The question asks for the location of the headquarters of the Asian Development Bank (ADB). This is a factual question related to international organizations and their geographical presence. To answer this, one needs to recall or know the established headquarters of the ADB.
B) Philippines — The headquarters of the Asian Development Bank (ADB) is located in Mandaluyong, Metro Manila, Philippines. This is a well-known fact about the organization.
Two triangles are similar if their corresponding angles are equal (AA similarity criterion) or if their corresponding sides are in proportion (SSS similarity criterion) or if two sides are proportional and the included angle is equal (SAS similarity criterion). We will check each option against these criteria.
D) The ratios of corresponding sides are equal: \[\frac{AB}{PQ} = \frac{BC}{QR} = \frac{CA}{RP} = \frac{1}{2}\]. Thus, \(\Delta ABC \sim \Delta PQR\).
This is a syllogism problem that can be solved using Venn diagrams or by analyzing the logical relationships between the given premises. We need to find a conclusion that logically follows from both statements.
This means that the set of 'teachers' is entirely contained within the set of 'hardworking persons'. If we represent this with Venn diagrams, the circle for 'teachers' would be inside the circle for 'hardworking persons'.
This means that a significant portion (more than 50%) of 'hardworking persons' are 'women'. It does not mean all, nor does it mean only some specific hardworking persons. It implies an overlap between the set of 'hardworking persons' and the set of 'women'.
From premise 1, all teachers are hardworking. From premise 2, most hardworking persons are women. Since teachers are a subset of hardworking persons, and most hardworking persons are women, it is certain that there is an overlap between 'hardworking persons' and 'women'. This overlap implies that at least some hardworking persons are women. The statement 'Most hardworking persons are women' directly implies that 'Some hardworking persons are women'.
Correct Option: C) Some women are hardworking persons
This question tests the fundamental relationship between Amount, Principal, and Simple Interest. Understanding the definitions of these terms is key to identifying the correct formula.
Using the given symbols:
\[ A = P + SI \]A) A = P + SI is correct because the total amount received or paid back is always the sum of the initial principal and the interest accrued on it.
The question asks to classify a list of items: Altimeter, Barometer, Dynamometer, Thermometer. We need to identify the common function or category that best describes all these instruments.
C) Measuring instruments — All the listed items (Altimeter, Barometer, Dynamometer, Thermometer) are devices specifically designed to measure different physical quantities (altitude, atmospheric pressure, force/power, and temperature, respectively). Therefore, "Measuring instruments" is the most accurate classification.
The perimeters of two similar triangles Δ ABC and Δ PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then what is the measure of AB?
\( \frac{20}{3} \) cm
\( \frac{200}{3} \) cm
\(\frac{10\sqrt{6}}{3}\) cm
15 cm
When two triangles are similar, the ratio of their corresponding sides is equal to the ratio of their perimeters. We will use this property to find the length of the unknown side.
Understand the property of similar triangles: For similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides.
Given that \(\Delta \text{ABC}\) is similar to \(\Delta \text{PQR}\) (denoted as \(\Delta \text{ABC} \sim \Delta \text{PQR}\)), we have:
\[ \frac{\text{Perimeter}(\Delta \text{ABC})}{\text{Perimeter}(\Delta \text{PQR})} = \frac{\text{AB}}{\text{PQ}} = \frac{\text{BC}}{\text{QR}} = \frac{\text{AC}}{\text{PR}} \]Identify the given values:
We need to find the length of side \(\text{AB}\).
Set up the ratio: Using the property from step 1, we can write:
\[ \frac{\text{Perimeter}(\Delta \text{ABC})}{\text{Perimeter}(\Delta \text{PQR})} = \frac{\text{AB}}{\text{PQ}} \]Substitute the given values into the equation:
\[ \frac{36}{24} = \frac{\text{AB}}{10} \]Solve for AB:
First, simplify the ratio on the left side:
\[ \frac{36}{24} = \frac{3 \times 12}{2 \times 12} = \frac{3}{2} \]Now, substitute this back into the equation:
\[ \frac{3}{2} = \frac{\text{AB}}{10} \]Multiply both sides by 10 to isolate \(\text{AB}\):
\[ \text{AB} = \frac{3}{2} \times 10 \]\[ \text{AB} = 3 \times 5 \]\[ \text{AB} = 15 \text{ cm} \]D) 15 cm — The calculation shows that \(\text{AB} = 15 \text{ cm}\).
The problem asks us to identify a word-pair that shares the same relationship as "Butterfly : Insect". This is an analogy question, requiring us to determine the nature of the relationship between the given words and then find an option that replicates that relationship.
Based on this analysis, Option B is the only one that maintains the same "Specific member : General category" relationship as "Butterfly : Insect".
B) Ostrich : Bird — An ostrich is a specific type of bird, just as a butterfly is a specific type of insect. The relationship is "Specific member : General category".
The question asks to identify a substance that aids in food digestion. We need to recall the basic components and processes involved in the human digestive system.
Therefore, saliva directly helps in food digestion.
Correct Option: D) Saliva
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the second pair to find the missing term.
Correct Option: C) Direction — A compass is an instrument used to find or indicate direction, just as a map is used to find or indicate a location.
The question asks to identify the external oversight body of the United Nations system. This requires knowledge of the various bodies within the UN structure and their specific functions, particularly those related to oversight and inspection.
Correct Option: A) Joint Inspection Unit
The Joint Inspection Unit (JIU) is the only independent external oversight body of the United Nations system. It is mandated to conduct evaluations, inspections, and investigations system-wide. Its reports and recommendations aim to improve management and methods and to achieve greater coordination among organizations of the United Nations system.