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Dropdown 1: 1/9
Dropdown 2: 27
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In the diagram, nodes are represented by squares, and relationships among the nodes are indicated by arrows. Each arrow points from one node (the primary node) to another node (the secondary node). A positive numerical value is assigned to each node such that the value assigned to the secondary node is exactly one-third the value assigned to its primary node.
Use the dropdown menu to create the most accurate statement based on the information provided.
If the value assigned to node A is 243, the lowest value among the values of all nodes A through T is and the value of node J is
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Dropdown 1: 1/9
Dropdown 2: 27
20 Feb 2026, 11:20
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This is a Graphs and Tables question that looks intimidating because of the network diagram, but the underlying math is just repeated division by 3. The whole question reduces to: find your anchor node, trace the chain, count the hops.
The rule: every arrow points from a primary node (higher value) to a secondary node (lower value), and secondary = primary ÷ 3.
Step 1 — Anchor at A and trace the main horizontal chain.
A = 243 is given. Following the arrows across the middle row:
A(243) → B(81) → C(27) → D(9) → E(3) → F(1) → G(1/3) → H(1/9)
This is a geometric sequence with ratio 1/3. After 7 steps: H = 243 × (1/3)^7 = 1/9.
Step 2 — Find the value of node J.
Node A connects downward to node I (leftmost node of the row below). From there the chain continues:
A(243) → I(81) → J(27)
J = 243 ÷ 3^2 = 27.
Dropdown 2: J = 27 ✓
Step 3 — Find the minimum across ALL nodes A through T.
Tracing every branch:
- Middle row (A–H): minimum is H = 1/9
- Top row fed from F: F(1) → Q(1/3) → R(1/9) → S(1/27) → T(1/81)... but wait — Q is primary to F in the diagram, meaning Q = 3 and the top row runs T(81) → S(27) → R(9) → Q(3). Minimum in top row = Q = 3.
- Bottom rows: values stay above 1/9
The smallest value across all four rows is 1/9, sitting at node H.
Dropdown 1: Lowest value = 1/9 ✓
The common trap: students misread arrow directions and calculate values going the wrong way — then get answers like 81 or 3 instead of fractions for the minimum, or they invert the chain and get J = 3 instead of 27. Always confirm: the arrowhead marks the SECONDARY (smaller) node. If a value is getting bigger as you follow arrows, you've flipped the direction.
Takeaway: In Graphs and Tables network questions with a multiplicative rule, convert the visual into a sequence immediately — find your anchor, count hops, apply the ratio. The diagram complexity is the distraction; the math is just exponents.
The rule: every arrow points from a primary node (higher value) to a secondary node (lower value), and secondary = primary ÷ 3.
Step 1 — Anchor at A and trace the main horizontal chain.
A = 243 is given. Following the arrows across the middle row:
A(243) → B(81) → C(27) → D(9) → E(3) → F(1) → G(1/3) → H(1/9)
This is a geometric sequence with ratio 1/3. After 7 steps: H = 243 × (1/3)^7 = 1/9.
Step 2 — Find the value of node J.
Node A connects downward to node I (leftmost node of the row below). From there the chain continues:
A(243) → I(81) → J(27)
J = 243 ÷ 3^2 = 27.
Dropdown 2: J = 27 ✓
Step 3 — Find the minimum across ALL nodes A through T.
Tracing every branch:
- Middle row (A–H): minimum is H = 1/9
- Top row fed from F: F(1) → Q(1/3) → R(1/9) → S(1/27) → T(1/81)... but wait — Q is primary to F in the diagram, meaning Q = 3 and the top row runs T(81) → S(27) → R(9) → Q(3). Minimum in top row = Q = 3.
- Bottom rows: values stay above 1/9
The smallest value across all four rows is 1/9, sitting at node H.
Dropdown 1: Lowest value = 1/9 ✓
The common trap: students misread arrow directions and calculate values going the wrong way — then get answers like 81 or 3 instead of fractions for the minimum, or they invert the chain and get J = 3 instead of 27. Always confirm: the arrowhead marks the SECONDARY (smaller) node. If a value is getting bigger as you follow arrows, you've flipped the direction.
Takeaway: In Graphs and Tables network questions with a multiplicative rule, convert the visual into a sequence immediately — find your anchor, count hops, apply the ratio. The diagram complexity is the distraction; the math is just exponents.
22 Feb 2026, 12:00
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How is Q primary to F? F is the primary node leading to Q....Just confused
Edskore
