
- Exactly 475
- At least 475
- No conclusion is possible based on the given information
The Correct Option is A
Solution and Explanation
The correct answer is (A):
We are given that at least 100 satellites serve 0 regions. So, we take:
\[ y \geq 100 \]
From earlier equations, the number of satellites serving S is:
\[ \text{Satellites serving S} = 0.3x + z + 100 + y \]
Substitute the known expression: \[ = 725 - 2.5y \]
This value is minimum when \( y \) is maximum. From constraint (3), maximum possible \( y = 110 \).
So, minimum number of satellites serving S: \[ = 725 - 2.5 \times 110 = 725 - 275 = 450 \]
This value is maximum when \( y = 100 \).
So, maximum number of satellites serving S: \[ = 725 - 2.5 \times 100 = 725 - 250 = 475 \]
Therefore, the number of satellites serving S is at most 475.
If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
- The number of satellites serving C cannot be uniquely determined.
The number of satellites serving B is more than 1000 .
- All 1600 satellites serve B or C or S.
- The number of satellites serving B exclusively is exactly 250.
The Correct Option is A
Solution and Explanation
We are given relationships among the number of satellites serving regions B, C, and S. The goal is to find out the number of satellites serving at least two of B, C, or S.
Definitions:
- $x$: Number of satellites serving only one region
- $y$: Number of satellites serving all three regions (B, C, and S)
- $z$: Number of satellites serving exactly two of B, C, or S
- Total satellites serving at least two regions = $2z + y + 100$ (as given)
Also given:
- $z = 550 - 5y$
- $x = 5y + 250$
Step 1: Total satellites serving at least two of B, C, or S
Total = $z + z + y + 100 = 2z + y + 100$
Substitute $z = 550 - 5y$:
$2(550 - 5y) + y + 100 = 1200$
$1100 - 10y + y + 100 = 1200$
$1200 - 9y = 1200$
$\Rightarrow y = 0$
Step 2: Find values of $x$ and $z$
If $y = 0$:
- $x = 5y + 250 = 250$
- $z = 550 - 5y = 550$
Step 3: Satellites serving region C
Let number of satellites serving C be $k$.
Given:
$k = z + 0.3x + 100 + y$
Substitute the values:
$k = 550 + 0.3 \times 250 + 100 + 0 = 550 + 75 + 100 = 725$
Step 4: Satellites serving region B
Given: Satellites serving B = $2k = 2 \times 725 = 1450$
Conclusion:
- $y = 0$
- $x = 250$
- $z = 550$
- Satellites serving C = 725 (uniquely determined)
Hence, the statement "the number of satellites serving C cannot be uniquely determined" is false.
Correct Answer: (A)
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- Acrucial moderating factor in how people experience comparisons is self-esteem. Individuals with high self-esteem are more likely to interpret upward comparison as informative rather than threatening. They are more resilient in the face of others’ success and more likely to believe they can reach their own goals. In contrast, people with low self-esteem are more prone to interpret comparison as judgment, reinforcing negative self-views and triggering feelings of inadequacy.
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Self-esteem also influences how people choose their comparison targets. Research has found that individuals often engage in “selective comparison,” seeking out those who confirm their existing beliefs about themselves. This can become a subtle form of self-sabotage. Someone who feels unworthy may subconsciously seek out targets that reinforce that sense, perpetuating a narrative of inferiority. One of the most promising antidotes to social comparison is temporal comparison—evaluating oneself not against others, but against one’s own past. This method has been shown to increase motivation and satisfaction, especially when individuals can see concrete progress. Temporal comparison activates the same reward circuits as social comparison but avoids the threat systems associated with social ranking. It also reinforces agency: individuals focus on what they can control and improve rather than what others control. In therapeutic and coaching settings, temporal comparison is used to help clients build self-efficacy and track growth over time.
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- The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
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- Para Summary
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